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 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
- 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.
Formula
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.