Proportion Calculator

How to use the calculator

• Choose where the unknown is: a/b = c/x, a/b = x/d, a/x = c/d or x/b = c/d.
• Enter the three values you know. a and b form the first ratio, c and d the second.
• Keep the same order on both sides: if the first ratio is pounds over dollars, the second one must be pounds over dollars too.
• Read the result: the value of x, the completed proportion and the common ratio that both sides share.

Cross-multiplication

a / b = c / d   ⇔   a × d = b × c
d = b × c ÷ a     c = a × d ÷ b
b = a × d ÷ c     a = b × c ÷ d

In a true proportion, the cross products are equal. Multiply diagonally across the equals sign, then divide by the number left next to the unknown.

Solving proportion word problems

If 2 pounds cost $4, how much do 6 pounds cost? Set up 2/4 = 6/x and solve: x = 4 × 6 ÷ 2 = 12, so 6 pounds cost $12. This works whenever the two quantities are directly proportional: if one doubles, so does the other. (In some countries this method is known as the rule of three.)

When there's no solution

• The denominators (b and d) can't be 0.
• The number you divide by when solving for x can't be 0, because division by zero is undefined.

Example

If 3 notebooks cost $7.50, how much do 8 notebooks cost? Set up 3/7.5 = 8/x and cross-multiply to get x = 20: 8 notebooks cost $20.

1. 3 × x = 7.5 × 8
2. 3x = 60
3. x = 60 ÷ 3 = 20

Common mistakes

• Using a direct proportion when the relationship is inverse: if 4 workers take 6 days, 8 workers take 3 days, not 12.
• Setting up the ratios in a different order on each side, such as pounds/dollars = dollars/pounds.
• Mixing units, like cups on one side and tablespoons on the other, without converting first.