- Simplify a ratio. Enter two numbers separated by the colon. The calculator finds the Greatest Common Factor (GCF) and divides both sides by it. Example: 12:18 has GCF of 6, so 12/6 = 2 and 18/6 = 3, giving the simplified ratio 2:3. The result also shows the ratio as 1:n and as a fraction.
- Scale a ratio. Enter the base ratio and a scale factor to proportionally increase or decrease both values. Useful for scaling recipes (triple a 2:3 ratio to get 6:9) or architectural plans (1:50 scale means 1 cm = 50 cm).
- Solve for a missing value. Enter three known values in the proportion a:b = c:? format and leave the unknown blank. The calculator uses cross-multiplication to find the missing fourth value. Example: 3:4 = 9:? gives ? = (4 × 9) / 3 = 12.
Ratio Calculator
Simplify ratios, find missing values, and compare ratios to find equivalents.
:
Simplified Ratio
2:3
| Original | 12:18 |
| Simplified | 2:3 |
| As 1:n | 1:1.5 |
| As fraction | 12/18 = 2/3 |
How to Use the Ratio Calculator
Ratio Formulas and Applications
Simplify ratio a:b: divide both by GCF(a, b) Scale ratio a:b by f: (a × f):(b × f) Solve proportion: a:b = c:d Cross-multiply: a × d = b × c Find d: d = (b × c) / a Find c: c = (a × d) / b
Real-world ratio applications:
| Application | Ratio | Meaning |
|---|---|---|
| Concrete mix | 1:2:3 | 1 part cement, 2 sand, 3 gravel |
| Map scale | 1:50,000 | 1 cm = 50,000 cm = 500 m |
| Recipe scale | 2:3 eggs to cups | 4 eggs needs 6 cups |
| Aspect ratio (HD) | 16:9 | 1920px × 1080px |
| Gear ratio | 3:1 | 3 engine turns per 1 wheel turn |
| Debt-to-equity | 1.5:1 | $150K debt per $100K equity |
Frequently Asked Questions
A ratio compares two (or more) quantities showing their relative sizes. The ratio 3:4 means for every 3 of the first quantity, there are 4 of the second. Ratios can be written three ways: 3:4, 3/4, or as the decimal 0.75. They appear in cooking (1:2 oil to vinegar for dressing), construction (1:2:3 concrete mix), maps (1:50,000 scale), and finance (price-to-earnings ratios). Unlike fractions, ratios compare parts to parts, not parts to a whole.
Find the Greatest Common Factor (GCF) of both numbers and divide each by it. For 24:36: factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36; GCF is 12. So 24/12 = 2 and 36/12 = 3, giving 2:3. You can also simplify step by step by dividing by small primes: 24:36 → divide by 2 → 12:18 → divide by 2 → 6:9 → divide by 3 → 2:3.
A proportion states two ratios are equal: a:b = c:d. To solve for a missing value, use cross-multiplication: a × d = b × c. Example: 5:8 = 15:? Cross-multiply: 5 × ? = 8 × 15 = 120. So ? = 120/5 = 24. Proportions are the foundation for unit conversions, scale drawings, and any situation where you maintain a consistent relationship between two quantities.
Ratios let you scale recipes without needing the original serving size. A cookie recipe with a 3:2 ratio of flour to sugar (3 cups flour, 2 cups sugar) can be halved to 1.5:1, doubled to 6:4, etc. Bread baking uses baker's percentages: flour is always 100%, and other ingredients are ratios relative to flour weight. A 65% hydration bread means 65g water per 100g flour. Cocktails use ratios like 2:1:1 (spirit:sweet:sour) for balanced drinks.
A ratio compares two quantities with the same units (3 cats to 4 dogs, both counts). A rate compares two quantities with different units (60 miles per hour, price per pound). Miles per hour is a rate, not a ratio, because miles and hours are different unit types. However, rates can be written in ratio notation: 60 mph = 60:1 (miles per hour). Unit price ($2.50 per pound) is a rate that acts like a ratio for comparison shopping.