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Ratio Calculator

Simplify ratios, find equivalent ratios, scale ratios up or down, and solve for missing values in proportions.

Simplify a Ratio

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How to Use This Tool

  1. Choose a mode: Simplify, Equivalent Ratios, Scale to Total, or Solve Proportion.
  2. For Simplify, enter values A and B to reduce the ratio to its lowest terms.
  3. For Equivalent Ratios, enter values A and B to generate a table of equivalent ratios.
  4. For Scale to Total, enter A, B, and the total quantity to split proportionally.
  5. For Solve Proportion, enter any three of the four values (A, B, C, D) in A:B = C:D and leave the unknown one blank to solve for it.

Formula & How It Works

Simplifying a Ratio

Simplified A:B = (A ÷ GCD) : (B ÷ GCD)

Dividing both parts of a ratio by their Greatest Common Divisor reduces it to its lowest terms.

Equivalent Ratios

A×m : B×m

Multiplying both parts of a ratio by the same number m produces an equivalent ratio.

Scaling a Ratio to a Total

Part A = (A / (A+B)) × Total, Part B = (B / (A+B)) × Total

Splits a total quantity into two parts that keep the same ratio as A:B.

Solving a Proportion

A:B = C:D → A × D = B × C

Cross-multiplication lets you solve for any one missing value when the other three are known.

Practical Examples & Common Use Cases

Example: Simplify 12:8

GCD(12, 8) = 4, so 12 ÷ 4 = 3 and 8 ÷ 4 = 2. The simplified ratio is 3:2 (decimal 1.5, or 150%).

Example: Scale 2:3 to a Total of 100

A + B = 5. Part A = (2/5) × 100 = 40. Part B = (3/5) × 100 = 60. So 100 splits into 40 and 60.

Example: Solve 3:4 = 9:x

Using cross-multiplication, x = (4 × 9) / 3 = 36 / 3 = 12, so the complete proportion is 3:4 = 9:12.

Frequently Asked Questions

Divide both values by their Greatest Common Divisor (GCD). For example, 12:8 → GCD(12,8)=4 → 3:2.

A proportion states that two ratios are equal: A:B = C:D. If three values are known, the fourth can be found using cross-multiplication: A × D = B × C.

Add both parts of the ratio together, then divide the total by the sum to get each part. Example: split 100 in 2:3 → total parts = 5 → A = 40, B = 60.

Equivalent ratios have the same simplified form. You can create them by multiplying both parts by the same number. Example: 1:2, 2:4, 3:6 are all equivalent.

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