Ratio Calculator
Simplify a ratio, solve a missing value in a proportion, scale a ratio up or down, or split an amount by ratio. Every answer comes with steps.
Example loaded: 12 : 8. Change the numbers and select Calculate.
Your ratio
Solve a : b = c : d (leave one box empty)
Your results
Quick answer
A ratio compares two or more quantities. To simplify one, divide every term by their greatest common divisor. For example 12 : 8 becomes 3 : 2, because both numbers divide by 4.
To find a missing number in a proportion, cross-multiply: if 6 : 4 = 12 : x, then x = (4 × 12) ÷ 6 = 8. Use the modes above for simplifying, solving, scaling, splitting an amount and comparing two ratios.
How to calculate a ratio
Simplify a ratio
- Write the ratio, for example 18 : 24.
- Find the greatest common divisor (GCD) of the terms. For 18 and 24 it is 6.
- Divide each term by the GCD: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The simplified ratio is 3 : 4.
Solve a proportion
- Write the two ratios as fractions: a/b = c/d.
- Cross-multiply: a × d = b × c.
- Divide to find the missing term, for example d = (b × c) ÷ a.
Split an amount by a ratio
- Add the ratio terms: for 3 : 2 that is 5 shares.
- Divide the total by the number of shares: 500 ÷ 5 = 100 per share.
- Multiply each term by one share: 3 × 100 = 300 and 2 × 100 = 200.
Ratio with decimals
Multiply every term by 10, 100 or 1,000 until they are whole numbers, then simplify. 0.5 : 1.5 : 2 becomes 5 : 15 : 20, which simplifies to 1 : 3 : 4.
Types of ratio
- Part-to-part: compares one part with another, such as 3 boys to 2 girls (3 : 2).
- Part-to-whole: compares one part with the total, such as 3 boys out of 5 children (3 : 5, or 60%).
- Ratio to 1: scales the ratio so one term equals 1, such as 3 : 2 = 1.5 : 1. The calculator shows this for two-term ratios.
- Ratio as a fraction or percent: a 3 : 2 split means 3/5 (60%) and 2/5 (40%) of the total. The calculator shows the share of the total for each term.
Worked examples
- Recipe: a mix uses flour, sugar and butter in the ratio 4 : 2 : 1. With 280 g in total, one share is 280 ÷ 7 = 40 g, so you need 160 g, 80 g and 40 g.
- Sharing money: split 500 in the ratio 3 : 2 and you get 300 and 200.
- Scaling: a paint mix of 3 : 2 for a bigger job, multiplied by 4, becomes 12 : 8.
- Proportion: if 5 notebooks cost 20, then 8 notebooks cost x, so 5 : 20 = 8 : x and x = (20 × 8) ÷ 5 = 32.
- Compare: 3 : 2 is 1.5 and 5 : 3 is about 1.667, so 5 : 3 is the greater ratio.
Select Load example above to try one in the calculator.
Common ratios simplified
| Ratio | Simplified | a ÷ b | Share of each term |
|---|---|---|---|
| 1920 : 1080 | 16 : 9 | 1.7778 | 64% / 36% |
| 1280 : 720 | 16 : 9 | 1.7778 | 64% / 36% |
| 1024 : 768 | 4 : 3 | 1.3333 | 57.14% / 42.86% |
| 100 : 25 | 4 : 1 | 4 | 80% / 20% |
| 18 : 24 | 3 : 4 | 0.75 | 42.86% / 57.14% |
| 250 : 1000 | 1 : 4 | 0.25 | 20% / 80% |
| 45 : 60 | 3 : 4 | 0.75 | 42.86% / 57.14% |
| 84 : 36 | 7 : 3 | 2.3333 | 70% / 30% |
1920 : 1080 and 1280 : 720 both simplify to 16 : 9, the aspect ratio of most screens.
Frequently asked questions
What is a ratio?
A ratio compares two or more quantities of the same kind. 12 boys to 8 girls is written 12 : 8, and it can be simplified to 3 : 2.
How do I calculate a ratio between two numbers?
Write them as a : b, then divide both by their greatest common divisor. For 15 and 25 the divisor is 5, so the ratio is 3 : 5.
How do I simplify a ratio?
Divide every term by the greatest common divisor. If the terms are decimals, multiply them all by 10, 100 or 1,000 first so they become whole numbers.
How do I find a missing value in a ratio?
Set up a proportion and cross-multiply. For 6 : 4 = 12 : x, multiply 4 × 12 and divide by 6 to get x = 8. Choose Solve missing value and leave one box empty.
Does the order of the numbers matter?
Yes. 3 : 2 is not the same as 2 : 3. The first number always belongs to the first quantity you named.
How do I split an amount by a ratio?
Add the terms to get the number of shares, divide the total by the shares, then multiply each term by one share. Choose Split an amount to see this worked out.
How do I convert a ratio to a fraction or percentage?
Divide each term by the sum of all terms. In 3 : 2 the sum is 5, so the parts are 3/5 = 60% and 2/5 = 40%.
What is the difference between a ratio and a fraction?
A fraction compares a part with the whole. A ratio can compare a part with another part. In 3 : 2 the parts are 3/5 and 2/5 of the whole.
What are equivalent ratios?
Ratios that simplify to the same form, such as 3 : 2, 6 : 4 and 12 : 8. Use Compare to check any two ratios.
Can I use decimals?
Yes, up to six decimal places. Negative numbers are not used in ratios, so the calculator asks for positive values.
Is my data stored?
No. Everything is calculated in your browser and nothing is sent anywhere.
About this calculator
Written by Umar Khan. The calculator simplifies ratios with exact whole-number arithmetic and the greatest common divisor, and solves proportions by cross-multiplication. Your numbers stay in your browser. Last updated November 10, 2026. Questions or corrections: [email protected].
Written by Umar Khan
Umar Khan is a PhD student in engineering at NTNU, the Norwegian University of Science and Technology, in Norway. Every formula and worked example on this page is shown in full so you can check each result yourself. Corrections are welcome at [email protected].
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For information only, not professional advice.
Written by Umar Khan. Last updated: November 10, 2026.