Math & Statistics

Math & Statistics Calculators

Work through the everyday math that shows up in study, work, and life — percentages and percentage change, converting a fraction or decimal into a percent and back, the spread of a dataset (mean, median, mode, variance, and standard deviation), a weighted course grade or the score needed on a final, and a GPA across multiple courses. Each tool shows the formula and a worked example so you can check the method, not just copy the answer.

Statistics

MathStandard Deviation CalculatorSample and population standard deviation, plus variance, mean, median, quartiles, z-scores, outliers, and confidence intervals.Best for: Analysing the spread, shape, and outliers of a dataset, with every statistic at once.MathOdds Ratio to Risk Ratio CalculatorConvert an odds ratio to a risk ratio at any baseline risk, with the interval converted too and the same odds ratio shown across eleven baselines.Best for: Turning a published odds ratio into a risk anyone can act on MathVIF CalculatorVariance inflation factors with Belsley-Kuh-Welsch condition indices and variance-decomposition proportions, so a near-dependency is named rather than only detected.Best for: Finding which predictors overlap, not merely that some of them do MathTwo-Proportion Z-Test CalculatorCompares two rates with the pooled z-test and a Newcombe interval for the difference, and shows that z² equals the 2×2 chi-square statistic exactly — so the “z-test or chi-square” question has no content.Best for: A/B tests and any comparison of “x of n” against “y of m”.MathKruskal-Wallis CalculatorApplies the tie correction and shows it against the uncorrected value, because on ordinal data it moves p from 0.054 to 0.027 — across the conventional threshold, on identical data.Best for: Three or more groups on ordinal or skewed data.MathBirthday Paradox CalculatorAnswers both questions the paradox conflates — 50.73% that some pair shares a birthday in a room of 23, and 5.86% that anyone shares yours — with the pair count that explains the gap.Best for: Coincidence odds, and hash collision thresholds.MathSimpson's Paradox CalculatorDetects when a pooled comparison contradicts every subgroup, then repairs it by standardising — which takes the real Berkeley admissions gap from +14.16 points to −4.26 and changes its sign.Best for: Rate comparisons where the groups are mixed unevenly.MathProbability CalculatorTwo events, repeated trials and Bayes, with the three usual errors handled — the dropped overlap in P(A or B), n×p instead of the complement, and the base rate that makes a 99% test 17% right.Best for: Combining events without the classic mistakes.MathSkewness CalculatorAll three skewness conventions at once with the standard error beside them, because Excel SKEW runs 18.6% above the textbook formula at n=10 and a normal sample of 30 swings ±0.85 by chance.Best for: Asymmetry, judged against its own noise.MathNegative Binomial CalculatorShows both conventions at once — failures before the rth success and total trials differ by exactly r, so the same k gives two answers 32% apart and nobody says which they meant.Best for: Waiting for the rth success, and overdispersed counts.MathWeibull Distribution CalculatorReliability probabilities with the hazard curve drawn beside the density — because the shape parameter is the hazard story: below 1 the risk falls, at 1 it is exactly an exponential, above 1 it rises.Best for: Deciding whether preventive replacement is worth anything.MathPoisson Distribution CalculatorPoisson probabilities with a dispersion test against your own variance — because a Poisson forces variance to equal the mean, and real count data usually does not, which is exactly where the tail goes wrong.Best for: Checking a Poisson fits before trusting its tail.MathNormal Distribution CalculatorProbabilities under a normal curve in all four directions with the region shaded — and the empirical rule given exactly, because two standard deviations is 95.45% and the 95% everyone quotes sits at 1.96σ.Best for: Tail probabilities a printed z-table stops short of.Matht-test CalculatorOne-sample, two-sample and paired t-tests defaulting to Welch, with Student's pooled version printed beside it — and a warning when the two disagree on the verdict.Best for: Not inheriting an equal-variance assumption you never checked.MathStandard Error CalculatorStandard error of a mean or proportion, printed beside the standard deviation it gets confused with — the ratio is always √n, and at n = 50 that is a factor of seven.Best for: Telling a spread apart from a precision before you draw the error bars.MathMargin of Error CalculatorMargin of error for a percentage or an average, shown across seven sample sizes so the square-root law is visible — every doubling buys exactly 29.3%, never more.Best for: Seeing what precision actually costs before you buy it.Mathp-value CalculatorA p-value from a t or z statistic, one- or two-tailed — with a panel that holds an effect fixed and grows the sample, so you can watch significance appear from nothing but n.Best for: Seeing why a small p-value does not mean a large effect.

