Proportion Calculator

Quick Answer

Last updated: 10 November 2026 ·How we calculate this: cross multiplication (A × D = B × C)

How This Proportion Calculator Works

A proportion says two ratios are equal, such as 4/6 = 10/15. Enter any three of the four numbers A, B, C and D and leave the missing one empty. The calculator cross multiplies, solves for the unknown and shows each step. If you fill in all four boxes, it checks whether the two ratios really are equal.

How to Use the Proportion Calculator

1. Write your problem as A/B = C/D, keeping the same units in the same places.
2. Enter the three numbers you know.
3. Leave the unknown box empty, or type x.
4. Press Calculate to see the missing value and the steps.
5. Fill in all four boxes instead to check whether two ratios are equal.

Proportion Formulas

• Proportion: A/B = C/D, where B and D are not 0
• Cross products: A × D = B × C
• Solve for A: A = B × C ÷ D
• Solve for B: B = A × D ÷ C
• Solve for C: C = A × D ÷ B
• Solve for D: D = B × C ÷ A

Key Terms

• Ratio: a comparison of two quantities, written as a:b or a/b.
• Proportion: an equation stating that two ratios are equal.
• Cross products: the products A × D and B × C, which are equal in a true proportion.
• Means and extremes: in A:B = C:D, B and C are the means and A and D are the extremes.
• Direct proportion: two quantities that grow or shrink by the same factor.

Worked Example

A car uses 4 gallons of fuel to go 6 laps of a test track. How many laps can it go on 10 gallons at the same rate?

• Set up the proportion: 4/6 = 10/x
• Cross multiply: 4 × x = 6 × 10 = 60
• Divide: x = 60 ÷ 4 = 15 laps
• Check: 4 ÷ 6 = 0.6667 and 10 ÷ 15 = 0.6667, so the ratios match.

Real-Life Examples

• Recipes: a recipe for 4 people uses 300 g of rice. For 10 people, 4/300 = 10/x gives x = 750 g.
• Map scale: 2 cm on a map is 5 km. A 7 cm route is 2/5 = 7/x, so x = 17.5 km.
• Shadows: a 1.8 m person casts a 2.4 m shadow while a tree casts a 16 m shadow. 1.8/2.4 = x/16 gives a tree height of 12 m.
• Unit price: 3 cans cost $4.50. Eight cans cost 3/4.5 = 8/x, so x = $12.00.

Proportion vs Ratio

• A ratio compares two numbers, such as 3:4 or 3/4.
• A proportion is an equation that says two ratios are equal, such as 3/4 = 9/12.
• Use the Ratio Calculator to simplify or scale one ratio, and this calculator to solve for a missing term.

Proportion Examples

Setting Up a Proportion Correctly

The most important step is keeping the units in the same places. If the first ratio is gallons over laps, the second must also be gallons over laps. You can also line up the ratios the other way, as gallons over gallons equals laps over laps: 4/10 = 6/x gives the same answer, x = 15.

Proportions only work when the two quantities change at a constant rate. Doubling the ingredients in a recipe is proportional. The time needed to paint a room with more painters is not, because more people means less time, which is an inverse relationship.

Where Proportions Are Used

Proportions are one of the most useful tools in everyday maths. Cooks scale recipes, nurses work out doses from a concentration, map readers turn centimetres into kilometres with a scale, and shoppers compare unit prices. In geometry, similar triangles have proportional sides, which lets surveyors find the height of a tree from its shadow.

Common Mistakes to Avoid

• Mixing up the units. If the first ratio is cups over people, the second must be cups over people too.
• Multiplying straight across. Cross multiply diagonally: A with D, and B with C.
• Using a proportion for an inverse relationship. More workers means less time, so a simple proportion gives the wrong answer.
• Putting zero in a denominator. B and D can never be 0.
• Rounding too early. Keep full decimals until the final answer.

Frequently Asked Questions

References & Sources