Ratio Calculator & Simplifier

Simplify a ratio like 12:18 to its lowest terms (2:3) and compare to a target ratio.

Result

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How to use this calculator

Enter both quantities.
Read the simplified ratio plus the decimal and percentage forms.

About this calculator

A ratio compares two quantities by division. Simplifying a ratio means dividing both numbers by their greatest common divisor, just like simplifying a fraction. 12:18 simplifies to 2:3 (dividing both by 6). The calculator also shows the decimal equivalent and percentage split for a quick comparison.

How it works — the formula

a : b  is the same as  a/b
Simplify by dividing a and b by gcd(a, b)
Solve a:b = c:x  →  x = (b · c) / a

A ratio compares two quantities by division. Two ratios a:b and c:d are equal when ad = bc — the standard cross-multiplication identity that lets you solve any proportion for an unknown term. To put a ratio in lowest terms, divide both sides by their greatest common divisor; for an irrational ratio (e.g. the golden ratio) the simplest form is the symbolic expression itself.

Sources: NIST Digital Library of Mathematical Functions §1.5.5 — Proportionality · Math Open Reference — Ratios and proportions · Khan Academy — Intro to ratios

Worked examples

Example 1

Simplify a ratio

Inputs:: a = 12, b = 18
Output:: gcd(12,18) = 6 → simplest form 2 : 3

Example 2

Solve a proportion

Inputs:: 3 : 4 = 9 : x
Output:: x = (4 · 9) / 3 = 12

Example 3

Cross-multiplication check

Inputs:: a:b = 2:5, c:d = 8:20
Output:: ad = 40, bc = 40 → ratios equal

Limitations

Ratios are dimensionless when comparing same units; mixing units (e.g. miles to hours) gives a rate, not a ratio.
Order matters: a : b is not the same as b : a unless a = b.
Decimals or surds in either side require symbolic care — simplify by canceling rational factors only.
When one term is 0, "simplest form" is 0 : k for any non-zero k; treat carefully.

Ratios are exact rational arithmetic when both inputs are integers; floating-point inputs may produce small simplification artifacts.

Frequently asked

What does a 2:3 ratio mean?+

For every 2 of the first thing, there are 3 of the second. If you have 10 of the first, you have 15 of the second (multiply both sides by 5).

How does this differ from a fraction?+

A ratio compares two quantities (a:b); a fraction is the result of division (a/b). 2:3 and 2/3 represent the same comparison but the notation conveys different intent.

Can I have a ratio with non-integers?+

Yes — but simplification only works cleanly with integers. The calculator falls back to the decimal form when inputs aren't integer.

How do I extend a ratio?+

Multiply both sides by the same factor. 2:3 → 4:6 → 6:9. The proportion-solver tool handles "2:3 = ?:12" style problems.

What is the "golden ratio"?+

φ ≈ 1.618:1 — appears in art, architecture, and surprisingly often in nature. It satisfies a:b = (a+b):a.