Grades

MathGrade CalculatorCalculate your weighted overall grade from categories or points, or find the score you need on your final exam.Best for: Checking a current course grade or the score needed on a final.MathGPA CalculatorCalculate your GPA from letter grades or percentages and credit hours, or combine a new term with your existing cumulative GPA.Best for: Averaging grades across multiple courses on the standard 4.0 scale.

Percentages

MathPercentage CalculatorSolve X% of Y, what percent X is of Y, reverse percentage, increase/decrease, discounts, and tax, tip, or commission.Best for: Every everyday percentage question in one tool.MathPercentage Change CalculatorWork out percentage increase or decrease, reverse change, loss recovery, percentage points, multi-period change, and CAGR.Best for: Analysing how much a value rose or fell — and what it takes to reverse it.MathTip CalculatorCalculate the tip amount, total bill, and per-person share for restaurants, bars, delivery, and other services.Best for: Splitting a bill and tip evenly among any number of people.MathPercent to Goal CalculatorProgress against a target, plus the pace the remaining periods actually need — the number a progress bar never shows and nobody works out in their head.Best for: Quotas, campaigns and any target with a deadline.

Algebra

MathDiscriminant CalculatorEvaluate b² − 4ac, the cubic and quartic discriminants, or D = f_xx·f_yy − (f_xy)² for the second-derivative test, in exact arithmetic so the sign is never a rounding artefact.Best for: Knowing what the roots are like before you find them.MathFOIL CalculatorMultiply two binomials with all four products named — First, Outer, Inner, Last — shown as a grid too, with difference of squares and perfect squares recognised.Best for: Seeing the four products, not just the answer.MathMultiplying Polynomials CalculatorMultiply polynomials of any size in any number of variables, by grid, vertical or term-by-term layout, with the product count that catches a dropped term.Best for: Anything bigger than two brackets of two terms.MathRational Zeros CalculatorList every rational root candidate from the rational root theorem, test each one, divide out the hits by synthetic division, and use the bound rules to strike the rest off without testing them.Best for: Seeing the search, not just the roots it finds.MathDescartes' Rule of Signs CalculatorCount the sign variations in f(x) and f(-x), list every combination of positive, negative and complex roots the rule permits, and see which one is actually true.Best for: Reading a rule that gives possibilities, not a count.MathPerfect Square Trinomial CalculatorTest whether a trinomial is a perfect square against all three conditions, name which one failed, and give the constant that would fix it — plus the difference-of-squares answer when that is what you actually have.Best for: Finding out why a trinomial is not a perfect square.MathSquare of a Binomial CalculatorExpand (a plus or minus b) squared with the middle term named and a numeric example of exactly what the (a+b)^2 = a^2+b^2 mistake costs, plus the area model that makes it stick.Best for: Never dropping the middle term again.MathInverse Variation CalculatorFind k from one pair and predict any other for y = k/x or y = k/x^n, with the asymptotes treated as content, plus joint and combined variation in the same place.Best for: The constant product, and why x = 0 is not in the domain.MathInterval Notation CalculatorConvert between inequality, interval notation, set-builder form and a number-line graph in every direction, including absolute values, unions and the empty set.Best for: Getting the brackets and the or-versus-and right.MathGraphing Quadratic Inequalities CalculatorSolve a quadratic inequality by sign chart rather than by four memorised cases, and shade the region for the two-variable form, with the repeated-root case where all four relations differ.Best for: One method that keeps working past quadratics.MathMultiplying Binomials CalculatorMultiply two to six binomials with the 2^n product count as the check, the build-up shown one bracket at a time, and the roots reading that turns a product of (x − r) into its polynomial.Best for: Past two brackets, where FOIL runs out of letters.MathInequality to Interval Notation CalculatorSolve a linear, chained or absolute-value inequality and write the answer in interval notation, with the sign flip marked at the step where it happens and exact fractional endpoints.Best for: Solving first — the notation page does not.MathGraphing Inequalities on a Number LinePlot up to six inequalities on one shared number line, read the overlap and the union straight off it, and see which conditions conflict and which are doing no work at all.Best for: Comparing several conditions at once.MathAbsolute Value Equation CalculatorBoth cases written out, in interval and set-builder notation — with the distinction the topic turns on: a less-than is an AND, a greater-than is an OR.Best for: Not writing a greater-than as a chain, which describes the empty set.MathLogarithm Rules CalculatorExpand or condense a logarithm step by step, with the rule that produced each term — and an explicit statement that log(a + b) is not log a + log b.Best for: The fourth rule people apply, which does not exist.

