Percentage Calculator — How to Calculate Percentages, Differences & Changes

Percentages are ratios expressed as parts per hundred. The word "percent" comes from the Latin per centum, meaning "by the hundred." Understanding how to calculate percentages accurately is one of the most practically useful mathematical skills — from calculating discounts and tax rates to interpreting statistical data and tracking fitness progress.

What Is a Percentage?

A percentage is a way of expressing a proportion as a fraction of 100. If you score 42 out of 60 on a test, your percentage score is (42/60) × 100 = 70%. The % symbol means "divided by 100."

Basic conversion:

• Fraction → Percentage: multiply by 100 (e.g. 3/4 × 100 = 75%)
• Percentage → Decimal: divide by 100 (e.g. 35% = 0.35)
• Decimal → Percentage: multiply by 100 (e.g. 0.175 × 100 = 17.5%)

Mode 1: Percentage of a Number (X% of Y)

Formula: result = (X ÷ 100) × Y

This is the most common percentage calculation — finding a proportion of a total.

Example: What is 17.5% of £340?

• (17.5 ÷ 100) × 340 = 0.175 × 340 = £59.50

Practical uses:

• Calculating sales tax or VAT on a purchase
• Finding a tip amount (15% of a restaurant bill)
• Determining a discount (25% off a £120 jacket = £30 off)
• Computing interest on a loan or savings account

Mode 2: What Percentage Is X of Y?

Formula: result = (X ÷ Y) × 100

This "reverse percentage" calculation finds what proportion one number represents of another.

Example: 42 is what percentage of 280?

• (42 ÷ 280) × 100 = 0.15 × 100 = 15%

Practical uses:

• Calculating your exam score as a percentage
• Finding out what percentage of your income you spend on rent
• Analysing market share (company sold 42 units out of a total 280 in the market)

Mode 3: Percentage Difference

Formula: |V1 − V2| ÷ ((V1 + V2) ÷ 2) × 100

Percentage difference is a symmetric measure — it doesn't treat either value as the "original." It's used when comparing two values without implying that one came before the other.

Example: Percentage difference between 80 and 100

• |80 − 100| = 20
• Average = (80 + 100) ÷ 2 = 90
• 20 ÷ 90 × 100 = 22.2%

When to use percentage difference (vs. percentage change):

• Comparing prices from two different suppliers (neither is "original")
• Measuring the difference in concentration between two solutions
• Comparing populations of two cities

Mode 4: Percentage Change (Increase or Decrease)

Formula: ((New − Old) ÷ Old) × 100

Percentage change measures how much a value has increased or decreased relative to a starting point.

Example: A stock price rises from £40 to £52

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

Example: Weight drops from 85 kg to 79 kg

• (79 − 85) ÷ 85 × 100 = −6 ÷ 85 × 100 = −7.06% (a decrease of 7.06%)

Practical uses:

• Tracking year-on-year revenue growth
• Measuring weight loss or fitness progress
• Calculating inflation (CPI percentage change)
• Evaluating investment returns

Percentage Points vs. Percentages

A common source of confusion: percentage points and percentages are different.

• If interest rates rise from 2% to 3%, they increased by 1 percentage point but by 50% (percentage change: (3−2)/2 × 100 = 50%).
• "The unemployment rate fell by 2 percentage points" means from, say, 8% to 6% — not a 2% reduction in unemployment.

Common Percentage Shortcuts

Percentage	Shortcut
10% of X	Divide by 10
5% of X	Divide by 20 (or halve 10%)
20% of X	Divide by 5
25% of X	Divide by 4
50% of X	Divide by 2
1% of X	Divide by 100
15% of X	10% + half of 10%

Real-World Applications

Finance: VAT (20%), income tax bands, mortgage interest rates, investment growth

Retail: Discount percentages, markup pricing (cost × 1.margin%)

Health: Body fat percentage, BMI changes, clinical trial success rates

Science: Concentration of solutions, purity percentages, error rates

Statistics: Confidence intervals, survey response rates, probability

Related Resources

Related Calculators

• Fraction Calculator — Turn percentages into fractions.
• Exponent Calculator — Use percentages in compound growth.

External Authority Resources

• Wolfram MathWorld: Percentages — Mathematical overview of percents.
• Khan Academy: Introduction to Percents — Tutorial on understanding percentages.