Ratio Calculator
Simplify a ratio, scale it up, or solve for a missing term in a proportion.
A ratio compares quantities: 4:6 and 2:3 are the same relationship written at different scales, and simplifying divides both sides by their greatest common divisor.
How the ratio calculator works
A ratio compares quantities: 4:6 and 2:3 are the same relationship written at different scales, and simplifying divides both sides by their greatest common divisor.
A proportion sets two ratios equal — a:b = c:d — and solving for a missing term is cross-multiplication: the products of the diagonals are equal, so a·d = b·c. That single fact underlies scale drawings, recipe scaling, map distances and unit pricing.
Enter a ratio to simplify it, or fill in three of the four proportion terms and leave the unknown at zero to solve for it.
Formula: a:b = c:d ⟺ a·d = b·c
Worked examples
| Inputs | Result | Note |
|---|---|---|
| Simplify 4:6 | 2:3 | 2:3 |
| Solve 4:6 = 10:? | D = 15 | D = 15 |
| Check whether two ratios match | Yes — 4:6 equals 10:15 | yes, they are equal |
FAQFrequently asked questions
How do I simplify a ratio?
Divide both sides by their greatest common divisor. 4:6 both divide by 2, giving 2:3.
How do I solve a proportion?
Cross-multiply: in a:b = c:d, a×d equals b×c, so any missing term follows from the other three.
What is the difference between a ratio and a fraction?
A ratio compares two parts to each other; a fraction compares a part to the whole. 2:3 is the same relationship as 2/5 and 3/5 of the total.
Can a ratio have decimals?
Yes, though it is usually scaled to whole numbers. This page shows the "per 1" form for decimal ratios.
How do I scale a recipe with ratios?
Set up the proportion with the known quantity and the target, then cross-multiply for the unknown.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.