CALCULATE WITH CONFIDENCE

Percentages & Ratios

Rule of Three Calculator

Solve a direct or inverse proportional relationship from three known values.

Percentages & Ratios

Enter known values

Exact rational arithmetic with explicit interpretations
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Use signed finite decimals. List tools accept commas, colons, semicolons, or new lines. Your values stay in this browser.

Exact result

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Enter valid values to see the result.

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Understand the subject

What is the rule of three?

The rule of three solves a missing quantity from a stated direct or inverse proportional relationship.

Use it to scale a known relationship while keeping the relationship type explicit.

The relationship

Write the relationship first

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

If 3 items cost 12, then 5 items cost 12×5÷3 = 20 in a direct relationship.

Interpret with care

Common mistake to avoid

Direct and inverse relationships behave oppositely—choose the model before calculating.

For another view of the same relationship, use the Percentage Calculator.

Quick guide

How to use this calculator

  1. Enter the known values using ordinary signed decimals.
  2. Choose an interpretation or relationship when the calculator provides one.
  3. Read the exact result, decimal preview, and any domain explanation.

Calculation method

Use the stated percentage or ratio relationship

direct: y₂=y₁x₂/x₁; inverse: y₂=x₁y₁/x₂

The calculator keeps finite-decimal inputs as exact reduced fractions and rejects a zero reference or denominator whenever the requested relative quantity would be undefined.

Worked example

Worked interpretation

If 3 items cost 12, then 5 cost 20 under direct proportion.

direct: y₂=y₁x₂/x₁; inverse: y₂=x₁y₁/x₂

Supported inputs

Precision and limits

Input precision

Each value may contain up to 30 digits and 15 decimal places. Scientific notation, fractions typed with a slash, and thousands separators are not accepted.

Exactness

Finite decimals are converted to reduced rational numbers. Detected repeating digits appear in parentheses, while previews that exceed the display limit end with an ellipsis; the exact fraction remains available.

Lists and ratios

List-based tools accept 2–12 entries separated by commas, colons, semicolons, or new lines. Ratio parts must satisfy the positivity rules shown by the calculator.