OmniTools
mathDifficulty: 2/5

Ratio Calculator

Simplify ratios to their lowest terms, solve proportions for a missing value, and scale a ratio to a known quantity using exact arithmetic.

What do you want to do

Reduce a:b to its lowest terms.

Leave one of the four terms blank to solve a:b = c:d.

Keep the proportions and set one term to a new value.

Exact arithmetic: Ratios are reduced using the integer greatest common divisor of BigInt values, and scaled or solved terms are held as exact fractions rather than decimals. That matters for large numbers: a floating-point calculation loses digits past about fifteen significant figures, and cannot represent a third exactly — so a chain of decimal steps drifts. Here the exact value is always shown, with the decimal marked as recurring when it does not terminate, rather than presenting a rounded figure as if it were the answer.

How it works

  1. Choose whether you want to simplify a ratio, solve a proportion, or scale one.
  2. Enter whole numbers. For a proportion, leave exactly one of the four terms blank.
  3. Results are computed exactly with integer arithmetic, in your browser.
Privacy & Processing: Everything runs in your browser. Nothing you enter is uploaded, stored, or sent to analytics.

Frequently Asked Questions

How are ratios simplified?

By dividing every term by the greatest common divisor of ALL of them, so 2:4:6 becomes 1:2:3 rather than being reduced pairwise. 1920:1080 becomes 16:9.

Is the arithmetic exact?

Yes. Terms are handled as arbitrary-precision integers, so very large values simplify exactly instead of drifting through floating point. When solving a proportion gives a non-integer, the answer is shown as an exact fraction — 3:4 = x:10 gives 15/2, not a rounded 7.5.

Can it work out percentages of a whole?

Yes. Each term is also shown as its share of the total, so a 1:3 ratio reports 25% and 75%.

What about negative numbers?

Ratios of negative quantities are not meaningful for the comparisons this tool makes, so negatives are refused with a message rather than producing a confusing answer.

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