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How to Calculate Percentages

Updated June 2025 · 5 min read

Percentages show up everywhere — discounts, tips, tax rates, test scores, interest rates. Once you understand the three core calculations, you can handle almost any percentage problem you will encounter in daily life.

The Three Core Percentage Calculations

1. What is X% of Y?

Use this when you want to find a portion of a whole. For example: what is 20% of $85?

Formula:

Result = (Percentage / 100) x Total

Examples:

  • 20% of $85 = (20 / 100) x 85 = $17.00
  • 15% tip on $60 = (15 / 100) x 60 = $9.00
  • 8.5% sales tax on $120 = (8.5 / 100) x 120 = $10.20

2. X is What Percent of Y?

Use this when you want to express one number as a percentage of another. For example: 45 is what percent of 180?

Formula:

Percentage = (Part / Whole) x 100

Examples:

  • 45 out of 180 = (45 / 180) x 100 = 25%
  • 32 correct out of 40 = (32 / 40) x 100 = 80%
  • You spent $340 of a $500 budget = (340 / 500) x 100 = 68%

3. Percentage Change

Use this to calculate how much something increased or decreased relative to the original value. Works for price changes, salary raises, population changes, and more.

Formula:

% Change = ((New Value - Old Value) / Old Value) x 100

Examples:

  • Price went from $50 to $65 → (65 - 50) / 50 x 100 = +30%
  • Salary went from $72k to $68k → (68 - 72) / 72 x 100 = -5.6%
  • Stock went from $120 to $156 → (156 - 120) / 120 x 100 = +30%

A positive result means an increase; negative means a decrease.

Finding the Original Value

Sometimes you know the result and the percentage, but need to find the original amount. For example, if an item costs $68 after a 15% discount, what was the original price?

Formula:

Original = Result / (1 - Discount Rate)

Example:

Sale price $68 after 15% off:
Original = 68 / (1 - 0.15) = 68 / 0.85 = $80.00

For a tax-inclusive price:

Price with 8% tax is $54: Pre-tax = 54 / 1.08 = $50.00

Quick Reference Table

What You WantFormula
X% of Y(X / 100) × Y
X is what % of Y(X / Y) × 100
% change from A to B((B − A) / A) × 100
Original before % increaseResult / (1 + rate)
Original before % discountResult / (1 − rate)

Common Percentage Shortcuts

  • 10% — move the decimal one place left. 10% of 340 = 34.
  • 5% — find 10% then divide by 2. 5% of 340 = 17.
  • 25% — divide by 4. 25% of 200 = 50.
  • 50% — divide by 2. 50% of 90 = 45.
  • 1% — move the decimal two places left. 1% of 4,500 = 45.

Skip the math

Use our Percentage Calculator to instantly solve any of the three percentage types above, plus find original values before discounts or markups.

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