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)