A ratio compares quantities by how many times one contains another: 3 cups of flour to 4 cups of milk, 2 parts sand to 1 part cement, 1 inch on a map to 5 miles on the ground. Most practical ratio questions are one of three kinds — find a missing value so two ratios match, resize a ratio, or split a total in a fixed ratio — and this calculator handles all three with exact arithmetic.
How to use the ratio calculator
- Choose a task from the menu.
- Solve a proportion: pick which term is unknown (A, B, C or D) and enter the other three. The proportion reads A : B = C : D.
- Scale a ratio: type the ratio with colons (for example
2:3:5), then choose whether to multiply by a factor or set the first or last term to a target value. - Split an amount: type the ratio and the total to divide.
- The tape shows the answer; the steps show the cross-multiplication or share arithmetic.
Ratio and proportion formulas
Two ratios form a proportion when their cross products match:
So any missing term follows from the other three, for example D = B × C ÷ A.
Scaling multiplies every term by the same factor k, which never changes the ratio itself:
Sharing an amount T in the ratio a : b : c gives each part its fraction of the total:
Worked examples
Mixing paint
A color recipe calls for 3 parts blue to 4 parts white. You have 7.5 liters of blue. How much white do you need?
Set up: 3 : 4 = 7.5 : D
Cross-multiply: 3 × D = 4 × 7.5 = 30
Solve: D = 30 ÷ 3 = 10 liters of white
Sharing a prize
Three volunteers split a $500 prize in the ratio 2 : 3 : 5 according to hours worked.
Total shares: 2 + 3 + 5 = 10
One share: $500 ÷ 10 = $50
Parts: 2 × 50 = $100, 3 × 50 = $150, 5 × 50 = $250
Setting up a proportion correctly
The most common error is mixing up positions. Keep matching quantities in matching places: if A is “blue paint” then C must also be “blue paint”, and B and D both “white paint”. Writing it as a table helps:
| Blue | White | |
|---|---|---|
| Recipe | 3 | 4 |
| Your batch | 7.5 | ? |
Read across for the ratio and down for the scale factor. Here the batch is 7.5 ÷ 3 = 2.5 times the recipe, so the white paint is 4 × 2.5 = 10. The calculator lists this scale factor so you can check the reasoning.
Where ratio problems appear
- Cooking: scale a recipe that serves 4 to serve 10 (a factor of 2.5).
- Maps and models: at 1 : 24,000, 3 cm on a topographic map is 72,000 cm, or 720 m, on the ground.
- Construction: concrete mixed 1 : 2 : 3 (cement : sand : gravel) for a 0.6 m³ pour needs 0.1 m³ of cement, 0.2 m³ of sand and 0.3 m³ of gravel.
- Finance: splitting profit among partners by investment, or rent among roommates by room size.
- Screens and photos: an image with a 16 : 9 aspect ratio that is 1,280 pixels wide is 720 pixels tall.
Related tools
To reduce a ratio such as 2.4 : 3.6 to lowest terms, use the ratio simplifier. To express a ratio as a fraction of the whole, try the ratio to fraction calculator. For “per one” comparisons like price per ounce or miles per hour, the unit rate calculator is the better fit.
Frequently asked questions
How do I find the missing value in a ratio A:B = C:D?
Cross-multiply: in a true proportion, A × D = B × C. Rearrange for the unknown. For 3:4 = 7.5:D, D = 4 × 7.5 ÷ 3 = 10.
How do I divide an amount in a ratio?
Add the ratio terms to get the number of equal shares, divide the amount by that number to find one share, then multiply by each term. $500 in the ratio 2:3:5 gives 10 shares of $50, so the parts are $100, $150 and $250.
How do I scale a ratio so one term equals a specific number?
Divide the target by the current term to get a scale factor, then multiply every term by it. To make the first term of 4:7 equal to 10, the factor is 2.5, giving 10:17.5.
Does the order of a ratio matter?
Yes. 3:4 compares the first quantity to the second; 4:3 is the reverse. In a proportion, A and C must describe the same kind of quantity, and so must B and D.
Can a proportion have decimal or fraction answers?
Yes. Real measurements rarely come out whole. The calculator gives exact results, marks repeating decimals with a bar and shows the fraction, so 3:7 = x:10 gives x = 4.285714… = 30/7.