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Proportion Calculator

Solve a missing value in a proportion A/B = C/D using cross multiplication.

  • proportion
  • cross multiplication
  • solve proportion
  • equivalent ratios
  • missing value

Choose which value to solve in A / B = C / D.

First numerator in A / B = C / D.

First denominator in A / B = C / D.

Second numerator in A / B = C / D.

Second denominator in A / B = C / D. Leave this blank when solving for D.

Status: initial

Results

Awaiting calculation

Explore your result

Both sides of the proportion

Explore the proportion calculator result visually while keeping this page's detailed guidance and examples.

Both sides of the proportion
Missing value12
Left ratio0.75
Right ratio0.75
Scaling factor3×

Use this result well

  1. 1Verify the calculator inputs.
  2. 2Compare the key result relationships.
  3. 3Review the page guidance before acting.

Equivalent ratios have equal cross-products.

Calculator guide

Introduction

The Proportion Calculator solves one missing value in A / B = C / D using cross multiplication, then checks equivalent ratios, cross products, scaling factor, decimal ratio, percent form, and common real-world interpretations.

What is a proportion?

A proportion states that two ratios or fractions are equal. Proportions are used for recipe scaling, maps, model sizes, unit rates, percentages, and similar-figure problems.

Cross multiplication method

For A / B = C / D, cross multiply to get A x D = B x C. Rearrange that equation to solve for whichever value is missing, then substitute the result back into both ratios to check the answer.

Variable explanations

Understand what each input and result means before calculating.

A

First numerator in the proportion.

B

First denominator in the proportion.

C

Second numerator in the proportion.

D

Second denominator in the proportion.

Cross products

The products A x D and B x C.

Scaling factor

How one corresponding value scales to the other.

Equivalent ratios

Ratios that simplify to the same relationship.

Reviewed by the Calculator.org.in Editorial Team

Formula behavior, validation cases, explanatory examples, and cited sources are checked before publication. This review supports educational accuracy and is not a substitute for qualified professional advice.

Last reviewed: 2026-08-03

Review process

Formula guide

See the calculation logic, variable definitions, and practical meaning.

Solve for A

A = (B x C) / D

  • B, C, and D are known.
  • D cannot be zero.

Use this when the first numerator is missing.

Solve for B

B = (A x D) / C

  • A, C, and D are known.
  • C cannot be zero.

Use this when the first denominator is missing.

Solve for C

C = (A x D) / B

  • A, B, and D are known.
  • B cannot be zero.

Use this when the second numerator is missing.

Solve for D

D = (B x C) / A

  • A, B, and C are known.
  • A cannot be zero.

Use this when the second denominator is missing.

Cross product check

A x D = B x C

  • Both products should match after solving.

Use this to verify that the completed proportion is true.

Scaling factor

Scale factor = C / A

  • A and C should be corresponding values.

This shows how much the first numerator scales to the second numerator.

Ratio as percent

Percent = (A / B) x 100

  • The same percent should appear on both sides of a true proportion.

Use this when a proportion represents rates, shares, or percent problems.

Worked examples

Follow realistic inputs through the calculation step by step.

1

Worked example

Solve for D

  1. 13 / 5 = 9 / D
  2. 2D = (5 x 9) / 3
  3. 3D = 15.
2

Worked example

Solve for A

  1. 1A / 8 = 6 / 12
  2. 2A = (8 x 6) / 12
  3. 3A = 4.
3

Worked example

Scale a recipe

  1. 12 cups for 3 servings and x cups for 9 servings.
  2. 22 / 3 = x / 9.
  3. 3x = 6 cups.
4

Worked example

Map or model scale

  1. 1If 3.5 inches on a model represents 100 inches in real life, set 3.5 / 100 = model / actual.
  2. 2Enter the three known values in matching positions.
  3. 3The missing value keeps the scale proportional.

Common mistakes

Avoid these common input and interpretation errors.

Using zero as a denominator

B and D cannot be zero in A / B = C / D.

Cross multiplying the wrong pairs

Multiply A by D and B by C.

Forgetting to divide after cross multiplication

After multiplying the known cross pair, divide by the remaining known value.

Mixing units

Ratios should compare compatible units or clearly converted values.

Putting values in mismatched positions

Corresponding quantities must occupy matching numerator or denominator positions.

Using direct proportion for inverse relationships

This calculator solves direct proportions. Inverse proportions need a different setup.

Treating rounded decimals as exact

If your inputs are rounded, the solved value is also based on rounded information.

Frequently asked questions

Quick answers to the questions users ask most often.

What does this Proportion Calculator do?
It solves a missing value in A / B = C / D using cross multiplication and checks the completed ratios.
What is a proportion?
A proportion is an equation showing that two ratios or fractions are equal.
What is cross multiplication?
Cross multiplication compares A x D with B x C in the proportion A / B = C / D.
How do I solve for D?
Use D = (B x C) / A when A, B, and C are known.
How do I solve for A?
Use A = (B x C) / D when B, C, and D are known.
How do I solve for B?
Use B = (A x D) / C when A, C, and D are known.
How do I solve for C?
Use C = (A x D) / B when A, B, and D are known.
Can denominators be zero?
No. B and D cannot be zero in a valid proportion.
Can I use decimals?
Yes. Decimal values are supported.
Can I use negative numbers?
Yes, if the proportion makes sense for your problem.
What does A / B = C / D mean?
It means the ratio A to B equals the ratio C to D.
What is the scaling factor?
It shows how much one corresponding value changes to the other, such as C divided by A.
Why show the percent form?
Percent form helps when the proportion represents a rate, part-to-whole relationship, or percentage problem.
Can this scale recipes?
Yes. Proportions are useful for scaling recipe amounts when the quantities correspond.
Can this solve map scale problems?
Yes, if you enter corresponding known values in the same proportion order.
Can this solve model scale problems?
Yes. Keep model values on one side of the ratio and real values in the matching positions.
Can this solve inverse proportions?
No. This calculator solves direct proportions in fraction form.
How do I check the answer?
Substitute the result back into A / B = C / D and compare both ratios or cross products.
Is this the same as a ratio calculator?
It is related, but this page focuses on solving one missing value in a proportion.
Can this compare two ratios?
It compares the completed left and right ratios after solving the missing value.
Can this solve complex algebraic proportions?
No. It solves one numeric missing value among A, B, C, and D.

References

Sources used to support the calculator guidance.

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Version history

A transparent record of calculator content updates.

Updated 2026-08-03
  • 1.1.0 · 2026-08-03

    Added scaling factor, equivalent ratio, percent form, ratio comparison, application examples, table steps, and expanded cross-multiplication guidance.

  • 1.0.0 · 2026-07-06

    Initial proportion calculator release.