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Ratio Calculator

Simplify ratios, solve proportions, scale, compare, and generate equivalent ratios. Convert between ratios, decimals, and percentages.

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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

Compare Two Ratios

Convert each ratio to a decimal to determine which is larger:

  • 3:4 = 0.75 and 5:7 ≈ 0.714 → 3:4 is larger
  • If both decimals are equal (within rounding), the ratios are equivalent

Equivalent Ratios

Multiply both parts of a ratio by the same number to get equivalent ratios:

  • 2:3 → 4:6 → 6:9 → 8:12 → 10:15 ...
  • Useful for scaling recipes, maps, or any proportional relationship

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%

Related Calculators

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Frequently Asked Questions

How do you simplify a ratio?

Divide both numbers by their greatest common divisor. For 8:12 the greatest common divisor is 4, so the ratio simplifies to 2:3. Equivalent ratios describe the same relationship, so 2:3, 4:6, 6:9 and 8:12 are all equal. A ratio is fully simplified when the only whole number dividing both terms is 1.

How do you solve a proportion for x?

Cross multiply and divide. If A/B = C/x, then x = (B × C) / A. For 2/3 = 8/x, cross multiplying gives 2x = 24, so x = 12. A proportion is simply a statement that two ratios are equal, such as 2:3 = 8:12, so solving one means finding the missing term that keeps them equal.

How do you convert a ratio to a percentage?

Divide the first term by the second and multiply by 100: for 3:4, 3 / 4 = 0.75, so the first quantity is 75% of the second. If you want each share of the total instead, divide by the sum of the parts: in 3:4 the first part is 3/7 of the whole, about 42.9%.

How do you split an amount in a given ratio?

Add the ratio parts, divide the total by that sum, then multiply each part by the result. To split 25 in the ratio 3:2, the parts sum to 5 and 25 / 5 = 5, giving 15 and 10. The same method scales recipes, mixtures and budgets to any total while keeping the proportions fixed.