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Rule of Three Calculator

Learn, practice, and solve proportionality problems step by step

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How it works: Enter 3 known values and leave the unknown field empty. Choose if the relationship is direct or inverse, then click Calculate to see the step-by-step solution.

Leave one field empty — that’s the unknown (x) the calculator will find.

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Compound Rule of Three: Used when 3 or more quantities are involved. Set the unknown (x) in the first column, then add the other quantities. For each, choose if it’s directly or inversely proportional to the unknown.
Quantity Name Value 1 Value 2 Relation to X
← Solving for x
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Percentages with Rule of Three: Every percentage problem is a simple direct rule of three in disguise. Enter the total value and the percentage to find the corresponding amount — or vice versa.
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Practice Mode: Solve randomly generated problems to sharpen your skills. Choose a difficulty level, solve the problem, and check your answer. A step-by-step solution is always available.
✅ Correct: 0 ❌ Wrong: 0 🏆 Streak: 0

📘 What Is the Rule of Three?

The rule of three is a mathematical method that allows you to calculate an unknown value from three known values that share a proportional relationship. With three known values, you determine the fourth.

General Formula:
a / b = c / x → x = (b × c) / a

⚖️ Direct vs. Inverse Proportionality

↑↑ Direct

Both quantities vary in the same direction. If one doubles, the other also doubles.

Example: More liters of milk → Higher price

↑↓ Inverse

Quantities vary in opposite directions. If one doubles, the other is halved.

Example: More workers → Fewer days to finish

Quick Test: Ask yourself — “If I double Quantity A, what happens to Quantity B?” If B also doubles → Direct. If B is halved → Inverse.

📊 Simple Rule of Three — Steps

  1. Identify the two quantities and organize them in a table.
  2. Determine if the relationship is direct or inverse.
  3. Set up the proportion. If inverse, invert one of the ratios.
  4. Cross-multiply and isolate x.
  5. Check the answer — does it make sense in context?

🔗 Compound Rule of Three — Steps

  1. Place x in its own column as the reference.
  2. List all other quantities in the table.
  3. Analyze each quantity: is it directly or inversely proportional to x?
  4. If direct, keep the ratio as-is. If inverse, invert it.
  5. Multiply all ratios on one side and set equal to x’s ratio.
  6. Solve for x.

⚠️ Common Mistakes to Avoid

1 Confusing direct and inverse

Always ask: “If one goes up, does the other go up or down?”

2 Forgetting to invert

In inverse proportion, you must invert one ratio before cross-multiplying.

3 Mixing units

Convert everything to the same unit before setting up the table.

4 Wrong cross-multiplication

Numerator of one × Denominator of the other. Practice until automatic.

📐 Rule of Three with Fractions

The method is identical — treat fractions like any number. The key tip:

Dividing by a fraction = Multiplying by its reciprocal
a ÷ (3/4) = a × (4/3)

💯 Percentages as Rule of Three

Every percentage problem is a simple direct rule of three:

100% → Total Value
x% → Unknown Value

Unknown = (x × Total) / 100

📚 Rule of Three Calculator — Interactive Educational Tool