Quick Answer
A ratio is simplified by dividing both numbers by their Greatest Common Divisor (GCD) — for example, the ratio 12:8 simplifies to 3:2 because the GCD of 12 and 8 is 4.
What Is a Ratio Calculator?
A ratio expresses the relationship between two or more quantities, showing how many times one value contains or is contained within another. Ratios appear constantly in everyday contexts — recipe scaling, mixing solutions (e.g. paint-to-water ratios), financial ratios, map scales, and aspect ratios for images and screens.
Simplifying a ratio to its lowest terms (similar to simplifying a fraction) makes it easier to understand and compare — a ratio of 12:8 carries the same proportional relationship as 3:2, but the simplified form is immediately clearer. This is done by dividing both parts of the ratio by their Greatest Common Divisor (GCD).
Solving a proportion — finding an unknown value when two ratios are set equal to each other — is one of the most common practical uses, such as scaling a recipe up or down while maintaining the same ingredient proportions.
How to Use This Ratio Calculator
- 1To simplify a ratio: enter both numbers, and the calculator divides both by their greatest common divisor.
- 2To solve a proportion: enter three known values in a ratio equation (A:B = C:?) and the calculator solves for the missing value.
- 3To scale a ratio: enter the ratio and a target value for one side, and the calculator scales the other side proportionally.
The Formula Explained
Simplified Ratio = (A ÷ GCD(A,B)) : (B ÷ GCD(A,B))If A:B = C:D, then D = (B × C) ÷ AExample: Simplifying the ratio 18:24, and scaling a recipe ratio of 2:3
- Simplify 18:24: GCD(18,24) = 6 → 18÷6 : 24÷6 = 3:4
- Scaling 2:3 to find the second value when the first becomes 10:
- 2:3 = 10:? → ? = (3 × 10) ÷ 2 = 15
Tips & Things to Know
- When scaling recipes or mixtures, always apply the same scaling factor to every ingredient/component in the ratio, not just one — this keeps the proportional relationship intact.
- A ratio and a fraction represent related but distinct ideas — 3:4 as a ratio compares two separate quantities, while 3/4 as a fraction typically represents a part of a single whole; context determines which interpretation applies.
- For three-or-more-part ratios (e.g. concrete mix ratios like 1:2:3 for cement:sand:gravel), simplify all parts together using their shared GCD, maintaining the relationship across all terms.
- Double-check the order of terms in a ratio — 3:4 and 4:3 represent different relationships, and reversing the order by mistake is a common source of calculation errors.