Math & Statistics

Arithmetic & Number Theory Calculators

Calculators for everyday arithmetic and for the properties of whole numbers. The Percentage Calculator and the Percentage Change Calculator answer percent-of, what-percent and increase or decrease questions, and the Fraction Calculator adds, subtracts, multiplies and divides fractions, with the Simplify Fractions Calculator and the Decimal to Fraction Calculator for reducing and converting them. The Square Root Calculator, the Exponent Calculator and the Scientific Calculator evaluate roots, powers and whole expressions, and the Rounding Calculator and the Significant Figures Calculator set the precision of a result. For number theory, the GCF Calculator and the LCM Calculator find greatest common factors and least common multiples, the Prime Factorization Calculator breaks a number into primes, and the Modulo Calculator gives the remainder of a division. The Ratio Calculator simplifies and scales ratios, the GPA Calculator averages grades weighted by credits, and the Binary Arithmetic Calculator does arithmetic in base two.

Percentages

Percentage CalculatorSolve X% of Y, what percent X is of Y, reverse percentage, increase/decrease, discounts, and tax, tip, or commission.
Percentage Change CalculatorWork out percentage increase or decrease, reverse change, loss recovery, percentage points, multi-period change, and CAGR.
Percentage Increase CalculatorFind the percentage increase between two values, raise a value by a percentage, or recover what it was before the increase.
Percentage Difference CalculatorCompare two values against their average, so the answer is the same whichever one you write first — with both percentage changes shown beside it.
Fraction to Percent CalculatorConvert a fraction, mixed number, or decimal to a percent and back, with every step of the working shown.
Percentage of a Percentage CalculatorWork out X% of Y%, combine successive percentage changes into one overall change, or solve for the percentage you are missing.
Tip CalculatorCalculate the tip amount, total bill, and per-person share for restaurants, bars, delivery, and other services.
Average Percentage CalculatorAveraging 50% and 100% gives 99.02%, not 75%, when the groups are 2 and 100 — the page weights by group size and shows the naive answer beside it.
Percentage Point CalculatorA move from 4% to 6% is two percentage points and a 50% increase. Both are computed and named, so the two can never be quietly swapped.
Percent 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.

Fractions

Fraction 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.
Simplify Fractions CalculatorReduce a fraction to lowest terms with both routes to the divisor shown side by side — Euclid line by line and the shared primes — and a stated proof when nothing can be cancelled.
Decimal to Fraction CalculatorTurn any decimal into its exact fraction, repeating ones included, with the four algebra lines that cancel the infinite tail instead of rounding it away.
Fraction 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.
Comparing Fractions CalculatorOrder up to eight fractions with all three methods shown on your own numbers, and a figure for how many decimal places the closest pair need before they stop looking equal.
Mixed Number CalculatorAdd, subtract, multiply and divide mixed numbers with the borrow shown where it happens, plus a second independent check worked through improper fractions.

Basic Math

Scientific CalculatorTrigonometry, logarithms, powers, roots, and factorials with correct order of operations, memory registers, history, and keyboard entry.

Powers & Roots

Square Root CalculatorThe exact square root first — 72 gives 6 root 2 — then the decimal to as many as sixty places, computed on whole numbers rather than a double.
Exponent CalculatorPowers with the awkward cases right — a negative exponent is a reciprocal not a sign, a fractional one is a root, and zero to the zero is reported as contested.
Cube Root CalculatorCube roots exactly, negatives included — the cube root of minus 27 is minus 3, a real answer — with the two complex roots named alongside.
Factorial 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.

Grades

GPA CalculatorCalculate your GPA from letter grades or percentages and credit hours, or combine a new term with your existing cumulative GPA.
Grade CalculatorCalculate your weighted overall grade from categories or points, or find the score you need on your final exam.

Precision & Rounding

Rounding 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.
Significant Figures CalculatorMarks each digit significant or not with the reason, reports when the notation is genuinely ambiguous, and applies the different rules for multiplying and for adding.

