Descartes' Rule of Signs Calculator
Last reviewed 6 September 2026
The true split is found numerically by the Aberth–Ehrlich method, so the rule is shown doing its job rather than asserted.
Perfect Square Trinomial Calculator
Last reviewed 6 September 2026
Gives the difference-of-squares factorisation when that is what the input actually is, instead of only reporting that the perfect-square test failed.
Square of a Binomial Calculator
Last reviewed 6 September 2026
Multivariate throughout — (2x + 3y)² is an ordinary question and a single-variable engine cannot state it.
Diamond Problem Calculator
Last reviewed 6 September 2026
Names the AC-method connection explicitly, since the diamond is that step of factoring by grouping rather than a puzzle of its own.
Direct Variation Calculator
Last reviewed 6 September 2026
Refuses x = 0 as a defining pair, because every direct variation passes through the origin and that point identifies none of them.
Inverse Variation Calculator
Last reviewed 6 September 2026
Covers joint and combined variation in the same place, since they are the same constant-finding step with more variables.
Interval Notation Calculator
Last reviewed 6 September 2026
Covers absolute-value inequalities, unions written with ∪ or the word or, and the and/or distinction that turns a compound inequality into an empty set.
Graphing Quadratic Inequalities Calculator
Last reviewed 6 September 2026
Spells out the repeated-root case, where >, ≥, < and ≤ give four genuinely different answers from one parabola.
Power Set Calculator
Last reviewed 6 September 2026
Spells out the ∈ versus ⊆ distinction using the reader's own elements, which is the commonest error in the topic.
Subset Calculator
Last reviewed 6 September 2026
States the ⊂ ambiguity rather than picking a convention silently, and writes ⊆ and ⊊ instead.
Union and Intersection Calculator
Last reviewed 6 September 2026
Refuses to invent a universe for complements — without one, A′ has no meaning, and the page says so instead of treating everything mentioned as the universe.
Truth Table Generator
Last reviewed 6 September 2026
Reads DNF and CNF off the table itself, which is a constructive proof that every truth function has a formula.
Complex Number Calculator
Last reviewed 6 September 2026
States where exactness genuinely ends: |z|² is exact, its square root usually is not, and the argument is an arctangent.
Complex Conjugate Calculator
Last reviewed 6 September 2026
Derives the real quadratic with z and z̄ as its roots, which is the mechanism behind conjugate root pairs rather than a rule to remember.
Complex Root Calculator
Last reviewed 6 September 2026
Checks the sum and product of the roots against what the geometry requires, computed from the roots themselves.
Hyperbolic Functions Calculator
Last reviewed 6 September 2026
Gives each inverse in closed form with its domain, and names the arcosh x ≥ 1 requirement as a consequence of cosh's range.
Error Function Calculator
Last reviewed 6 September 2026
Gives the normal-distribution conversion with the one-sided and two-sided probabilities separated, since substituting one for the other is the commonest error in using either.
Gamma Function Calculator
Last reviewed 6 September 2026
Explains the poles through the reflection formula, which accounts for both their positions and the sign flips between them.
Bessel Function Calculator
Last reviewed 6 September 2026
States the measured accuracy per family, from quadrature and Wronskian comparison, rather than implying uniform exactness.
Binomial Coefficient Calculator
Last reviewed 6 September 2026
Shows Pascal's rule and the row sum as computed checks, and puts permutations beside combinations with the k! between them.
Quaternion Calculator
Last reviewed 6 September 2026
Reads a unit quaternion as a rotation with axis, angle, matrix and Euler angles, and names the gimbal-lock case instead of returning a plausible wrong answer there.
Million, Billion and Trillion Converter
Last reviewed 6 September 2026
Exact integer arithmetic throughout, since the top of the range is 10¹⁸ — far past the 9,007,199,254,740,991 where ordinary floating point stops holding integers exactly.
Area Converter
Last reviewed 6 September 2026
Area factors are derived by squaring the exact length factors rather than stored separately, so two units cannot disagree. Carries the cent (one hundredth of an acre) and deliberately omits the bigha, katha and gunta, which genuinely differ by Indian state.
Speed Converter
Last reviewed 6 September 2026
Also separates average speed from instantaneous speed, since dividing total distance by total time is not the mean of the speeds along the way.
Pressure Converter
Last reviewed 6 September 2026
Lists the torr and the millimetre of mercury with their own separate factors rather than treating them as identical, since they are defined differently and agree only to about one part in seven million.
Data Storage Converter
Last reviewed 6 September 2026
Neither prefix system is presented as the true meaning of the other — both are exact, and property tests assert every binary unit is a power of two and every decimal one a power of ten.
Energy Converter
Last reviewed 6 September 2026
Energy and power are kept in separate dimensions, so asking the tool to convert one into the other throws rather than returning a plausible number.
Power Converter
Last reviewed 6 September 2026
Notes the third unrelated meaning of “ton” — a ton of refrigeration is 12,000 BTU/h, and cooling capacity is output rather than consumption.
Angle Converter
Last reviewed 6 September 2026
Covers degrees-minutes-seconds as a compound format, where reading 40° 26′ 46″ as 40.2646° puts a coordinate about 22 km out with nothing obviously wrong about it.
Volume to Weight Converter
Last reviewed 6 September 2026
The arithmetic stays exact — the volume and weight factors are the same defined constants used elsewhere on the site — so all the uncertainty sits in the density and none in the conversion.
Roman Numerals Converter
Last reviewed 6 September 2026
All 3,999 values are asserted to round-trip, to be in standard form, to repeat no symbol four times, and never to repeat V, L or D.
Percentage Increase Calculator
Last reviewed 5 September 2026
Published the percentage increase calculator: the increase between two values, a value raised by a percentage, and the value that came before an increase — each answer shown with its three-step working, plus six practice questions whose answers come from the same engine.
Fraction to Percent Calculator
Last reviewed 5 September 2026
Added a 28-row fraction-to-percentage conversion chart generated by the calculator's own engine, and step-by-step working for every conversion.
Percentage of a Percentage Calculator
Last reviewed 5 September 2026
Added to the Math category's Percentages group alongside the Percentage Calculator and Percentage Change Calculator; percentage-points questions are linked to the latter rather than duplicated here.
Batting Average Calculator
Last reviewed 5 September 2026
Launched the Sports category, the site's eleventh public category, with this as its first tool.
Interest Ledger Calculator
Last reviewed 1 September 2026
Published with all five day-count conventions, the three payment allocation rules, a prepayment-saving proof, eight reconciliation checks, and English and Hindi output.