Ratio Calculator
Simplify any ratio to its lowest terms in seconds. Enter two values and the calculator reduces the ratio and shows the decimal equivalent.
What Is a Ratio?
A ratio is a way to compare two quantities by division. When we say a recipe calls for a 2:1 ratio of flour to water, we mean use twice as much flour as water. Ratios can be expressed as A:B, A to B, or the fraction A/B — all equivalent representations.
Ratios are simplified using the Greatest Common Divisor (GCD) — the largest number that divides both values evenly. The ratio 15:10 simplifies to 3:2 because GCD(15, 10) = 5. A simplified ratio is in its lowest terms when the GCD of the two numbers is 1.
Common Ratios Reference Table
| Original Ratio | Simplified | Context |
|---|---|---|
| 16:9 | 16:9 | HD video aspect ratio |
| 4:3 | 4:3 | Classic TV aspect ratio |
| 12:8 | 3:2 | Common proportion |
| 50:1 | 50:1 | Two-stroke fuel mix |
| 100:25 | 4:1 | 4:1 ratio |
| 360:270 | 4:3 | Equivalent to 4:3 |
The GCD Method for Simplifying Ratios
The Euclidean algorithm is the fastest method for finding the GCD: start with two numbers, divide the larger by the smaller, take the remainder, and repeat until the remainder is zero. The last non-zero remainder is the GCD. For 48 and 36: 48 ÷ 36 = remainder 12. 36 ÷ 12 = remainder 0. GCD = 12. So 48:36 simplifies to 4:3.
For large numbers, this algorithm is extremely efficient. For small numbers up to a few hundred, you can also find the GCD by listing factors and finding the largest common one — but the Euclidean algorithm is faster for any size number and is how this calculator works internally.
Frequently Asked Questions
What is a ratio?
A ratio expresses the quantitative relationship between two numbers, showing how many times one value contains or is contained within the other. Written as A:B or A/B. A ratio of 3:1 means for every 3 of A, there is 1 of B. Ratios are used in cooking recipes, financial analysis (debt-to-equity), maps (scale 1:50,000), mixing chemicals, aspect ratios (16:9), and probability. Unlike fractions, ratios compare two quantities of the same type.
How do you simplify a ratio?
Divide both terms by their Greatest Common Divisor (GCD). Example: simplify 12:8. GCD(12, 8) = 4. Simplified ratio = 12/4 : 8/4 = 3:2. To find the GCD, use the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is 0. The last non-zero remainder is the GCD. Example: GCD(12, 8) → GCD(8, 4) → GCD(4, 0) = 4.
What are common ratio applications?
Aspect ratios: standard HD video is 16:9, the old TV format was 4:3. Finance: a debt-to-equity ratio of 1.5:1 means $1.50 debt per $1.00 equity. Maps: a 1:25,000 scale means 1 cm = 250 m. Cooking: a recipe ratio of 1:2 flour to water. Fuel mixing: 50:1 oil to gas for two-stroke engines means 50 parts gas to 1 part oil. Concrete mix: a 1:2:3 mix is 1 part cement, 2 parts sand, 3 parts aggregate.
How do you solve for a missing value in a proportion?
Use cross-multiplication. If A:B = C:D (A/B = C/D), then A × D = B × C. To find D: D = (B × C) / A. Example: if 3:4 = 9:x, then 3x = 4 × 9 = 36, so x = 12. This is the proportionality rule — useful for scaling recipes, converting units, and solving similar triangle problems. Always check your answer by verifying both ratios reduce to the same simplified form.