Ratio calculator
Simplify a ratio or find the missing number in a proportion, with the steps shown.
1,920 : 1,080 simplified
16 : 9
Decimal ratio 1.7778 : 1
Steps
- GCF(1920, 1080) = 120
- 1920 ÷ 120 : 1080 ÷ 120 = 16 : 9
How to use the ratio calculator
- To simplify, enter both sides of the ratio.
- To solve a proportion, enter three values A, B and C.
- Read the simplified ratio or the missing value D, with the working.
About this calculator
A ratio compares two quantities, like 3 cups of flour to 2 cups of milk. Simplifying divides both sides by their greatest common factor, so 1920:1080 becomes 16:9.
A proportion says two ratios are equal. If you know three of the four numbers you can find the fourth: scale a recipe, resize an image without stretching it, or convert a map distance.
Proportion
A : B = C : D ⇒ D = B × C ÷ A
To simplify A:B, divide both A and B by their greatest common factor.
Example
A 1920×1080 image resized to 1280 px wide keeps its shape at 1920:1080 = 1280:D, so D = 1080 × 1280 ÷ 1920 = 720 px high.
Frequently asked questions
How do you simplify a ratio?
Find the greatest common factor of both numbers and divide each by it. 24:36 has GCF 12, so it simplifies to 2:3.
How do you solve a proportion?
Cross-multiply: if A/B = C/D, then A × D = B × C, so D = B × C ÷ A.
How do I scale a recipe?
Use the proportion original servings : new servings = original amount : new amount. Going from 4 to 6 servings multiplies every ingredient by 1.5.
Can ratios have decimals?
Yes. To simplify, multiply both sides by a power of ten to remove decimals first: 1.5:2.5 becomes 15:25, which simplifies to 3:5.