Proportion calculator
Fill in three of the four values; the empty one is solved by cross-multiplication.
Missing value
Missing value: 12
- As a fraction
- 12
Step by step
- 3 / 4 = 9 / x
- x = 4 × 9 ÷ 3
- x = 12
How it works
A proportion says two ratios are equal: a/b = c/d. Multiplying both sides by b and d gives a × d = b × c, the cross-multiplication rule.
To find the missing term, multiply the two values on the diagonal you know and divide by the remaining one. This is also called the rule of three.
Formula
a/b = c/d ⇔ a × d = b × c d = b × c ÷ a c = a × d ÷ b
Worked example
3/4 = 9/x: cross-multiplying gives 3 × x = 4 × 9, so x = 36 ÷ 3 = 12.
Questions people ask
What is the rule of three?
It is another name for solving a proportion: if 3 items cost 4, then 9 items cost 4 × 9 ÷ 3 = 12.
Does this work for inverse proportion?
No. In an inverse proportion a × b = c × d instead. If 4 workers take 6 days, 8 workers take 4 × 6 ÷ 8 = 3 days.
Can the values be negative or decimals?
Yes. Any numbers work, as long as the denominators b and d are not zero.