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Proportion Calculator

Solve a proportion A/B = C/D for whichever value is missing, using cross-multiplication with every step shown.

Level: Grades 6–7

  • Common Core standard 6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • Common Core standard 7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Printable worksheet

Proportion Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve A/B = C/D for

Result

Missing value D

20

D = 20, so 3/4 = 15/20.

Completed proportion
3/4 = 15/20
Value of each ratio
0.75
Cross product (A × D = B × C)
60

See the step-by-step solution ↓

Step-by-step solution

  1. Write the proportion with the unknown D as x

    34=15x

  2. Cross-multiply: the product of one diagonal equals the product of the other (A × D = B × C)

    3×x=4×15

  3. Multiply out the side with two known numbers

    3x=4×15=60

  4. Divide both sides by 3 so x is left on its own

    x=603=20

  5. Check the answer: both ratios should now have the same value

    34=0.75,1520=0.75

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find the missing number when two ratios should match, like scaling a recipe or a price. A proportion says that two ratios are equal: A/B = C/D. If 3 notebooks cost $4, then 15 notebooks cost $20, because 3/4 = 15/20. Whenever you know three of the four numbers, the fourth is fixed. A quick trick called cross-multiplication finds it.

This calculator solves for any of the four positions, not just the last one. It writes the unknown as x and cross-multiplies. Then it divides to get x on its own and checks that both ratios come out equal. It also tells you when a proportion has no answer. For example, that happens when the missing value would have to be a 0 on the bottom of a fraction.

Where it's used

Why this math matters outside the classroom:

  • Scaling recipes. A recipe using 3 cups of flour for 24 cookies needs x cups for 40, and 3/24 = x/40 gives x = 5.
  • Map scales. On a map where 1 in stands for 25 miles, 3.5 in solves 1/25 = 3.5/x for x = 87.5 miles.
  • Fuel needs. A car that uses 4 gallons per 120 miles needs 4/120 = x/300, or 10 gallons, for a 300-mile trip.
  • Scale models. A 1:24 model of a 4.8 m car is 4.8 ÷ 24 = 0.2 m, or 20 cm, long.
  • Mixing paint. If 2 parts blue to 5 parts white makes a shade, 3 liters of blue needs 2/5 = 3/x, or 7.5 liters of white.

Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.RP.A.3, 7.RP.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose which value is missing: A, B, C or D in A/B = C/D.
  2. Enter the three values you know. The field for the missing value is hidden.
  3. Read the missing value and the completed proportion.
  4. Follow the steps to see the cross-multiplication worked through.

What the inputs mean

Solve A/B = C/D for
The position of the missing number. A and C are the numerators (top numbers); B and D are the denominators (bottom numbers).
A (first numerator)
The first ratio's top number. In a word problem, keep the same kind of quantity in A and C.
B (first denominator)
The first ratio's bottom number. It can't be zero.
C (second numerator)
The second ratio's top number, measured in the same units as A.
D (second denominator)
The second ratio's bottom number, in the same units as B. It can't be zero.

Formula and method

A/B = C/D  ⇔  A × D = B × C
A = B × C / D
B = A × D / C
C = A × D / B
D = B × C / A

A and B are the top and bottom of the first fraction, and C and D are the top and bottom of the second. Multiplying both sides of A/B = C/D by B × D clears both bottom numbers and leaves A × D = B × C. This is cross-multiplication: multiply along each diagonal, and the two answers are equal.

With one value unknown, one diagonal holds two known numbers and the other holds the unknown and one known number. Multiply out the known diagonal. Then divide by the known number that shares a diagonal with the unknown.

The final check divides each side to confirm that both ratios now have the same value.

Worked example

3 notebooks cost $4. At the same rate, how many dollars do 15 notebooks cost?

  1. Set up the proportion with notebooks on top and dollars below: 3/4 = 15/x.
  2. Cross-multiply: 3 × x = 4 × 15.
  3. Multiply out the known side: 3x = 60.
  4. Divide by 3: x = 60/3 = 20.
  5. Check: 3/4 = 0.75 and 15/20 = 0.75.

Result: D = 20, so 15 notebooks cost $20 and the completed proportion is 3/4 = 15/20.

Understanding the result

The missing value keeps the two ratios equal. In a word problem, it's in the same units as the other number in its row or column of the setup.

The 'value of each ratio' is A ÷ B, the shared rate; in the example, 0.75 notebooks per dollar.

The cross product is the common value of A × D and B × C once the proportion is complete.

Assumptions and limitations

  • The relationship is directly proportional: doubling one quantity doubles the other. Inverse relationships, such as more workers taking less time, need a different setup.
  • Corresponding quantities are entered in matching positions and units.
  • Only one unknown can be solved at a time.
  • If the known value you'd divide by is 0, cross-multiplying gives either no solution or infinitely many. The calculator explains which, instead of returning a number.
  • Answers are computed with ordinary computer decimals (floating point), so tiny rounding can occur. They're shown to your chosen precision.

Frequently asked questions

How is this different from the ratio calculator?

The ratio calculator works with ratios written A : B and solves for the fourth term only. This calculator treats the proportion as two fractions and solves for any one of the four positions, showing the cross-multiplication.

Does it matter which quantity goes on top?

Not as long as you're consistent. 3/4 = 15/x and 4/3 = x/15 both give x = 20. Mixing them, such as 3/4 = x/15, sets up a different relationship and a wrong answer.

Why can't B or D be zero?

They are denominators, and division by zero is undefined. A ratio like 3/0 has no value, so it can't be equal to another ratio.

Can I use cross-multiplication to check whether two fractions are equal?

Yes. If A × D equals B × C, the fractions are equal; otherwise they are not. For example, 2/3 and 4/6 are equal because 2 × 6 = 3 × 4 = 12.

How this calculator is checked

Method: Cross-multiplication of an equation of two ratios, a standard result of algebra. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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