— Everyday Math
Ratio Calculator
Everything you do with a ratio in one place: simplify it to its lowest terms, solve a proportion to find a missing value, scale it up or down, or convert it to a fraction, decimal and percentage. Works with two- or three-part ratios.
Simplified ratio
16 : 9
- GCD (common factor)
- 120
- As a fraction
- 16/9
- As a decimal (a ÷ b)
- 1.78
- As percentages
- 64% : 36%
— Equivalent ratios
| Multiple | a | b |
|---|---|---|
| ×1 | 16 | 9 |
| ×2 | 32 | 18 |
| ×3 | 48 | 27 |
| ×4 | 64 | 36 |
| ×5 | 80 | 45 |
| ×6 | 96 | 54 |
| ×7 | 112 | 63 |
| ×8 | 128 | 72 |
— How it works
Simplify by dividing every part by their greatest common divisor. Solve a proportion a : b = c : x with x = b × c ÷ a. Convert a : b so each part is a ÷ (a + b) × 100% of the whole.
Simplifying a ratio
A ratio compares quantities, and like a fraction it has a simplest form: divide every part by their greatest common divisor and you reach the smallest whole numbers that express the same relationship. 1920 to 1080 looks unwieldy, but both share a common factor of 120, so it reduces to 16 : 9 — the familiar widescreen aspect ratio. Simplifying does not change the ratio, only how it is written; 16 : 9, 32 : 18 and 1920 : 1080 are all equal. The calculator shows the greatest common divisor it used, the equivalent fraction and decimal, and a list of equivalent ratios.
Worked example — 1920 : 1080: The greatest common divisor is 120, so 1920 ÷ 120 : 1080 ÷ 120 = 16 : 9. That is the fraction 16/9, a decimal of about 1.78, and a split of 64% : 36%.
Solving a proportion
A proportion says two ratios are equal — a : b = c : x — and the everyday task is to find the missing value. Cross-multiplying gives x = b × c ÷ a. This is the engine behind scaling a recipe, working out a map distance, or converting between units that keep a fixed ratio: if 2 cups of flour need 3 eggs, then 5 cups need 3 × 5 ÷ 2 = 7.5. Choose “Solve a : b = c : x”, enter the three known values, and the calculator returns x and the completed proportion.
Scaling and converting
Scaling multiplies every part by the same factor to resize a ratio while keeping its shape — handy for enlarging a mix or a model. Scale to a target total instead and the calculator splits that total in the ratio you gave: a 3 : 2 split of 500 becomes 300 : 200. Converting expresses the ratio in the other common forms — a fraction, a decimal, and each part as a percentage of the whole — which is how you turn “2 : 3” into “40% and 60%”. Every mode guards the obvious traps: you cannot simplify or split when the parts are all zero, and a proportion needs a non-zero first term.
— Reader questions
How do I simplify a ratio?
Divide every part by their greatest common divisor (GCD). For 1920 : 1080 the GCD is 120, giving 16 : 9. The ratio is unchanged — just written in its smallest whole numbers. The calculator shows the GCD it divided out.
How do I solve a proportion like 2 : 3 = 8 : x?
Cross-multiply: x = b × c ÷ a. For 2 : 3 = 8 : x, that is 3 × 8 ÷ 2 = 12. Choose the proportion mode, enter a, b and c, and the calculator returns x.
How do I convert a ratio to a percentage?
Divide each part by the total and multiply by 100. For 2 : 3, the total is 5, so the parts are 40% and 60%. Use the convert mode to see the fraction, decimal and percentage at once.
How do I split an amount in a given ratio?
Use scale mode and set “scale to a total”. To split 500 in the ratio 3 : 2, enter 3 and 2 and a total of 500 — the calculator returns 300 : 200.
Can I work with three-part ratios?
Yes. Open the advanced options and enter a third part (c) to simplify, scale or convert an a : b : c ratio — for example reducing 2 : 4 : 6 to 1 : 2 : 3.