Ratio Calculator
Simplify ratios, scale them up or down, or solve proportions with one missing value.
To simplify: divide by GCF (12:18 → 2:3). To solve a:b = c:d: cross multiply (a×d = b×c). Scaling: multiply both parts by the same factor. Ratios are used in recipes, maps, scale models, and finance.
Ratio Notation by Country
| Country | Ratio notation | Proportion name | Taught as |
|---|---|---|---|
| 🇺🇸 USA | a:b or a/b | Proportion | Cross multiplication |
| 🇬🇧 UK | a:b | Ratio and proportion | GCSE core topic |
| 🇩🇪 Germany | a:b | Dreisatz (rule of 3) | Verhältnis, Proportion |
| 🇫🇷 France | a:b or a/b | Règle de trois | Proportionnalité |
| 🇯🇵 Japan | a:b (比) | Hirei (比例) | 比の値 (ratio value) |
| 🇮🇳 India | a:b | Ratio and Proportion | CBSE Class 6+ |
| 🇪🇸 Spain | a:b | Regla de tres | Proporcionalidad |
Frequently Asked Questions
How do you simplify the ratio 15:25?
GCF(15, 25) = 5. Divide both: 15÷5 : 25÷5 = 3:5. The ratio 3:5 is equivalent to 15:25 in lowest terms.
What is the difference between ratio and proportion?
A ratio compares two quantities (3:4). A proportion states that two ratios are equal (3:4 = 6:8). Solving a proportion finds a missing value using cross-multiplication.
How is the rule of three used in practice?
Example: If 5 workers finish a job in 8 days, how long for 10 workers? Set up: 5/8 = 10/x → x = 10×8/5 = 16... wait, this is inverse proportion: 5×8 = 10×x → x = 4 days. Ratios and proportions appear in cooking, construction, finance, and medicine dosing.
How do map scales work as ratios?
A map scale of 1:50,000 means 1 cm on the map = 50,000 cm (500 m) in reality. To find real distance: multiply map distance by 50,000. Different countries use different scales: UK Ordnance Survey uses 1:25,000 and 1:50,000; USGS uses 1:24,000 and 1:100,000.