Ratio Calculator
Simplify a ratio to its lowest terms, or fill in three numbers of a proportion to find the fourth. Whole numbers and decimals both work.
Last updated October 20, 2026
Leave blank for a 2-term ratio.
Result
3 : 2
Divided by 4
Per one: 1.5 : 1
Show the work
Formula: divide every term by their greatest common divisor
- Ratio: 12 : 8
- Greatest common divisor: 4
- Divide each term by 4: 12 / 4 = 3; 8 / 4 = 2
- Per one (each term / 2): 1.5 : 1
Result: 3 : 2
How ratios are simplified and solved
a : b = (a ÷ g) : (b ÷ g), where g is the greatest common divisor
To simplify a ratio, divide every term by their greatest common divisor, the largest whole number that divides all of them. Decimals are first scaled to whole numbers, so 1.5 : 2 becomes 15 : 20 and simplifies to 3 : 4.
To solve a proportion a : b = c : d, cross-multiply: a × d = b × c. The missing term is the product of the two terms that sit diagonally from each other, divided by the term left over.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Slope Calculator, Fraction Calculator and Exponent Calculator.
Solving a proportion
A proportion says two ratios are equal. Enter any three of the four terms and leave one empty. For 2 : 3 = 4 : ?, cross-multiplying gives 3 × 4 ÷ 2 = 6, so the proportion is 2 : 3 = 4 : 6.
This is how scaling works: if a recipe uses 2 cups of flour for 3 cups of milk, then 4 cups of flour needs 6 cups of milk.
Decimals and three-part ratios
A decimal ratio is scaled by a power of ten until every term is a whole number, then simplified. For 0.75 : 1.25, multiplying by 100 gives 75 : 125, and the greatest common divisor 25 reduces it to 3 : 5. Up to 6 decimal places are supported.
A ratio can have three terms, such as the mix of three ingredients. The greatest common divisor of all three is removed at once, so 6 : 9 : 12 becomes 2 : 3 : 4 after dividing by 3. The calculator also shows each term per one unit of the last term: 3 : 2 is 1.5 per 1.
Where ratios and proportions are used
Sharing in a ratio: to split 500 in the ratio 3 : 2, add the parts (3 + 2 = 5), so each part is 500 ÷ 5 = 100. The shares are 300 and 200. In a simplified ratio a : b, the first share is a ÷ (a + b) of the total, so 3 : 2 means 60% and 40%.
Resizing a screen or image: a 1920 × 1080 image has the ratio 16 : 9. To keep that shape at a width of 1280, solve 16 : 9 = 1280 : ?, which gives 9 × 1280 ÷ 16 = 720. The new size is 1280 × 720.
Rates and fuel: if a car uses 12 liters in 150 km, then 400 km needs 12 × 400 ÷ 150 = 32 liters, assuming steady driving. Any problem of the form “if this much gives that much, how much for this other amount” is a proportion.
Order matters and units must match
The ratio 3 : 2 is not the same as 2 : 3. The first term always belongs to the first quantity you name, so keep the same order on both sides of a proportion. Both terms of a ratio must also be in the same unit: compare 30 minutes with 2 hours as 30 : 120, which simplifies to 1 : 4, not as 30 : 2.
How to use the Ratio Calculator
- Choose Simplify a ratio or Solve a proportion.
- Enter the numbers. For a proportion, leave the one you want to find empty.
- Read the simplified ratio, or the missing term and the full proportion.
- Use Copy, Print or Share to keep the result.
Worked example
To simplify 12 : 8, the greatest common divisor of 12 and 8 is 4. Dividing both terms by 4 gives 3 : 2, which is the same as 1.5 : 1. The ratio 12 : 8 and the ratio 3 : 2 describe the same relationship. To check, 3 × 4 = 12 and 2 × 4 = 8, so multiplying 3 : 2 by 4 gives the original ratio back.
| Ratio | Simplified |
|---|---|
| 10 : 5 | 2 : 1 |
| 12 : 8 | 3 : 2 |
| 15 : 10 | 3 : 2 |
| 20 : 15 | 4 : 3 |
| 24 : 18 | 4 : 3 |
| 36 : 24 | 3 : 2 |
| 1920 : 1080 | 16 : 9 |
Frequently asked questions
How do I simplify a ratio?
Divide every term by the greatest common divisor. For 12 : 8 that divisor is 4, so the ratio becomes 3 : 2.
Can I use decimals, and are my numbers stored?
Yes, up to 6 decimal places. The calculator scales the numbers to whole numbers first, then simplifies. Everything runs in your browser and nothing you enter is saved or uploaded.
What is a proportion?
A statement that two ratios are equal, such as 2 : 3 = 4 : 6. You can find a missing term by cross-multiplying.
Can a ratio have three parts?
Yes. Enter a third number in Simplify mode, for example 6 : 9 : 12 simplifies to 2 : 3 : 4.
Does the order of the numbers matter?
Yes. 3 : 2 and 2 : 3 are different ratios. Keep the same order on both sides of a proportion, and use the same unit for both terms.