Sets & Logic

MathSubset CalculatorTest whether one set is a subset, a proper subset, equal or disjoint — and when the answer is no, name the exact element that breaks it.Best for: An answer with a witness, not just a verdict.MathUnion and Intersection CalculatorSix set operations on two or three sets at once, with the Venn regions, inclusion-exclusion checked against the real counts, and De Morgan verified on your own sets.Best for: Identities computed rather than quoted.

Complex Numbers

MathComplex Conjugate CalculatorThe conjugate, and everything it does: the sum, difference, product and quotient identities computed on your number, the reflection geometry, and the real quadratic behind conjugate root pairs.Best for: Why the conjugate matters, not just how to write it.MathComplex Root CalculatorAll n roots of any complex number by De Moivre, exact wherever a root is a Gaussian rational, arranged as the regular n-gon they form, with the sum and product checked.Best for: All n of them, not just the principal one.MathQuaternion CalculatorExact quaternion arithmetic showing both pq and qp every time, both quotients rather than one, and the rotation a unit quaternion represents with axis, angle, matrix and the gimbal-lock case named.Best for: Non-commutativity treated as the subject, not a footnote.

Special Functions

MathError Function Calculatorerf, erfc and the inverse to full double precision through the incomplete gamma function, with the normal-distribution conversion and a demonstration of why 1 minus erf fails.Best for: Tail probabilities that survive past x = 3.MathGamma Function CalculatorGamma, log-gamma, digamma and beta with the factorial shift stated every time, values reconstructed past the double overflow, and the poles explained through the reflection formula.Best for: Factorials of non-integers, and past 170.MathBessel Function CalculatorJ, Y, I and K plus the spherical pair, with the zeros that set drum modes and waveguide cutoffs, the recurrence and Wronskian checked, and the measured accuracy stated per family.Best for: The zeros, which are what the physics needs.

Fractions

MathFraction CalculatorAdd, subtract, multiply and divide fractions and mixed numbers exactly, with the least common denominator chosen, the cross-cancelling done first, and the true repeating decimal beside the answer.Best for: When the working is what gets marked, not the answer.MathFraction to Decimal CalculatorConvert a fraction to its exact decimal, with the length of the repeat worked out from the denominator before dividing and the long division shown remainder by remainder.Best for: Knowing how long the repeat is before you divide.

Number Theory

MathGCF CalculatorThe greatest common factor of two to six numbers with all three routes shown — the shared primes to their lower powers, Euclid line by line, and the full factor lists when they are short enough to be honest.Best for: When you want to see where the divisor came from.MathPrime Factorization CalculatorBreak any number into primes with the division ladder shown, the number of trial divisions reported, and the argument for why the search can stop at the square root.Best for: Seeing why trial division to the root is enough.MathDivisibility Test CalculatorEvery divisibility rule from 2 to 16 applied to your number, each with its working, the reason it holds, and the true remainder beside it as a check.Best for: Rules you can verify rather than believe.

Powers & Roots

MathFactorial CalculatorFactorials with every digit exact — 100 factorial is 158 of them — plus the trailing-zero count derived from Legendre's formula and Stirling's error.Best for: Exactness past where a calculator gives up.

