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Proportion Calculator

Solve a proportion for the missing value — a/b = c/d — with the cross-multiplication worked through, or check whether two ratios are equal.

Enter three of the four values to solve the proportion.

Exact calculation. Given your inputs, this is the answer — no estimation involved.

How this calculator works

A proportion says two ratios are equal: 3/4 = x/10. To solve it, cross-multiply. Multiply each top by the opposite bottom, set them equal, and divide to leave the unknown on its own: 3 × 10 = 4 × x, so x = 30 ÷ 4 = 7.5.

Leave any one of the four values blank and the calculator solves for it. Fill in all four and it checks whether they form a proportion, by testing whether the cross products are equal.

The arithmetic is exact. Values are read as the fractions they are typed as, so an answer like 10/3 is given exactly as well as as a decimal, and marked when the decimal repeats forever.

Proportions are how most everyday scaling works: doubling a recipe, converting between units, working out a map distance, or estimating how much paint covers a wall.

The formula

Exactly what happens to your numbers, step by step.

A proportion

a/b = c/d   exactly when   a × d = b × c

Solving for each value

a = b × c ÷ d      b = a × d ÷ c
c = a × d ÷ b      d = b × c ÷ a

A worked example

A recipe uses 3 cups of flour for 12 cookies. How much flour for 30 cookies?

What you enter

a (flour): 3
b (cookies): 12
c (flour): blank
d (cookies): 30

Step by step

Set it up: 3/12 = x/30
Cross-multiply: 3 × 30 = 12 × x
Solve: x = 90 ÷ 12 = 15/2

7.5 cups of flour

Keep the units in the same places on both sides: flour over cookies on the left means flour over cookies on the right. Mixing them up gives the wrong answer with no error.

Proportion questions, worked out

Cross-multiplication, applied to homework and everyday scaling.

1.Solve for x: 3/4 = x/10
1. Write it out: 3/4 = x/10
2. Cross-multiply: 3 × 10 = 4 × x
3. So x = 3 × 10 ÷ 4 = 30 ÷ 4 = 15/2
4. As a decimal: 7.5
x = 7.5
2.Solve for x: 2/3 = 8/x
1. Write it out: 2/3 = 8/x
2. Cross-multiply: 2 × x = 3 × 8
3. So x = 3 × 8 ÷ 2 = 24 ÷ 2 = 12
x = 12
3.A recipe uses 3 cups of flour for 12 cookies. How much flour for 30 cookies?
1. Set it up as flour over cookies: 3/12 = x/30.
2. Cross-multiply: 3 × 30 = 12 × x
3. So x = 3 × 30 ÷ 12 = 90 ÷ 12 = 15/2
4. As a decimal: 7.5
7.5 cups of flour.
4.A gallon of paint covers 350 square feet. How many gallons for 1,200 square feet?
1. Gallons over square feet: 1/350 = x/1,200.
2. Cross-multiply: 1 × 1200 = 350 × x
3. So x = 1 × 1200 ÷ 350 = 1200 ÷ 350 = 24/7
4. As a decimal: 3.428571… (repeating)
About 3.4286 gallons, so buy 4.
5.Are 2/4 and 3/6 proportional?
1. Cross-multiply: a × d = 2 × 6 = 12
2. b × c = 4 × 3 = 12
3. The products are equal, so the ratios are equal.
Yes. Both ratios equal 0.5.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

The two ratios compare the same things in the same order.
The relationship is directly proportional: double one, and the other doubles.

What this cannot tell you

Not everything scales in proportion. Baking times, for example, do not double when a recipe does.
Inverse relationships, where one value goes down as the other goes up (more workers, less time), are not proportions of this form.
A zero underneath either ratio is undefined, and some zeros leave the unknown free to be anything. Both are reported rather than given an answer.

Questions people ask

How do you solve a proportion?

Cross-multiply and divide. For 2/3 = 8/x, multiply across: 2 × x = 3 × 8, so 2x = 24 and x = 12. Whichever value is missing, multiply the two numbers diagonal from each other and divide by the one opposite the unknown.

What is the difference between a ratio and a proportion?

A ratio compares two quantities, such as 3 cups to 12 cookies. A proportion is an equation saying two ratios are equal, such as 3/12 = 7.5/30. You solve a proportion; a ratio on its own is just a comparison.

How do I check if two ratios are proportional?

Cross-multiply and compare. 2/4 and 3/6 give 2 × 6 = 12 and 4 × 3 = 12, so they are proportional; both equal 0.5. If the two products differ, the ratios are not equal.

Why does my proportion have no answer?

Usually a zero. A ratio with 0 underneath is undefined. And if the value the unknown has to be divided by is 0, then either no value works or every value does. The calculator says which.

Sources and review

This calculator uses standard arithmetic with no external rules or published rates, so there is nothing to cite beyond the formulas shown above.

Methodology version 1.0.0 · Last reviewed October 5, 2026

Cite this calculator

For coursework, a resource list or your own site. How every calculator is built and checked is set out on the methodology page.

Citation

Chalk Calculator. (2026, October 5). Proportion Calculator (Methodology version 1.0.0). https://chalkcalculator.com/proportion-calculator/

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