Proportion Calculator Formula

Understand the math behind the proportion calculator. Each variable explained with a worked example.

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Formulas Used

D (missing value)

d = (b * c) / a

A/B

ratio1 = a / b

C/D

ratio2 = c / ((b * c) / a)

Cross Product (A*D)

cross_product = a * ((b * c) / a)

Variables

VariableDescriptionDefault
aA (numerator 1)3
bB (denominator 1)4
cC (numerator 2)12

How It Works

How to Solve a Proportion

Formula

If A/B = C/D, then D = (B * C) / A

A proportion is an equation stating that two ratios are equal. Cross-multiplication gives A*D = B*C. Solve for any missing value by rearranging. This is fundamental to scaling, unit conversion, and similar triangles.

Worked Example

If 3/4 = 12/x, find x.

a = 3b = 4c = 12
  1. 01Cross-multiply: 3 * x = 4 * 12
  2. 023x = 48
  3. 03x = 48 / 3 = 16
  4. 04Check: 3/4 = 0.75, 12/16 = 0.75. Confirmed.

Frequently Asked Questions

What is a proportion used for?

Proportions are used for scaling recipes, map distances, currency conversion, unit conversion, similar figures in geometry, and any problem where two ratios must be equal.

Is a proportion the same as a ratio?

A ratio compares two values (A:B). A proportion is an equation stating two ratios are equal (A:B = C:D). All proportions involve ratios, but not all ratios are part of a proportion.

Can proportions work with negative numbers?

Mathematically yes, cross-multiplication works with any nonzero values. However, proportions are most commonly used with positive quantities in applied contexts.

Learn More

Guide

How to Calculate Ratios and Proportions

Learn how to set up and solve ratios and proportions with clear examples. Understand the difference between ratios and proportions and apply them in real-world situations like recipes, maps, and scaling.

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