Averages

MathWeighted Average CalculatorEach value carries the weight you give it, with every item's share of the total shown as a percentage so you can see what is actually driving the answer.Best for: Course grades, portfolio returns, anything where the items are not equally important.

Precision & Rounding

MathRounding CalculatorAll seven rounding rules on the same number at once, so the disagreement at a tie is visible rather than buried inside whichever one your software happened to pick.Best for: Deciding how a half should be treated, and matching a spreadsheet that disagrees.

Modular Arithmetic

MathModulo CalculatorAll three conventions at once, because −7 mod 3 is −1 in JavaScript and 2 in Python and a page that gives only one of those is wrong for half its readers.Best for: Matching a language's answer, and understanding why they differ.MathModular Exponentiation Calculator7^128 mod 13 without ever building the 109-digit power. Square-and-multiply is shown one exponent bit at a time, with the count of multiplications it saved.Best for: Working through an RSA or Diffie-Hellman example by hand.MathModular Inverse CalculatorThe number that undoes a multiplication modulo n, from the extended Euclidean algorithm — or the shared factor that proves no such number exists.Best for: Cipher keys, RSA exponents, and dividing where division does not exist.MathChinese Remainder Theorem CalculatorSolves a system of congruences including the moduli that are not coprime, which most tools refuse — with the merge shown one congruence at a time.Best for: Counting puzzles with several leftover conditions, and CRT exercises.

Sequences

MathPascal’s Triangle CalculatorThe triangle drawn to any row up to 40, exact on big integers, with the row sum as a power of two and each diagonal's meaning named.Best for: Binomial expansions and choosing-k-from-n by inspection.MathCollatz Conjecture CalculatorHalve it or triple it until 1 — with the climb drawn on a log scale, the peak, the stopping time, and a plain statement that the conjecture is unproven.Best for: Exploring one of the simplest unsolved problems in mathematics.

Angles

MathCoterminal Angle CalculatorThe principal angle between 0° and 360°, the nearest negative one, and the family θ + 360n they all belong to — reduced by exact division, not by looping.Best for: Normalising an angle before anything else is done with it.MathComplementary and Supplementary Angles CalculatorBoth at once, plus the explement — and an honest answer when there is none, since an obtuse angle has no complement and a negative number is not one.Best for: School geometry, and checking which of the two a problem means.

Trigonometry

MathUnit Circle CalculatorWhere an angle lands, with exact surd coordinates and the radian measure as a multiple of π — because the coordinates ARE the cosine and sine.Best for: Seeing where the trig values come from rather than memorising them.

Coordinate Geometry

MathMidpoint CalculatorThe midpoint of a segment, plus the reverse problem nobody else solves: given one endpoint and the midpoint, where is the other endpoint?Best for: The endpoint problem, which is the one that gets set in exams.MathPolar Coordinates CalculatorCartesian to polar and back, in two dimensions or three — with the angle from atan2, so a point in a left-hand quadrant is not reported 180° away from where it is.Best for: The quadrant, which atan(y/x) throws away.

Number Properties

MathAbsolute Value CalculatorAbsolute value as a distance from zero — plus the distance between two numbers, and a relative change from zero reported as undefined rather than as infinity.Best for: Absolute change versus relative change, and when the second has no value.MathFloor and Ceiling CalculatorFloor, ceiling and truncation side by side — because for negative numbers those are three different answers, and floor(−2.5) is −3 while truncating gives −2.Best for: The negative-number case that agrees on every positive and disagrees on every negative.MathPlace Value CalculatorEvery digit named and valued, in all three expanded forms and in words — including the decimals, where the first place after the point is tenths and not 'oneths'.Best for: Whichever expanded form the worksheet actually asked for.MathConsecutive Integers CalculatorThe run that sums to your target, or the reason there is not one — plus every run a number admits, and why the powers of two admit none.Best for: The 'no solution' case, where the reason is worth more than the answer.

