Proportion Calculator
Two ratios that are equal. Fill in any three of the four numbers and we solve for the fourth, showing the cross-multiplication.
- Runs in your browser
- Solves any position
- Shows the working
- Free
Solve the proportion
Leave exactly one box empty, or type x in it.
Show the working
How to solve a proportion
Cross-multiply
In a/b = c/d, the cross products are equal: a × d = b × c. For 2/3 = x/9: 2 × 9 = 3 × x.
Simplify
18 = 3x.
Divide
x = 18 ÷ 3 = 6. Check: 2/3 and 6/9 both equal 0.667.
Where proportions show up
Recipes
A recipe for 4 uses 300 g of flour. For 6 people: 300/4 = x/6, so x = 450 g.
Maps and models
A 1:50,000 map: 3 cm on paper is 3 × 50,000 = 150,000 cm, or 1.5 km.
Percentages
"What is 35% of 80?" is the proportion 35/100 = x/80, so x = 28. Ratio calculator →
Questions people ask
What is a proportion?
A statement that two ratios are equal, written a/b = c/d or a:b = c:d. If three of the numbers are known, the fourth can be found by cross-multiplying.
How do I solve for x in a proportion?
Cross-multiply, then divide. In 2/3 = x/9, cross-multiplying gives 3x = 18, so x = 6.
Can I solve for the bottom number?
Yes. Leave whichever box is unknown empty, top or bottom on either side, and the calculator solves for it.
What if two boxes are empty?
A proportion with two unknowns has infinitely many answers. Fill in three values so only one is missing.
Why does it say undefined?
If the calculation would divide by zero, for example solving for a when d is 0, there is no valid answer.