Ratios Calculator
Ratio and Proportion Calculator works out Ratio in lowest terms and Greatest common divisor used from Task, Ratio and Second ratio (to compare). The default figures on this page give ratio in lowest terms of 3 : 4; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Terms: 12 : 16
- Greatest common divisor of the terms: 4
- Divide every term by it: 3 : 4
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Ratio and Proportion Calculator calculates
Simplifies ratios to lowest terms, solves a proportion for its missing term by cross multiplication, divides a total in a given ratio, checks whether two ratios are equivalent and scales a ratio to a target term.
How to use this Ratio and Proportion Calculator
Enter Task, Ratio, Second ratio (to compare) and Total amount to share. Ratio in lowest terms updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Ratio in lowest terms, Greatest common divisor used and First term / second term.
The method follows OpenStax, Prealgebra 2e §5.6 "Ratios and Rate" and §6.5 "Solve Proportions" (cross products a·d = b·c) and Euclid, Elements Book VII, Proposition 2 (Euclidean algorithm for the greatest common divisor, used to reduce a ratio to lowest terms).
Simplify 12:16 example
With Task: simplify, Ratio: 12:16, the calculator returns Ratio in lowest terms: 3 : 4, Greatest common divisor used: 4, First term / second term: 0.75. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Ratio in lowest terms, Greatest common divisor used and First term / second term. The inputs you can vary are Task, Ratio, Second ratio (to compare), Total amount to share, a and b.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How do I do ratios on a calculator?
Simplifies ratios to lowest terms, solves a proportion for its missing term by cross multiplication, divides a total in a given ratio, checks whether two ratios are equivalent and scales a ratio to a target term. Open “How this is worked out” beside the result to see each step for your own figures.
What is the easiest way to calculate ratios?
It needs Task, Ratio, Second ratio (to compare), Total amount to share, a and b. Nothing else is required, and the figures stay in your browser.
How do you calculate a 2 to 3 ratio?
The result gives Ratio in lowest terms, Greatest common divisor used, First term / second term, Resulting parts, Resulting parts (list) and Each term as a percentage of the total, each labelled with its unit so the figure can be read on its own.
How to calculate a 3 to 1 ratio?
The page opens with worked default figures: ratio in lowest terms of 3 : 4. Replace them with your own and every figure updates as you type.
What information do I need for the Ratio and Proportion Calculator?
You need Task, Ratio, Second ratio (to compare), Total amount to share, a, b, c and d. The page opens with default figures that give ratio in lowest terms of 3 : 4, so you can see the scale before entering your own.
What does this Ratio and Proportion Calculator show?
It shows Ratio in lowest terms, Greatest common divisor used, First term / second term, Resulting parts, Resulting parts (list), Each term as a percentage of the total, Missing term and Ratios are equivalent, with the working and any warnings for your entries.