Proportion Calculator
Solve any proportion in the form a/b = c/d. Leave one box empty and this proportion calculator finds the missing value by cross multiplication, and shows the steps.
Reviewed & updated for 2026 by Rakesh Choudhary, PhD · How we calculate
How to solve a proportion
A proportion says two ratios are equal: a/b = c/d. To find an unknown, use cross multiplication, multiply the two diagonal pairs and set them equal: a × d = b × c. Then divide both sides by the number next to your unknown to isolate it.
Example: solve 3/4 = x/20. Cross multiply to get 4 × x = 3 × 20, so 4x = 60 and x = 15. The same three steps, cross multiply, then divide, work no matter which of the four positions is unknown.
In the calculator, type the three numbers you know and leave the fourth box empty. It returns the missing value and shows the cross-multiplication it used.
Worked examples
| Situation | Proportion | Answer |
|---|---|---|
| Recipe: 2 cups flour → 12 cookies, for 30 cookies? | 2/12 = x/30 | 5 cups |
| Map scale: 1 in = 50 mi, how far is 3.5 in? | 1/50 = 3.5/x | 175 mi |
| Price: 4 items cost $9, cost of 10 items? | 4/9 = 10/x | $22.50 |
| Paint: 1 gal covers 350 sq ft, for 1,200 sq ft? | 1/350 = x/1200 | 3.43 gal |
Where proportions show up in real life
Any time two ratios have to stay equal while one quantity changes, you have a proportion. A few everyday cases, each solved by cross-multiplying:
- Scaling a recipe: 2 eggs make 12 cookies, so for 30 cookies, 2 ÷ 12 = x ÷ 30 → x = 5 eggs.
- Reading a map: if 1 inch represents 50 miles, then 3.5 inches represents 1 × 3.5 ÷ 1 × 50 = 175 miles.
- Comparing unit prices: $4.50 for 3 lb scales to 4.50 ÷ 3 = x ÷ 5 → $7.50 for 5 lb.
- Mixing solutions: a 1:8 concentrate in a 64 oz bottle needs 64 ÷ 8 = 8 oz of concentrate to 56 oz water.
- Heights from shadows: a 6 ft person casts a 4 ft shadow when a tree casts 30 ft, so 6 ÷ 4 = h ÷ 30 → the tree is 45 ft tall.
FAQs
How do you solve a proportion?
A proportion is two equal ratios, a/b = c/d. To solve for a missing value, cross multiply: a × d = b × c. Then divide to isolate the unknown. For example, in 3/4 = x/20, cross multiply to get 4x = 60, so x = 15. The calculator above does this automatically when you leave one box blank.
What is cross multiplication?
Cross multiplication turns a proportion a/b = c/d into the equation a × d = b × c by multiplying diagonally. It works because multiplying both sides of the equation by b and by d clears the fractions. It's the fastest way to solve for an unknown in a proportion.
How do I find the missing value in a proportion?
Leave the unknown box empty in the calculator and fill the other three. To do it by hand: cross multiply the two known diagonal values, then divide by the remaining known value. For a/b = c/d, the missing value equals the product of the two opposite-corner numbers divided by the third.
What is a real example of a proportion?
Scaling a recipe: if 2 cups of flour make 12 cookies, how much flour makes 30 cookies? Set up 2/12 = x/30, cross multiply (12x = 60), and x = 5 cups. Proportions also handle map scales, unit conversions, paint coverage, and mixing ratios.
Are a/b = c/d and a:b = c:d the same?
Yes. A ratio written with a colon (a:b) and a fraction (a/b) mean the same thing, and a proportion states that two of them are equal. So 3:4 = 9:12 is identical to 3/4 = 9/12, and both are solved by cross multiplication.
Related calculators
Tip: defaults show 3/4 = x/20. Clear a box to solve a different position.