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Percentage Calculator

Free online percentage calculator. Calculate percentage of a number, percentage change, percentage difference, and what percent one number is of another. Instant results.

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What Is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin per centum, meaning "by the hundred." The symbol % is used to denote percentages.

Percentages are one of the most practically useful mathematical concepts in everyday life — from calculating discounts at a store, to understanding your tax bill, to reading a nutrition label, to evaluating investment returns. Mastering percentages is essential for financial literacy.

For related financial calculations, explore our Salary Calculator or Loan Calculator.

The 4 Core Percentage Calculations

1. What is P% of X?

Formula: Result = (P ÷ 100) × X

Example: What is 30% of $250?

  • (30 ÷ 100) × 250 = 0.30 × 250 = $75

Real-world uses: Calculating discounts, tips, commissions, tax amounts.

2. X is What Percent of Y?

Formula: Percentage = (X ÷ Y) × 100

Example: 45 is what percent of 180?

  • (45 ÷ 180) × 100 = 0.25 × 100 = 25%

Real-world uses: Finding your score on a test, measuring progress toward a goal, comparing two quantities.

3. Percentage Change (Increase or Decrease)

Formula: % Change = ((New − Old) ÷ Old) × 100

  • If the result is positive, it is a percentage increase.
  • If the result is negative, it is a percentage decrease.

Example (Increase): A stock went from $40 to $52. What is the percentage gain?

  • ((52 − 40) ÷ 40) × 100 = (12 ÷ 40) × 100 = 30% gain

Example (Decrease): Your electric bill dropped from $120 to $96. What is the savings?

  • ((96 − 120) ÷ 120) × 100 = (−24 ÷ 120) × 100 = −20% (a 20% decrease)

Real-world uses: Tracking price changes, comparing year-over-year revenue, understanding inflation (use our Inflation Calculator).

4. Percentage Difference Between Two Values

Formula: % Difference = (|A − B| ÷ ((A + B) ÷ 2)) × 100

This is used when you want to compare two values without treating either as the "base" or "original" value.

Example: City A has 85,000 residents. City B has 115,000. What is the percentage difference?

  • |85,000 − 115,000| = 30,000
  • Average = (85,000 + 115,000) ÷ 2 = 100,000
  • (30,000 ÷ 100,000) × 100 = 30% difference

Real-World Percentage Examples

Shopping & Discounts

If a jacket is $120 and is on sale for 35% off:

  • Discount amount = 35% of $120 = (35 ÷ 100) × 120 = $42 off
  • Sale price = $120 − $42 = $78

Tipping at a Restaurant

For a $65 dinner bill, a 20% tip is:

  • Tip = (20 ÷ 100) × 65 = $13
  • Total with tip = $65 + $13 = $78

Grade Calculations

If you scored 78 out of 95 points on an exam:

  • Grade % = (78 ÷ 95) × 100 = 82.1% (approximately a B)

Salary Raise

If your salary was $55,000 and you got a 4.5% raise:

  • Raise amount = (4.5 ÷ 100) × 55,000 = $2,475
  • New salary = $55,000 + $2,475 = $57,475

Use our Salary Calculator to see how a raise affects your take-home pay.

Investment Returns

If you invested $10,000 and it grew to $13,500:

  • Return = ((13,500 − 10,000) ÷ 10,000) × 100 = 35% return

Common Percentage Mistakes to Avoid

Mistake 1: Confusing Percentage Points with Percentages

If an interest rate rises from 4% to 6%, it increased by 2 percentage points. But the rate itself increased by 50% (because (6−4)/4 × 100 = 50%). Politicians and media often blur this distinction intentionally.

Mistake 2: Not Knowing the Base

"10% off the original price" and "10% off the sale price" are very different. Always clarify what the percentage is of.

Mistake 3: Adding and Subtracting Percentages Incorrectly

If a price increases by 20% and then decreases by 20%, you do NOT end up at the original price.

  • Start: $100
  • After +20%: $120
  • After -20% of $120: $120 × 0.80 = $96 (not $100!)

This is because the second 20% is applied to a different base number.

Percentage Quick Reference Table

| To Calculate | Formula | Example | |-------------|---------|---------| | P% of X | (P/100) × X | 25% of 80 = 20 | | X is what % of Y | (X/Y) × 100 | 20/80 × 100 = 25% | | % Increase | ((New−Old)/Old) × 100 | (110−100)/100 = 10% | | % Decrease | ((Old−New)/Old) × 100 | (100−90)/100 = 10% | | Add P% to X | X × (1 + P/100) | 100 × 1.20 = 120 | | Subtract P% from X | X × (1 − P/100) | 100 × 0.80 = 80 |

Frequently Asked Questions

To find what percentage X is of Y, use the formula: (X ÷ Y) × 100. For example, to find what percent 25 is of 200: (25 ÷ 200) × 100 = 12.5%. So 25 is 12.5% of 200.
To find P% of a number N, use the formula: (P ÷ 100) × N. For example, to find 15% of 80: (15 ÷ 100) × 80 = 12. So 15% of 80 is 12.
Percentage increase = ((New Value - Old Value) ÷ Old Value) × 100. For example, if a price went from $50 to $65: ((65 - 50) ÷ 50) × 100 = 30% increase.
Percentage decrease = ((Old Value - New Value) ÷ Old Value) × 100. For example, if a price dropped from $80 to $60: ((80 - 60) ÷ 80) × 100 = 25% decrease.
Percentage difference = (|Value1 - Value2| ÷ ((Value1 + Value2) ÷ 2)) × 100. This measures the relative difference between two values without specifying which is the 'old' or 'new' value.
To add P% to a number N: Result = N × (1 + P/100). For example, to add 20% to $150: $150 × (1 + 20/100) = $150 × 1.20 = $180.
To subtract P% from N: Result = N × (1 - P/100). For example, to subtract 15% from $200: $200 × (1 - 0.15) = $200 × 0.85 = $170.
Sales tax amount = Price × (Tax Rate ÷ 100). For a $50 item with 8% sales tax: $50 × 0.08 = $4 tax. Total = $50 + $4 = $54.
Percentage points is the arithmetic difference between two percentages. If interest rates go from 3% to 5%, that is a 2 percentage point increase. But it is a 66.7% increase in rate. The two terms are different and often confused.
Tip amount = Bill × (Tip % ÷ 100). For a $75 restaurant bill with a 20% tip: $75 × 0.20 = $15 tip. Total bill = $75 + $15 = $90.