Ratio Calculator
Simplify ratios to lowest terms and find the missing value in a proportion (a:b = c:?).
Covers part-to-part and part-to-whole for cooking, maps, and mixing.
A ratio expresses the relative sizes of two or more quantities. A proportion is a statement that two ratios are equal. These concepts underpin everything from cooking and mixing to map reading, financial analysis, and engineering.
Expressing a ratio: A ratio of A to B can be written as A:B, A/B, or “A to B.” In its simplest form, divide both parts by their GCD.
Scaling a ratio (proportion): A₁/B₁ = A₂/B₂ → A₂ = A₁ × (B₂/B₁)
Cross-multiplication to solve proportions: If A/B = C/D, then A × D = B × C
Worked example — Recipe scaling: A recipe for 4 people uses 3 cups of flour. How much for 10 people? 3/4 = x/10 x = 3 × (10/4) = 7.5 cups of flour
Worked example — Map scale: A map has a scale of 1:50,000. Two points are 7.3 cm apart on the map. Real distance = 7.3 × 50,000 = 365,000 cm = 3.65 km
Splitting a total in a given ratio: To split $5,400 between partners in a 2:3:4 ratio: Total parts = 2+3+4 = 9 parts Value per part = $5,400 / 9 = $600 Partner 1: 2 × $600 = $1,200 Partner 2: 3 × $600 = $1,800 Partner 3: 4 × $600 = $2,400
Common ratios to know:
- Concrete mix (by volume): 1:2:3 (cement:sand:gravel)
- Golden ratio: 1:1.618 (φ) — appears in art, architecture, nature
- Screen aspect ratios: 16:9 (widescreen), 4:3 (standard), 1:1 (square)
- Debt-to-income ratio: ideally below 36% (total debt payments / gross income)
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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