Ratio Calculator

How to Use the Ratio Calculator

This calculator handles three ratio operations: Simplify reduces a ratio to its simplest form using GCD. Find Missing solves for the unknown value in a proportion (a:b = c:?). Scale multiplies a ratio by any factor.

Ratio and Proportion Formulas

Simplify: A:B → (A/GCD):(B/GCD) Proportion: a/b = c/d → d = b×c/a Scale: A:B × k → (A×k):(B×k)

Common Ratio Applications

Application	Example
Recipe scaling	2:3 ratio of flour:sugar, scaled 5× = 10:15
Map scale	1:50,000 — 1 cm = 500 m
Aspect ratio	16:9 TV screen (1920×1080 pixels)
Financial	Debt-to-equity 1:3 — $1 debt per $3 equity
Mixture	Concrete mix 1:2:3 (cement:sand:gravel)

Frequently Asked Questions

A ratio compares two or more quantities (2:3 means 2 for every 3), while a fraction represents a part of a whole (2/5 means 2 out of 5). They are related: the ratio 2:3 can be expressed as the fraction 2/3 when comparing the first part to the second. In a ratio 2:3, the first part is 2/5 and the second is 3/5 of the total.

Cross multiply and divide. For a/b = c/d: d = b×c/a. Example: 3/4 = 9/? → ? = 4×9/3 = 12. This works because equal fractions maintain their cross-product relationship: a×d = b×c.

A unit rate is a ratio with a denominator of 1. For example, 60 miles per 1 hour (60 mph) or $3.50 per 1 pound ($3.50/lb). To find a unit rate, divide the first quantity by the second: 150 miles / 3 hours = 50 miles per hour.

4:3 (traditional TV and monitors), 16:9 (HDTV, most modern screens, YouTube), 16:10 (laptop screens), 1:1 (square — Instagram posts), 9:16 (portrait phone video), 21:9 (ultrawide monitors, cinematic). Photography commonly uses 3:2 (35mm film) and 4:3 (point-and-shoot cameras).