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Calculator Answers

Proportion Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A proportion calculator is an algebraic tool that solves for an unknown value in a proportion equation of the form a/b equals c/d. When any three of the four variables are provided, the calculator uses cross-multiplication to solve for the missing variable. It can also verify whether a given pair of ratios form a true proportion by cross-multiplying and comparing the products. Students, chefs, and designers use this tool to scale recipes, adjust design dimensions, and solve ratio-based word problems.

Enter three known values in A : B = C : D and leave one slot blank or type x. The calculator solves the proportion by cross multiplication and shows the worked step.

Quick Answer

Solve for unknown values in proportion equations. Enter three known values in the ratio fields to calculate the missing term using cross-multiplication.

A : B = C : D (use x for the missing value)

e.g. 3

e.g. 4

e.g. x

e.g. 20

Leave exactly one field blank or type x. The calculator cross-multiplies to solve A ÷ B = C ÷ D.

Proportion

Missing value (C)

15

Completed: 3 : 4 = 15 : 20

A3
B4
C15
D20
Cross-multiplicationA · D = B · C → 3 × 20 = 4 × 15
FormulaC = A · D ÷ B = 3 × 20 ÷ 4
A · D (check)60

A proportion A ÷ B = C ÷ D is solved by cross multiplication: A × D = B × C. Rearrange to isolate the missing value.

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Examples

3 : 4 = x : 20

x = 15

8 : x = 2 : 5

x = 20

12 : 18 = 2 : 3

True (cross product 36 = 36)

How it works

A proportion is two equal ratios. Cross multiplication turns it into a simple linear equation that you can rearrange to isolate the missing value. The calculator picks the appropriate rearrangement automatically based on which slot is blank.

Definition · A ÷ B = C ÷ D

Cross multiply · A × D = B × C

Rearrange: A = B·C÷D · B = A·D÷C · C = A·D÷B · D = B·C÷A

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Ratio CalculatorSimplify a ratio A : B by dividing both sides by their greatest common factor. Optional cross-multiplication check against a second ratio C : D.

Frequently asked questions

A proportion is an equation that says two ratios are equal: A : B = C : D, equivalently A ÷ B = C ÷ D. When three of the four values are known, the fourth is fixed and can be solved with cross multiplication.

Multiply both sides of A ÷ B = C ÷ D by B and by D to clear the denominators. The result is A × D = B × C. Whichever of A, B, C, or D is missing, isolate it on one side to get the missing value. The calculator runs this rearrangement automatically.

Leave the field blank or type x (or ?). Exactly one field should be left blank. If you leave more than one blank, the proportion has too few knowns to solve; if you fill in all four, the calculator just checks whether the proportion is true.

The proportion is undefined when the denominator on the side opposite to the missing value is 0. The calculator detects this and flags it. To avoid the issue, double-check the three known values for typos.

A ratio is one comparison: A : B. A proportion is an equation between two ratios: A : B = C : D. The ratio calculator simplifies a single ratio; the proportion calculator solves for an unknown value in an equality between two ratios.

Anywhere you scale a known relationship. Recipe scaling (if 2 cups feed 4 people, how many cups feed 6?), map scales, unit conversions, percent problems (the proportion 'is over of equals percent over 100'), and similar-triangle geometry. Any time two quantities change together at a constant rate, a proportion captures that rate.