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Methodology
How the numbers on this site are produced, in plain terms. Every value is exact rational arithmetic, rounding happens only at display time, and one engine serves every calculator.
- Version
- 1.1
- Last updated
- 27 August 2026
- Reading time
- 4 min read
1.Exact arithmetic
Calculation state is exact fractions, never floating-point numbers.
Every value in the calculation state is held as an exact fraction of arbitrary-precision integers, never as a floating-point number. Decimals and fractions you type are converted to exact fractions before anything is calculated, so results do not drift. Floating-point numbers appear only in presentation code — for example the width of a bar segment on screen — never in a value that is reported as a result.
value = numerator / denominator (both exact integers)
1.5 becomes 3/2, and 0.1 becomes 1/10 — not the nearest binary approximation.
2.Rational engine
One engine, shared by every calculator on the site.
Parsing, normalisation, simplification, scaling, splitting and proportion solving all run through the same module. A ratio simplified on one page therefore matches the shares and splits shown on another.
3.Simplification rules
Scale to whole numbers, then divide by the greatest common divisor.
Parts are scaled to whole numbers, then divided by their greatest common divisor. Simplification is applied to all parts at once, so three-part ratios reduce correctly.
a : b : c → a/g : b/g : c/g, g = gcd(a, b, c)
A ratio is already simplest when g = 1.
- 12 : 18
- 2 : 3
4.Splitting and rounding
Money splits are exact first, rounded last, and always add up.
4.1Splitting money
Currency splits are calculated exactly, then converted to whole minor units. Each share is rounded down and the remaining minor units are allocated to the largest fractional remainders first, with ties going to the earlier share. The shares therefore always add up to the original amount.
4.2Decimal rendering
Rounding happens only when a value is displayed. Intermediate results inside the engine are never rounded, so a chain of calculations does not accumulate error. A displayed number may therefore be a shortened rendering of an exact value: what you see is rounded to a sensible number of digits, while the value carried into the next step is not.
round(display only) · never round(intermediate)
5.Common ratio pages
A fixed, curated list rather than generated permutations.
The common-ratio pages come from a fixed list of ratios people actually look up. Each page is generated from the same engine as the calculators and carries its own context, so no page exists purely to fill an index.
6.What we do not do
Some conversions require information a ratio does not carry.
We do not convert between volume and weight, because that requires a density value that a ratio does not contain. We do not guess which convention an instruction uses; where two readings exist, both are shown.