Proportion Size Calculator
Enter three of the four values in a proportion. The calculator finds the missing one by cross multiplying and shows each step of the working and a check.
- Missing value
- Cross multiplication
- Worked steps
Keep the matching quantities in the same position on both sides.
Two ratios are in proportion when they are equal. If a : b = c : x, then a × x = b × c, so x = b × c ÷ a. If 4 cups of flour make 10 cakes, 6 cups make 6 × 10 ÷ 4 = 15 cakes.
Proportion examples
Everyday uses. Search for an example.
| Problem | a : b | c : x | x |
|---|---|---|---|
| Recipe | 4 cups : 10 cakes | 6 cups : x | 15 |
| Map | 1 cm : 5 km | 7 cm : x | 35 km |
| Fuel | 40 L : 600 km | 25 L : x | 375 km |
| Wages | 8 h : 120 | 30 h : x | 450 |
| Mix | 1 part : 4 parts | 3 parts : x | 12 parts |
| Speed | 2 h : 150 km | 5 h : x | 375 km |
x = b × c ÷ a.
Change c, watch x
a = 4, b = 10. Slide c.
The bars show both sides of the proportion staying in step.
How to solve a proportion
Cross multiply. Step through it.
Write it
a : b = c : x.
If the answer looks wrong, check the values are in the same order on both sides.
Proportion, ratio or percentage
Related ideas. Compare them.
Compares two values.
Two equal ratios.
Out of 100.
A percentage is a proportion out of 100.
Before you solve
Proportion checks. Tick each item.
Tick each item as you go.
Only use a proportion when the two quantities really rise together at a fixed rate.
What you get
Proportion solving. Each tile explains one result.
Answer.
Written out.
Steps.
b ÷ a.
Both sides.
Cross multiplication works because multiplying both sides by the same thing keeps them equal.
Frequently Asked Questions
No question matches that search.
How do I solve a proportion?
Cross multiply, then divide by the remaining number. For a over b equals c over x, x equals b times c divided by a.
What is cross multiplication?
Multiplying the top of each fraction by the bottom of the other, so the two products are equal.
What is a proportion?
A statement that two ratios are equal.
Can a proportion have decimals?
Yes. Any numbers work as long as a is not zero.
How do I check my answer?
Divide b by a and x by c. The two results should match.
When should I not use a proportion?
When the quantities do not change at a steady rate, such as discounts or fixed fees.
Is a percentage a proportion?
Yes. It is a proportion with one side out of one hundred.
Solve it in one step
Set out the two ratios in the same order, cross multiply and divide. The check confirms you have it right.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.