Geometry

MathPolygon Area CalculatorThe shoelace formula on any number of corners, kept exact — with the signed area whose sign is the winding direction, and a clear warning where a self-intersecting outline breaks it.Best for: Areas from surveyed coordinates, without triangulating first.MathRegular Polygon CalculatorArea, perimeter, apothem, circumradius and angles from whichever measurement you have — plus whether the polygon can be drawn with compass and straightedge at all.Best for: The apothem, which the area formula wants and nobody measures.

Linear Algebra

MathMatrix Decomposition CalculatorLU, QR and Cholesky — with LU exact and the other two decimal, because square roots are irrational, and the page labels which is which rather than presenting them alike.Best for: Cholesky failing, which is the positive-definiteness test itself.

Solid Geometry

MathPrism CalculatorVolume and both surface areas for rectangular, triangular and trapezoidal prisms — with the triangular base solved from three measured side lengths, no perpendicular height needed.Best for: Measuring a real object, where the height is the one thing you cannot reach.

Useful guides

Explanations of the formulas and decisions behind these calculators.

Why a Percentage Loss and an Equal Percentage Gain Don't Cancel OutThe reverse-percentage trap explained: why a 25% drop then a 25% rise doesn't return to the start, worked with real numbers, plus loss recovery and CAGR.Adding, Multiplying and Dividing Polynomials — the Four OperationsHow the four operations on polynomials work, where each goes wrong, and why FOIL stops at two binomials — with the counting checks that catch a dropped term.

Who this is for

Students checking homework methodology against a shown formula, anyone working out a discount, tip, or percentage change in daily life, people who need the mean, median, mode, variance, or standard deviation of a dataset quickly and correctly, and students checking a weighted course grade, a GPA across multiple courses, or the score they need on a final.

How to choose a calculator

Choose by the shape of the problem. Everyday questions — a discount, a tip, what percent X is of Y — are for the Percentage Calculator, while how far a value rose or fell is the Percentage Change Calculator, which is the one to reach for when a whole series needs tracking, a growth rate annualising, or a rate’s move reading in percentage points. The Percentage Calculator keeps each question on its own tab — X% of Y, X is what % of Y, X is Y% of what, adding or subtracting a percentage, change and difference, a discount, and tax or tip — so the formula on screen always matches the question you asked. The Percentage Change Calculator does the same for movement: a basic change, reversing a change to find the starting value, a final value from a known change, the gain needed to recover a loss, percentage points, several periods chained together, and CAGR. For the tip itself, the total and each person’s share of a bill, use the Tip Calculator, with 15, 18, 20 and 25 per cent presets or any rate you type.

Algebra is its own cluster. To solve a quadratic — including the ones that will not factor — with exact roots rather than decimals, use the Quadratic Formula Calculator; to know in advance what those roots will be like, and whether the quadratic factors at all, use the Discriminant Calculator, which also covers the cubic and quartic discriminants and the second-derivative test that shares the name. When the question is about the curve rather than its roots — a maximum, a minimum, or the vertex form a(x − h)² + k — use the Completing the Square Calculator, which is also where the quadratic formula is derived. To break an expression into brackets rather than into roots, use the Factoring Trinomials Calculator. For two or more equations at once, the System of Equations Calculator handles any size and says whether a failure is inconsistency or a whole family of answers; when the question names a hand method instead, use the Elimination Method Calculator or the Substitution Method Calculator, which show two genuinely different sets of working. For arithmetic on polynomials themselves: two binomials are the FOIL Calculator, anything larger is the Multiplying Polynomials Calculator, combining them is the Adding and Subtracting Polynomials Calculator, and dividing one by another — with the remainder and factor theorems — is the Polynomial Division Calculator. Past the quadratic, the Cubic Equation Calculator solves degree 3 and says which of the three root patterns you have before it does; the Rational Zeros Calculator runs the finite p/q search that finds the rational ones, and the Descartes’ Rule of Signs Calculator counts how many roots of each sign there can be before any is found. For products of brackets: two binomials with the four products named is FOIL, three or more is the Multiplying Binomials Calculator — which also reads a product of (x − r) brackets back as the polynomial with those roots — and anything that is not a binomial is the Multiplying Polynomials Calculator. Squaring one bracket is the Square of a Binomial Calculator and recognising the result is the Perfect Square Trinomial Calculator, which names which of the three conditions failed; the two numbers that split a middle term are the Diamond Problem Calculator. When one quantity is a fixed multiple of another, use the Direct Variation Calculator; when their product is fixed instead, the Inverse Variation Calculator. Inequalities split three ways: solving one is the Inequality to Interval Notation Calculator, writing a finished answer in any of the four forms is the Interval Notation Calculator, comparing several conditions on one line is the number-line page, and a quadratic one needs the sign chart on the Graphing Quadratic Inequalities Calculator.