Number Theory

LCM CalculatorThe least common multiple of two to six numbers, with the prime table that produces it, the multiples themselves, and how far counting would have had to go.
GCF 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.
Prime 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.
Factor CalculatorEvery factor of a number listed in the pairs that generate them, with the count derived from the prime exponents and separately checked against the list.
Prime Number CalculatorWhether a number is prime, with a divisor named when it is not and the size of the search stated when it is. Deterministic, not probabilistic.
Divisibility 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.
RSA CalculatorGenerate a key pair from two small primes and watch a message encrypt and come back — with an explicit account of why textbook RSA is insecure even with large primes.

Ratio & Proportion

Ratio CalculatorSimplify a ratio and share a total by it, with each term's fraction of the whole shown — because 3 : 2 means three fifths, not three halves.
Proportion CalculatorSolve a : b = c : d for whichever term you leave blank, with cross multiplication derived rather than asserted — or fill all four and have it checked.

Modular Arithmetic

Modulo 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.
Remainder CalculatorQuotient, remainder and the multiplication that checks them — plus the repeated subtraction that shows why a division has to stop.
Modular 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.
Modular Inverse CalculatorThe number that undoes a multiplication modulo n, from the extended Euclidean algorithm — or the shared factor that proves no such number exists.
Chinese 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.
Coprime CalculatorSet coprimality and pairwise coprimality are different conditions: 6, 10 and 15 have gcd 1 and not one coprime pair. Both are reported, with the offending pairs named.

Number Properties

Absolute 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.
Floor 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.
Digital Root CalculatorEvery round of digit addition shown, with the mod-9 shortcut alongside — and a casting-out-nines checker that will show you a wrong sum passing.
Place 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'.
Consecutive 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.

Binary & Bitwise

Binary Arithmetic CalculatorAdd, subtract, multiply and divide in binary, octal or hex — with the carry row shown, and what a processor actually does instead of subtracting.
Bitwise CalculatorAND, OR, XOR, NOT, NAND, NOR and XNOR with truth tables and the bits laid out — at 8, 16, 32 or 64 bits, because NOT genuinely depends on the width.
Bit Shift CalculatorLeft, logical right, arithmetic right and rotate — with the two right shifts kept apart, because they differ for negatives and one of them floors rather than truncating.
Twos Complement CalculatorTwo's and one's complement at 8 to 64 bits, with the signed range and its asymmetry — and why negating the minimum gives back the minimum.
Floating Point CalculatorThe exact decimal value a double actually stores, written out in full — which is why 0.1 + 0.2 does not equal 0.3 in almost every programming language.

Compare arithmetic & number theory calculators

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

Comparison of Arithmetic & Number Theory calculators: what each is best for, its key inputs, what it shows, and its limitations.
Calculator	Best for	Key inputs	Shows	Keep in mind
Scientific Calculator	Evaluating multi-step math and trig expressions	Expression, angle mode DEG or RAD, trig, log, powers, roots, constants	Computed result with step notes and history	Rounding at chosen precision; verify critical work
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
Percentage Increase Calculator	A single percentage increase or decrease, with the working shown	Two values, or a starting value and a percentage, or a value after a change	The percentage, the amount of the change, and the growth multiplier	Divide by the original value, not the new one; a negative answer is a decrease
Fraction to Percent Calculator	Converting a fraction, mixed number, or decimal to a percent	Numerator and denominator, optional whole number, or a decimal or percent	Rounded and exact percent, decimal, and simplest-form fraction, with the steps shown	Repeating values are rounded for display; check the rounding your standard requires
Percentage of a Percentage Calculator	Taking a percentage of a percentage, or stacking successive percentage changes	Two percentages, or a list of percentage changes, with an optional base amount	The combined percentage against the naive sum of the rates	The answer is a share of the original whole, not of the second percentage
Percentage Difference Calculator	Comparing two values where neither one is the base	Two values, two percentages, or a list of values	The symmetric percentage difference against both percentage changes	Undefined when the two values average zero; not the same as percentage change
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

Best calculator path

All math calculators, by sub-hub