PureTools

Rule of Three Calculator: Solve Proportions Instantly

PureTools Team· 5 min read
Rule of Three Calculator: Solve Proportions Instantly

What Is the Rule of Three?

The rule of three is a mathematical method to find an unknown value when you know three related values. It's based on proportional relationships: if A relates to B, then C relates to X.

The Formula

// Direct proportion
A --- B
C --- X

X = (B * C) / A

// Example: If 5 apples cost $3, how much do 8 apples cost?
// 5 --- 3
// 8 --- X
// X = (3 * 8) / 5 = $4.80

Direct vs Inverse Proportion

TypeBehaviorExample
DirectBoth values increase togetherMore items = higher cost
InverseOne increases, other decreasesMore workers = less time

Inverse Rule of Three

// If 4 workers finish a job in 6 days,
// how long for 8 workers?
// 4 workers --- 6 days
// 8 workers --- X days
// X = (4 * 6) / 8 = 3 days

Everyday Applications

  • Cooking: A recipe serves 4 but you need to serve 7. Scale all ingredients proportionally
  • Shopping: Price per unit comparison. Which is cheaper: 500g for $5 or 750g for $7?
  • Travel: If your car does 12 km/L, how much fuel for a 300km trip?
  • Finance: If you earn $3,000/month working 40 hours/week, what's your hourly rate?
  • Construction: If 50 tiles cover 8 square meters, how many tiles for 25 square meters?

In Programming

The rule of three appears everywhere in code:

// Mapping a value from one range to another
function mapRange(value, inMin, inMax, outMin, outMax) {
  return outMin + (value - inMin) * (outMax - outMin) / (inMax - inMin);
}

// Progress bar: file download
const percent = (bytesDownloaded * 100) / totalBytes;

Solve any proportion instantly with the PureTools Rule of Three Calculator. Enter three values, get the fourth. Supports both direct and inverse proportions.

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