Sets and logic are their own cluster: every subset, whether one set sits inside another, the six operations between two or three, and the Truth Table Generator, which verifies the same De Morgan laws in logical notation. For complex numbers, the arithmetic is exact, the conjugate page covers what the conjugate actually does, the root page finds all n of them, and the Quaternion Calculator is the four-dimensional extension where multiplication stops commuting. Four special functions have their own pages, each with its own numerical method and its own stated accuracy: hyperbolic, error, gamma and Bessel. And for counting rather than computing, the Binomial Coefficient Calculator gives n choose k exactly, however many digits that takes.

To describe a whole dataset, from mean to spread to outliers, use the Standard Deviation Calculator. It reports the sample and population figures side by side, because dividing by n − 1 or by N changes the answer, along with the variance, quartiles and z-scores, and it points out values far enough from the rest to be worth checking for a typing slip. For a weighted or points-based course grade, or the score needed on a final, use the Grade Calculator, which keeps category weights and points possible apart because they are different numbers, and can show the result as a letter grade or on the German scale. To average grades across several courses on the 4.0 scale, use the GPA Calculator instead: credit hours rather than the number of courses decide the result, and a new term can be combined with the cumulative GPA you already have.

The arithmetic is exact for the numbers you enter; for graded or professional work, confirm the method and rounding your standard requires.

Compare math calculators

What each calculator is best for, the main inputs it needs, what it shows, and what to keep in mind.

