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Online Calculator & Converter

Ratio and Proportion Calculator

Use any of the three tools. Results update as you type.

Solve a proportion A : B = C : D

Leave one box empty.

Result

D = 12
Cross-multiplication: A × D = B × C

Simplify a ratio

Result

Lowest terms
2 : 3
As a decimal (A ÷ B)
0.666667
As 1 : n
1 : 1.5

Split a total by a ratio

Separate parts with colons, e.g. 2:3:5

Result

Shares
24 : 36 : 60

What this calculator does

A ratio compares quantities: a 2 : 3 mix of sand to cement has two parts sand for every three parts cement. This page handles the three questions that come up most often with ratios: reducing a ratio to lowest terms, finding the missing value in a proportion (two equal ratios), and dividing an amount according to a ratio.

Formulas

  • Proportion: A : B = C : D means A ÷ B = C ÷ D, so A × D = B × C. The missing term is the product of the opposite diagonal divided by the term across from it, e.g. D = B × C ÷ A.
  • Simplifying: divide both terms by their greatest common divisor (GCD). Decimals are first multiplied by a power of ten so both terms are whole numbers.
  • Splitting: each share = part ÷ (sum of parts) × total.

Worked examples

Scaling a recipe

A recipe uses 3 cups of flour for 4 servings. How much for 9 servings? Set up 4 : 3 = 9 : D. D = 3 × 9 ÷ 4 = 6.75 cups. Check: 3 ÷ 4 = 0.75 and 6.75 ÷ 9 = 0.75.

Map scale

On a 1 : 25,000 map, 7 cm on paper corresponds to 7 × 25,000 = 175,000 cm = 1.75 km. As a proportion: 1 : 25,000 = 7 : D, so D = 25,000 × 7 ÷ 1.

Sharing a bill 2 : 3 : 5

Total parts = 10. A $120 bill splits into 2/10 × 120 = $24, 3/10 × 120 = $36 and 5/10 × 120 = $60, which add back to $120.

Interpreting results and common mistakes

  • Order matters. 2 : 3 is not 3 : 2. Keep the same quantity in the same position on both sides of a proportion.
  • Mixing units. Convert both quantities to the same unit before comparing (use the length converter if needed).
  • Parts versus whole. In a 1 : 4 ratio, the first quantity is one fifth of the total, not one quarter.

Assumptions and limitations

Proportions assume a straight-line (directly proportional) relationship. Many real situations are not proportional: cooking time does not double when a recipe doubles, and costs often include fixed amounts. Ratios must use positive values to be simplified.

For percentages of a quantity, see the percentage calculator.

Frequently asked questions

How do I solve a proportion with a missing number?

Cross-multiply. In A : B = C : D, the products A × D and B × C are equal, so the missing term equals the product of the diagonal pair divided by the term opposite it. For 3 : 4 = 9 : D, D = 4 × 9 ÷ 3 = 12.

Can a ratio contain decimals?

Yes. To write it in whole numbers, multiply both terms by the same power of ten and divide by their greatest common divisor. 1.5 : 2.25 becomes 150 : 225, which reduces to 2 : 3.

Is a ratio the same as a fraction?

A two-part ratio A : B can be written as the fraction A/B, but a ratio compares parts with each other, while a fraction usually compares a part with a whole. In a 2 : 3 mix, the first part is 2/5 of the whole, not 2/3.