Math · Ratios and proportions
Proportion calculator.
Fill in three of the four boxes in a/b = c/d, leave one empty and get the missing value with the cross-multiplication shown.
Inputs
Missing value
Fill in three boxes and leave one empty.
How to solve a proportion
A proportion says two ratios or fractions are equal. To find a missing value, multiply across the known corners (the two numbers diagonal from each other) and divide by the third number.
Worked example. A dog's head is drawn 10 long on a body that is 20 long. How long should the head be on a 42 long body? Write x / 42 = 10 / 20. Then x = (42 × 10) ÷ 20 = 420 ÷ 20 = 21.
Percent as a proportion. A percent is a ratio out of 100, so part / whole = percent / 100. For 25% of 160, write part / 160 = 25 / 100, so part = (160 × 25) ÷ 100 = 40. For $12 as a percent of $80, write 12 / 80 = percent / 100, so percent = (12 × 100) ÷ 80 = 15. To try those here, enter 160 in b, 25 in c, 100 in d and leave a empty.
Frequently asked questions
What is a proportion?
A proportion is an equation that says two ratios or fractions are equal, such as 1/3 = 2/6.
How do you solve a proportion with cross multiplication?
Multiply across the two known corners that sit diagonally, then divide by the remaining known number. For x / 42 = 10 / 20 that is (42 × 10) ÷ 20 = 21.
How do I check whether two ratios are in proportion?
Fill in all four boxes. If the two cross products are equal (a × d = b × c) the ratios are in proportion.
Can a proportion solve a percent question?
Yes. Put part / whole = percent / 100 and solve for the unknown. 25% of 160 is 40, and 12 is 15% of 80.
Why does the calculator say there is no single answer?
If the setup would divide by zero (for example a zero in the box you must divide by) there is no single value that works.
Sources
Checked
Runs entirely in your browser. Nothing you type is sent or stored.
For learning
Works for any numbers, including decimals. Results are rounded for display. Check with your teacher's required method when you hand in homework.