Comparison of Math & Statistics calculators: what each is best for, its key inputs, what it shows, and its limitations.
Calculator	Best for	Key inputs	Shows	Keep in mind
Percentage Calculator	Percent of, discount, and tax or tip questions	Percentage, number, whole, price, tax or tip rate	Percentage result across eight selectable modes	Educational estimate; tax and tip rules vary by region
Percentage Change Calculator	Measuring growth or decline between two values	Original value, new value, or final value and rate	Percent change, direction badge, and CAGR	Undefined when starting value is zero; estimate only
Discriminant Calculator	What the roots are like before you find them	Coefficients of a degree 2, 3 or 4 polynomial, or three second partials	The sign, and for a quadratic whether it is also a perfect square	D greater than zero alone does not mean a minimum; the sign of f_xx decides which
FOIL Calculator	Multiplying exactly two binomials	Two terms in each bracket, in one variable or two	All four named products against the collected answer	FOIL names four products; three terms in a bracket gives six and is refused
Multiplying Polynomials Calculator	Any product bigger than two binomials	Two to five factors, any number of terms and variables	Grid, vertical and listed layouts of the same products	Count the products first; nothing later reveals a dropped one
Standard Deviation Calculator	Summarizing spread of a numeric dataset	Dataset values, sample or population basis, decimals	Sample and population SD, variance, mean, median	Sample SD undefined for one value; educational only
Grade Calculator	Weighted course grade or score needed on a final	Category weights and scores (percent or points), or current grade/weight/desired grade	Overall weighted percent with letter or German 1-6 grade, or the required final score	Does not know your school's exact rounding, curve, or drop-lowest rules
GPA Calculator	Averaging grades across multiple courses on the 4.0 scale	Letter grade or percentage and credit hours per course, optional current cumulative GPA	Term GPA and, optionally, a new combined cumulative GPA	Uses common scale conventions, not necessarily your school's exact policy
Tip Calculator	Working out a tip and splitting a bill	Bill total, tip percentage, number of people	The tip, the total, and the per-person share	A percentage tip on a tax-inclusive total tips on the tax as well
Multiplying Binomials Calculator	Products of two to six binomials, and roots to polynomial	Two to six bracketed binomials, any variables	The 2ⁿ product count against the terms that survive collecting	A bracket with three terms breaks the 2ⁿ count and is refused
Perfect Square Trinomial Calculator	Testing whether a trinomial is a perfect square, and why not	Any quadratic trinomial, fractional coefficients included	All three conditions separately, with the failing one named	Two square end terms do not make a square trinomial; the middle decides
Square of a Binomial Calculator	Expanding (a ± b)² with the middle term made unmissable	Two terms and a sign, in any number of variables	The expansion against the a² + b² mistake, priced as a number	(a + b)² is not a² + b²; it is short by exactly 2ab
Rational Zeros Calculator	Every rational root, with the whole search shown	Any polynomial of degree 2 to 8	Each ±p/q candidate against the value of f there	A zero constant term makes the candidate list infinite; factor x out first
Descartes' Rule of Signs Calculator	How many roots of each sign, before solving	Any polynomial of degree 1 to 12	Every combination the rule permits against the true split	Zero coefficients are skipped, not counted as sign changes
Inverse Variation Calculator	Inverse, joint and combined variation	One known pair, a power, or several varying quantities	Every product in a table against the others	x = 0 is not in the domain at all; it is an asymptote, not a value
Interval Notation Calculator	Converting between the four ways of writing a solution set	An inequality, an interval, set-builder, or an absolute value	All four written forms against each other and against a number line	Infinity always takes a round bracket; it is not a number any set contains
Inequality to Interval Notation Calculator	Solving an inequality, then writing it as an interval	A linear, chained, or absolute-value inequality	The solved answer against substitution of a value inside and outside	Dividing by a negative reverses the inequality; nothing else does
Graphing Inequalities on a Number Line	Comparing several conditions on one shared scale	Up to six conditions in any written form	Each condition against the AND and OR rows	A condition containing another entirely is doing no work at all
Graphing Quadratic Inequalities Calculator	Quadratic inequalities, on a line or as a shaded region	A quadratic inequality, in one variable or two	Each region's sign against a test value inside it	A negative leading coefficient reverses which side satisfies the inequality
Subset Calculator	Deciding containment, and naming what breaks it	Two finite sets	Every element of A against membership of B	∈ relates an element to a set; ⊆ relates two sets, and they are rarely both true
Union and Intersection Calculator	Six set operations at once, with the identities checked	Two or three sets, plus a universe for complements	Inclusion–exclusion and De Morgan, both computed rather than quoted	A complement has no meaning until the universal set is stated
Complex Conjugate Calculator	What the conjugate does, not just how to write it	One complex number	\|z\| against \|z̄\|, and the five identities against their values	Conjugate root pairs need REAL polynomial coefficients, or the pairing fails
Complex Root Calculator	All n roots of a complex number, not only the principal	A complex number and a root from 1 to 24	Each root raised back to the nth power against the original	Zero has one nth root, not n; the circle they sit on collapses
Quaternion Calculator	Quaternion arithmetic and the rotation it represents	Two quaternions, or one read as a rotation	pq against qp, and both quotients against each other	ij = k but ji = −k, so p/q is ambiguous until you say which side
Error Function Calculator	erf, erfc and the inverse, to full double precision	One real value	erfc computed directly against 1 − erf, which loses its digits	Past x = 3, computing erfc by subtraction destroys most of the answer
Gamma Function Calculator	The factorial extended to non-integers, plus beta	One real value, and two positives for the beta function	Γ against exact factorials, and the recurrence and reflection formulas	Γ(n) = (n − 1)!, so the argument is one MORE than the factorial you want
Bessel Function Calculator	J, Y, I and K, and the zeros physical problems need	A kind, an integer order 0 to 30, and a value	The recurrence and the Wronskian at your own argument	The zeros are not evenly spaced, which is why a drum has no pitch

Best calculator path

Common mistakes and limits

Rounding intermediate steps — carry full precision through the working and round only the final answer.
Confusing percentage change with percentage points: moving from 10% to 12% is two points, but a 20% increase.
Applying population standard deviation to a sample, or the reverse — dividing by N versus N − 1 changes the result.
Treating a weighted grade as a simple average of the category percentages — categories with a bigger weight need to count for more, not the same as a 5% quiz.
Averaging GPA as a simple mean of course grades instead of weighting by credit hours — a 4-credit A counts for more than a 1-credit A.

