A ratio A:B compares two quantities, showing how many times one contains the other. 3:4 means for every 3 units of A there are 4 units of B.

How do I solve a proportion?

Cross-multiply: if A/B = C/D, then A × D = B × C. Solve for the unknown by isolating it on one side.

What is the difference between ratio and fraction?

A ratio A:B compares two separate parts. A fraction A/B represents part of a whole. 3:4 as a fraction of the total is 3/7.

Ratio Calculator

Simplify any ratio to its lowest terms, solve a missing value in a proportion A/B = C/D, or split a total amount according to a multi-part ratio (e.g. 2:3:5).

How to use this calculator

Select the mode: simplify a ratio, solve a proportion, or split a total.
For simplification: enter A and B — the calculator divides both by their GCF.
For proportion: enter three known values and set the unknown to 0.
For splitting: enter the total amount and a ratio like 2:3:5 to get each share.

Formula & method

Ratio simplification and proportion solving

Simplified ratio = A/GCF : B/GCF · Proportion: A × D = B × C · Split: unit = Total / ΣParts, share_i = part_i × unit

GCF = greatest common factor. Use the GCF Calculator to find it step by step.

Example

12:16 → GCF = 4 → 3:4. Proportion: 3/4 = 6/? → D = (4×6)/3 = 8. Split 500 in 2:3:5 → 100:150:250.

Key insights

A ratio a:b is simplified by dividing both terms by their greatest common factor (GCF).
Proportions A/B = C/D are solved by cross-multiplication: A × D = B × C.
Dividing 500 in ratio 2:3:5 gives 10 equal parts, worth 50 each: 100, 150, 250.
Ratios are used in map scales, recipe scaling, finance (debt-to-equity), and image aspect ratios.

How to interpret your result

Simplified ratio

Dividing A and B by their GCF gives the simplest form. 12:16 → GCF = 4 → 3:4.

Cross-multiplication

If A/B = C/D then A × D = B × C. This finds the missing term when three values are known.

Frequently asked questions

What is a ratio?: A ratio A:B compares two quantities, showing how many times one contains the other. 3:4 means for every 3 units of A there are 4 units of B.
How do I solve a proportion?: Cross-multiply: if A/B = C/D, then A × D = B × C. Solve for the unknown by isolating it on one side.
What is the difference between ratio and fraction?: A ratio A:B compares two separate parts. A fraction A/B represents part of a whole. 3:4 as a fraction of the total is 3/7.

Related calculators

GCF Calculator — Find the Greatest Common Factor (GCF/GCD) and all common factors of two or more integers using the Euclidean algorithm.
Percentage Calculator — Find X% of a number, what percent X is of Y, or the change between two values.
Fraction Calculator — Add, subtract, multiply, and divide fractions with step-by-step simplification and mixed number conversions.

See all math calculators · Explore all online calculators