Ratio Calculator — Solve and Simplify Ratios
Solve ratio proportions (A:B = C:?) and simplify ratios to their lowest terms. See also Fraction Calculator and Percentage Calculator.
Solve Ratio: A : B = C : ?
Simplify a Ratio
How to Solve Ratio Problems
A ratio compares two quantities. When you have a proportion like A:B = C:D, if three values are known, you can find the fourth. The key principle is cross-multiplication: A × D = B × C. To find D, rearrange to D = (B × C) / A. This calculator also simplifies ratios by dividing both parts by their greatest common divisor (GCD).
Ratio Formula
Proportion: A : B = C : D
Cross multiply: A × D = B × C
Solve for D: D = (B × C) / A
Simplify ratio A : B:
Divide both by GCD(A, B)
Example
2 : 3 = 4 : ?
Cross multiply: 2 × ? = 3 × 4
2 × ? = 12
? = 12 / 2 = 6
So 2:3 = 4:6
Frequently Asked Questions
What is a ratio?
A ratio is a comparison of two quantities showing how many times one value contains or is contained within the other. For example, a ratio of 3:2 means for every 3 of the first quantity, there are 2 of the second.
What is a proportion?
A proportion is an equation stating that two ratios are equal. For example, 1:2 = 3:6 is a proportion because both ratios simplify to the same value (1:2). Proportions are solved using cross-multiplication.
How do you simplify a ratio?
Divide both numbers by their greatest common factor (GCF). For example, 15:25 → GCF(15,25) = 5 → 15÷5 : 25÷5 = 3:5.
Can ratios have decimals?
Yes, ratios can involve decimals. To simplify a decimal ratio like 1.5:2.5, multiply both by 10 to get 15:25, then simplify to 3:5. This calculator handles decimal inputs automatically.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (A:B), while a fraction represents a part of a whole (A/B). The ratio 3:4 means "3 to 4," while the fraction 3/4 means "3 out of 4." They are related but used in different contexts.