Proportion Calculator

Proportion calculator at a glance#

A proportion calculator solves an equation of two equal ratios, a/b = c/d, for the one missing term. It works by cross-multiplying: the two ratios are equal only when a times d equals b times c. Rearrange that to isolate the unknown and you have your answer.

The cross-multiply rule is a x d = b x c. To solve a/b = x/d for x, multiply across and divide: x = (a x d) / b. For the form a/b = c/x, the same rule gives x = (b x c) / a.

Worked example: solve 3/4 = x/20. Cross-multiply to get 3 x 20 = 4 x x, which is 60 = 4x. Divide both sides by 4 and x = 15. You can check it: 3/4 and 15/20 both reduce to 3/4, so the ratios match.

Where this shows up in real life: scaling a recipe and reading a map. If 2 cups of flour serves 4 people, solve 2/4 = x/8 to serve 8, and x = 4 cups. On a map drawn at 1:50,000, a ratio of map distance to real distance, you solve the same proportion to turn centimetres on paper into kilometres on the ground.

Enter your three known values in the calculator above for the exact missing term. The math is exact for any numbers, though results that do not divide evenly will round to the decimals you ask for.

Setting up the proportion#

The result depends on keeping the two ratios in the same order. If the left ratio is parts to whole, the right ratio must be parts to whole too. Put the matching quantities in matching positions, then cross-multiply. Mixing the order (parts to whole on one side, whole to parts on the other) is the most common mistake and gives the wrong answer.

Worked example#

A car uses 5 litres of fuel per 100 km. How much for 250 km? Keep litres over kilometres on both sides: 5/100 = x/250. Cross-multiply to get 5 times 250 = 100x, so 1250 = 100x and x = 12.5 litres. The check: 5/100 and 12.5/250 both reduce to 1/20.

Direct vs inverse proportion#

This calculator solves direct proportions, where two quantities rise and fall together so their ratio stays constant. Inverse proportion is different: as one goes up the other goes down, and their product stays constant. If 4 workers finish a job in 6 hours, 8 workers finish in 3 hours, because 4 times 6 = 8 times 3 = 24 worker-hours. For inverse problems, set the two products equal rather than the two ratios.

How to check a proportion is true#

Two ratios form a true proportion when their cross-products match. For a/b = c/d, check that a times d equals b times c. For 6/9 and 8/12, cross-multiply: 6 times 12 = 72 and 9 times 8 = 72, so they are equal and the proportion holds. If the cross-products differ, the ratios are not equal.

Frequently asked questions#

What is a proportion?#

A proportion is a statement that two ratios are equal, written a/b = c/d. The calculator finds the one missing term when the other three are known, by cross-multiplying.

How do you solve a proportion?#

Cross-multiply and divide. To solve 3/4 = x/20, multiply across to get 3 times 20 = 4x, so 60 = 4x and x = 15.

What does it mean for two quantities to be inversely proportional?#

As one increases, the other decreases so that their product stays constant. If speed and travel time are inversely proportional, doubling the speed halves the time for the same distance.

How do equivalent ratios relate to proportions?#

Equivalent ratios are two ratios that reduce to the same value, like 2:4 and 1:2. Any two equivalent ratios form a true proportion, since their cross-products are equal.

Where are proportions used?#

Scaling recipes, resizing images to keep their aspect ratio, reading map scales, converting units, and adjusting medication doses by body weight. Any task that holds a ratio steady while one quantity changes is a proportion.