How to Use Ratios
A ratio compares two or more quantities. It can be written as A:B, A/B, or "A to B." This calculator helps simplify ratios, solve proportions, and scale to any total.
Simplify a Ratio
Divide both numbers by their greatest common divisor (GCD). For example, 15:25 → divide both by 5 → 3:5.
- 24:36 → GCD is 12 → 2:3
- 100:250 → GCD is 50 → 2:5
- 16:24:40 → GCD is 8 → 2:3:5
Solve for X (Proportions)
A proportion states two ratios are equal. Use cross multiplication to solve: if A/B = C/X, then X = (B × C) ÷ A.
Example: If 3 painters finish a job in 12 hours, how long for 4 painters?
- 3/12 = 4/X → X = (12 × 3) ÷ 4 = 9 hours
Scale to a Total
Divide a total amount by a ratio:
- Split $600 in ratio 1:2:3 → Total parts = 6
- First share = (1/6) × 600 = $100
- Second share = (2/6) × 600 = $200
- Third share = (3/6) × 600 = $300
Common Ratio Applications
- Cooking: A 2:1 sugar-to-water ratio for simple syrup means 2 cups sugar per 1 cup water
- Screen aspect ratios: 16:9 is standard widescreen. A 1920×1080 display has a 16:9 ratio (both divide by 120)
- Maps and blueprints: A 1:100 scale means 1 cm on the map = 100 cm (1 meter) in real life
- Finance: Debt-to-income ratio, price-to-earnings ratio, current ratio — all measure financial health
- Mixing: Concrete mix ratio of 1:2:3 means 1 part cement, 2 parts sand, 3 parts gravel
- Business: Splitting profits between partners, dividing costs proportionally
Ratio vs Fraction vs Percentage
- Ratio 3:4 = Fraction 3/4 = 75%
- Ratios compare parts to parts (3:4). Fractions compare part to whole (3/7 of the total). Percentages express fraction as a per-100 value
- To convert ratio to percentage: divide first number by second, multiply by 100. 3:4 → 3÷4 × 100 = 75%