Ratio Simplifier

What is the Ratio Simplifier?

A ratio simplifier reduces a ratio like 16:24 down to its simplest whole-number form (in this case 2:3), the same way you'd simplify a fraction. It works by finding the greatest common divisor (GCD) — the largest number that divides evenly into both values — using the Euclidean algorithm, then dividing both sides of the ratio by that GCD. To simplify a ratio by hand, find the largest number that divides evenly into both values (for 16 and 24, that's 8), then divide each side by it: 16 ÷ 8 = 2 and 24 ÷ 8 = 3, giving the simplified ratio 2:3. The decimal equivalent of any ratio is simply the first value divided by the second.

How it works

A ratio is simplified by dividing both numbers by their greatest common divisor (GCD) — the largest number that divides evenly into both. This is the exact same principle as simplifying a fraction to its lowest terms, since a ratio and a fraction represent the same underlying relationship.

UK context

Simplified ratios come up constantly in recipe scaling, mixing ratios (like the concrete and render mixes elsewhere on this site), map scales, and comparing quantities — a ratio like 16:24 is exactly the same relationship as 2:3, just expressed with larger numbers, and the simplified form is almost always easier to work with and understand at a glance.

Tips

• If you can't immediately see the GCD, repeatedly dividing both numbers by any common factor you do spot (2, 3, 5...) and continuing until no common factor remains gets you to the same simplified result.
• A ratio simplifies to itself (in lowest terms already) when the GCD of the two numbers is 1 — this is called being "coprime."

A quick note

This page explains the simplification method used in the calculator above.