Ratio Calculator & Simplifier

About the Ratio Calculator & Simplifier

A ratio compares the relative sizes of two or more quantities, written as A : B or as the fraction A/B. Ratios are used in screen aspect ratios (16:9), map scales, financial debt-to-equity metrics, and mixing solutions.

This Ratio Calculator reduces any ratio A:B to its simplest whole-number form and computes its unit rates (1 : B/A and A/B : 1).

Ratio Simplification & Proportion Formulas

Just like fractions, ratios are simplified by dividing both terms by their Greatest Common Factor (GCF):

How to Simplify a Ratio Step-by-Step

1. Find the GCF of Both Terms: Determine the Greatest Common Factor of A and B.
2. Divide Both Sides by the GCF: Divide A by the GCF and B by the GCF.
3. Write the Reduced Ratio: Express the simplified integers in a : b notation.

Worked Example: To simplify the ratio 12 : 16, find GCF(12, 16) = 4. Divide both numbers by 4 to get 3 : 4.

Frequently Asked Questions (FAQ)

Is a ratio the same thing as a fraction?

A ratio A:B can represent a part-to-part comparison (e.g., 3 apples to 4 oranges, where the total is 7) or a part-to-whole fraction (3/4). Mathematically, simplifying A:B follows the exact same GCD rule as simplifying A/B.

How do I solve for a missing value in a proportion A:B = C:X?

Use cross-multiplication: X = (B × C) ÷ A.