Ratio Calculator
Simplify ratios, solve proportions, and scale ratios to any size.
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Common Ratios Reference
| Ratio | Used For |
|---|---|
| 16:9 | HD video, widescreen monitors |
| 4:3 | Old TV, standard monitors |
| 1:1.618 (φ) | Golden ratio — art, architecture |
| 1:1 | Square format (Instagram) |
| 3:2 | DSLR camera photos |
| 1:3 | Blog header banners |
What a Ratio Really Means
A ratio compares two quantities of the same kind, written a : b and read "a to b". A ratio of 3 : 2 means that for every 3 units of the first quantity there are 2 of the second. Ratios stay the same when you multiply or divide both sides by the same number, which is exactly how you simplify 6 : 4 down to 3 : 2 or scale a recipe up.
Simplifying, Scaling and Proportions
To simplify a ratio, divide both terms by their greatest common divisor. To scale one, multiply both terms by the same factor. To solve a proportion such as 3 : 4 = x : 20, cross-multiply: x = 3 × 20 ÷ 4 = 15. This calculator handles all three so you never have to hunt for the common factor by hand.
Where Ratios Show Up
- Cooking: scaling a recipe from 4 servings to 6.
- Maps and models: a 1 : 50,000 scale means 1 cm equals 500 m.
- Finance: debt-to-income, price-to-earnings, and mixing ratios.
- Design: aspect ratios like 16 : 9 — see the aspect ratio calculator.
Frequently Asked Questions
Divide both numbers by their GCD to get the simplest form. Example: 12:8 → GCD=4 → 3:2.
Multiply both parts by the same factor. Example: ratio 3:2 at scale 5 → 15:10.
The golden ratio φ ≈ 1.618:1 (or 1:0.618). It appears in nature, art, and architecture. A rectangle is 'golden' if its length/width = φ.