Ratio Calculator
Simplify, solve, scale and compare ratios with full step-by-step workings
Enter any ratio to reduce it to its simplest form.
What Is a Ratio?
A ratio expresses the relative size of two or more quantities. A ratio of 3:4 means "for every 3 of A, there are 4 of B". Ratios are used everywhere — cooking recipes, maps, financial statements, mixing concentrations, and probability.
Formulas
Real-World Examples
Recipes: A recipe serves 4 in ratio 3:5 (flour to sugar). To serve 10, scale by 10/4 = 2.5× → new ratio 7.5:12.5.
Maps: A 1:50,000 scale map means 1 cm = 50,000 cm = 500 m in reality.
Finance: Profit split in ratio 3:7 means one partner gets 30% and the other 70% of total profit.
// Cross Multiply
To solve A:B = C:D for D, cross-multiply: D = B×C÷A. Always check your answer by verifying both ratios simplify to the same fraction.
// Ratio vs Fraction
A ratio 3:4 is not the same as the fraction 3/4. The fraction 3/4 means 3 out of 4 total parts (75%). The ratio 3:4 means 3 parts to 4 parts (7 total).
// Unit Rates
A unit rate is a ratio with 1 in the denominator. £12 for 3 items = £4 per item = a ratio of 4:1 (£:item).
// Scaling
To scale a ratio, multiply both parts by the same number. 3:4 × 5 = 15:20, which simplifies back to 3:4.