Rule of Three Calculator

Solve proportional relationships using the rule of three

Simple Rule of Three

If A is to B as C is to X, then X = (B × C) ÷ A

A : B = C : X
is to
as
is to
{{ simple.result || 'X' }}

Calculation Steps

Formula:
X = (B × C) ÷ A
Substitution:
X = ({{ simple.b }} × {{ simple.c }}) ÷ {{ simple.a }}
Calculation:
X = {{ simple.b * simple.c }} ÷ {{ simple.a }}
Result:
X = {{ simple.result }}

Common Examples

Compound Rule of Three

For problems involving multiple variables: If A₁ and B₁ produce C₁, then A₂ and B₂ produce X

Known Relationship

Find Unknown

{{ compound.result || 'X' }}

Relationship Types

Calculation Process

Formula:
{{ getCompoundFormula() }}
Substitution:
{{ getCompoundSubstitution() }}
Result:
X = {{ compound.result }}

Compound Examples

Inverse Rule of Three

When quantities are inversely proportional: as one increases, the other decreases

If A₁ × C₁ = A₂ × X, then X = (A₁ × C₁) ÷ A₂
with
equals
with
{{ inverse.result || 'X' }}

Inverse Calculation

Principle:
A₁ × C₁ = A₂ × X
Substitution:
{{ inverse.a1 }} × {{ inverse.c1 }} = {{ inverse.a2 }} × X
Solve for X:
X = ({{ inverse.a1 }} × {{ inverse.c1 }}) ÷ {{ inverse.a2 }}
Result:
X = {{ inverse.result }}

Inverse Examples

About the Rule of Three

What is it?

The rule of three is a mathematical method for solving proportion problems. It's used when three quantities are known and you need to find a fourth.

When to Use

  • Unit conversions
  • Recipe scaling
  • Currency exchange
  • Rate calculations
  • Time and work problems

Types of Relationships

  • Direct: Both increase or decrease together
  • Inverse: One increases as the other decreases
  • Compound: Multiple variables affecting the result

Tips

  • Identify the type of relationship first
  • Keep units consistent
  • Check if your answer makes logical sense
  • Use cross-multiplication for verification