When not to rely on calculators alone

These calculators help you verify a formula and check an example. For high-stakes academic, engineering, scientific, or statistical work, confirm the result with the method your course or standard requires, the original source data, a spreadsheet, or qualified review — a calculator cannot know which convention, rounding, or significant figures your context expects.

Source and calculation basis

Built on standard mathematical formulas — percentage and percentage-point arithmetic, sample or population standard deviation, weighted-average grade math, and the credit-hour-weighted GPA formula cross-verified against university registrar sources — not pulled from any external data feed. Every page shows the formula in full and a worked example you can check by hand.

See the Methodology for how calculators are built and reviewed, who runs the site, the Disclaimer for the full terms, and the Contact page to report an issue.

Created and maintained by Jay Sudha, finance educator · Last reviewed 2 July 2026. See a formula issue, unclear assumption, or broken result? Report it through the contact page.

Frequently asked questions

Common questions about math calculators and how to use them.

What calculators are in Math & Statistics?

A percentage calculator, a percentage change calculator, a standard deviation calculator that also reports the mean, median, mode, variance, range, count, and sum for a dataset, a grade calculator for a weighted or points-based course grade and the score needed on a final, a GPA calculator for averaging grades across multiple courses on the 4.0 scale, and a tip calculator for the tip, the total and each person’s share of a bill. Each shows the formula and a worked example.

Can I use these for homework?

Yes. Every page shows the formula and a worked example, so you can check your answer and learn the steps rather than just copy a result. Working through the example yourself is the best way to understand the method.

What is the difference between sample and population standard deviation?

Population standard deviation divides by N and is used when your data is the entire group. Sample standard deviation divides by N − 1 and is used when your data is a sample of a larger group. The Standard Deviation Calculator shows both, alongside the variance, mean, median, mode, and range.

Are the results accurate?

Yes — each result comes from a transparent formula shown on the page, and the worked examples are checked against it. For graded coursework or engineering work, confirm the method and rounding match what your instructor or standard requires.

Why do rounding differences happen?

Rounding differences come from when you round, not from an error. Round only the final answer and results match exactly; round an intermediate step first and small gaps appear, especially in standard deviation, where squaring amplifies early rounding.

Can math calculators replace understanding formulas?

No. Each page shows the formula and a worked example precisely so you can follow the steps, not skip them. Use the calculator to check an answer or save time on arithmetic, not as a substitute for knowing why the method works.

What is the difference between percentage and percentage change?

A percentage expresses one number as a share of another (15 is 30% of 50). Percentage change measures how much a value moved between two points, relative to the starting value. Use the Percentage Calculator for the first and the Percentage Change Calculator for the second.

How should I check important academic or professional calculations?

Use the calculator to confirm your method and arithmetic, then verify against what your course, standard, or field requires — the original data, a spreadsheet, or review by someone qualified. For graded or professional work the required method matters as much as the answer.

Is there a math solver, like Photomath, that shows step-by-step solutions to equations?

No — the calculators here work through specific formulas (percentages, statistics, grades) with every step shown, but none solves an algebraic equation symbolically the way Photomath or a computer algebra system does. For that, use a dedicated CAS such as Wolfram Alpha or SymPy.

Is this approved for exams or competitions like MATHCOUNTS?

No — exam and competition rules (MATHCOUNTS, university math departments, standardized tests) specify approved physical calculator models, since a website cannot be used during a proctored test. This is a free browser-based calculator for practice, homework, and everyday use, not a substitute for an approved exam device.

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