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Calculator Answers

Ratio Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A ratio calculator is an arithmetic utility designed to simplify, compare, and solve ratios. It simplifies a given ratio of two numbers (A : B) by dividing both terms by their greatest common divisor, reducing it to its simplest integer form. The calculator also compares two different ratios to check if they form an equivalent proportion, and solves for a missing value (X) using cross-multiplication. Chefs, designers, and students use this tool to scale recipes, adjust design dimensions, and solve math problems.

Enter a ratio A : B and the calculator simplifies it to lowest terms, returns the decimal and percent form, and optionally checks whether a second ratio C : D is equivalent.

See also: Scale Factor Calculator and Proportion Calculator.

Quick Answer

Simplify ratios to their lowest terms or solve for a missing value. Enter your ratio terms to reduce or equate them.

Ratio A : B

e.g. 12

e.g. 18

Optional second ratio C : D

Leave blank to skip the equivalence check. · e.g. 2

e.g. 3

Simplifies A : B by dividing both sides by their GCF. Add a second ratio to check whether A : B equals C : D.

Ratio

Simplified ratio

2 : 3

12 : 18 reduced to lowest terms

Input12 : 18
Simplified2 : 3
A ÷ B (decimal)0.666667
A ÷ B (percent)66.6667%

Divide both sides of A : B by their greatest common factor to simplify. Two ratios A : B and C : D are equivalent exactly when A · D equals B · C.

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Examples

12 : 18

= 2 : 3 · 0.667 · 66.67%

50 : 100

= 1 : 2 · 0.5 · 50%

2 : 3 vs 4 : 6

Equivalent (2 × 6 = 3 × 4)

How it works

A ratio compares two numbers by division. Simplifying a ratio means dividing both sides by their greatest common factor. Two ratios are equivalent when their cross products are equal: A × D = B × C.

Simplify · A : B → (A ÷ gcf) : (B ÷ gcf)

Equivalent · A : B = C : D iff A · D = B · C

Decimal form: A ÷ B. Percent form: (A ÷ B) × 100%.

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More tools from Education

Scale Factor CalculatorFind the scale factor between two dimensions, or enter an original length and scale factor to compute the new dimension.Proportion CalculatorSolve a proportion A : B = C : D for one missing value using cross multiplication. Returns the missing value and the worked step.

Frequently asked questions

A ratio compares two quantities by division. Written A : B, it expresses how big A is relative to B. For example, a ratio of 12 : 18 says that for every 12 units of the first quantity there are 18 units of the second. The decimal form, A ÷ B, is the size of A per unit of B.

Divide both sides by their greatest common factor. For 12 : 18, the GCF of 12 and 18 is 6, so the simplified ratio is 2 : 3. A ratio is in simplest form when its two sides share no common factor other than 1.

Two ratios A : B and C : D are equivalent exactly when A × D = B × C (cross multiplication). For example, 2 : 3 and 4 : 6 are equivalent because 2 × 6 = 3 × 4 = 12. The calculator runs this cross-product check whenever a second ratio is entered.

A fraction A/B is one number: the value of A divided by B. A ratio A : B compares two quantities and is most useful as a comparison, like a recipe (2 parts flour to 1 part sugar). Numerically they are equivalent: 2 : 3 means the same as 2/3 when used as a value.

One side can be 0, which means that quantity is absent. The ratio 0 : 5 simplifies to 0 : 1. Both sides being 0 is not a defined ratio and the calculator flags it.

Yes, but ratios are most useful with whole numbers. With integer inputs the calculator returns the simplest whole-number ratio. With decimal inputs it still computes the decimal and percent form, but the simplified line just echoes the input since there is no clean integer reduction.