Ratio Calculator
Solve a proportion for the missing number, reduce a ratio to its simplest form, or divide an amount in a ratio, with the cross-multiplication shown.
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Fill in three numbers and leave the one you want to find empty.
How this was calculated
- In a true proportion the cross products are equal: A × D = B × C.
- Rearrange for C: C = A × D ÷ B = 3 × 20 ÷ 4 = 15.
How this ratio calculator works
A ratio compares two or more quantities: 3 : 4 means "3 of one thing for every 4 of another". Two ratios that describe the same comparison form a proportion, written A : B = C : D. This ratio calculator does the three jobs that come up most: it solves a proportion for a missing value, reduces a ratio to its simplest whole-number form, and splits a total in a given ratio. Each answer comes with the working.
Solving a proportion by cross-multiplying
In any true proportion the cross products are equal: A × D = B × C. That gives a formula for whichever term is missing. For 3 : 4 = x : 20, cross-multiplying gives 4x = 3 × 20 = 60, so x = 15. The same rule resizes images: a 16 : 9 picture that is 1920 pixels wide must be 1920 × 9 ÷ 16 = 1080 pixels tall, and at 1280 wide it is 720 tall. It scales recipes too: if 2 cups of flour serve 6, then 2 : 6 = x : 15 means 5 cups for 15 people.
Simplifying a ratio
Divide every term by their greatest common factor. 12 : 18 shares a factor of 6, so it simplifies to 2 : 3. 1920 : 1080 shares 120 and becomes 16 : 9. If the terms are decimals, multiply them all by the same power of ten first: 1.5 : 2.5 becomes 15 : 25 and then 3 : 5. Three-part ratios work the same way: 0.25 : 0.5 : 1 becomes 25 : 50 : 100 and then 1 : 2 : 4. The calculator also shows the ratio as 1 : x, which is handy for comparing mixes (a 1 : 2.5 concentrate) and for unit prices.
Splitting an amount in a ratio
To share $100 in the ratio 2 : 3, add the parts (2 + 3 = 5), find what one part is worth ($100 ÷ 5 = $20) and multiply: $40 and $60. Check that the pieces add back up to the total.
Common mistakes
- Mixing up the order. 3 : 4 is not 4 : 3. Keep the quantities in the same order on both sides of a proportion.
- Confusing a ratio with a fraction. A 2 : 3 ratio of boys to girls means boys are 2/5 of the group, not 2/3.
- Mixing units. 30 minutes : 2 hours is 1 : 4, not 30 : 2. Convert to the same unit first.
When the result is misleading
Proportions assume a straight-line relationship. That holds for recipes, maps and image sizes, but not for things like baking times, which do not double when you double a cake, or for paint coverage on textured walls. For percentages of a price, the discount calculator is a better fit; to see a ratio as a fraction, use the decimal to fraction calculator.
Frequently asked questions
How do you solve a ratio with a missing number?
Cross-multiply. In 3 : 4 = x : 20, the cross products must be equal, so 4x = 3 × 20 = 60 and x = 15.
How do you simplify a ratio?
Divide every term by their greatest common factor. 12 : 18 has a GCF of 6, so it simplifies to 2 : 3. If the terms have decimals, multiply them all by 10, 100… first: 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5.
How do you split an amount in a ratio?
Add the parts, divide the total by that sum, and multiply by each part. Splitting $100 in the ratio 2 : 3 gives $100 ÷ 5 = $20 per part, so $40 and $60.
How do I calculate an aspect ratio?
Simplify the width and height. 1920 × 1080 simplifies to 16 : 9. To find the height for a 1280-pixel-wide 16 : 9 image, solve 16 : 9 = 1280 : x, giving x = 720.
What is the difference between a ratio and a fraction?
A ratio compares parts to each other, a fraction compares a part to the whole. A 2 : 3 ratio of boys to girls means boys are 2/5 of the class, not 2/3.
Learn more
Key terms
Glossary →- Greatest Common Factor (GCF)
- The greatest common factor (GCF) of two or more positive integers is the largest whole number that divides each of them with no remainder; it is also called the GCD or HCF.