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.

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.

Ratio Calculator & Simplifier

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

Result

Simplified ratio

2.0000 : 3.0000

12 : 18 → 2 : 3.

GCD6
Decimal0.6667
Percentage40.0% / 60.0%
Sum30.0000

Source: NIST DLMF §1.5.5 (Proportionality); Euclidean algorithm for GCD-based ratio simplification.

Note — Simplification works cleanly only on integer inputs; the calculator falls back to decimal form for non-integer inputs.

Step-by-step

Original: 12 : 18.
GCD(12, 18) = 6.
Simplified: (12 ÷ 6) : (18 ÷ 6) = 2 : 3.

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.