How to Calculate Percentages: Every Method Explained

A percentage is a fraction with 100 as the denominator: 25% means 25 out of every 100. Every percentage problem reduces to one of a handful of formulas, which this page works through with examples: the basic formula, conversions, percent of a number, percentage change, percentage difference, and the difference between percent and percentage points.

The Basic Formula

Percentage = (Part ÷ Whole) × 100

If you scored 18 out of 20 on a quiz: (18 ÷ 20) × 100 = 0.9 × 100 = 90%.

Converting Between Percentages, Decimals and Fractions

Percentage to decimal: divide by 100, or move the decimal point two places left.

75% = 75 ÷ 100 = 0.75
8.5% = 8.5 ÷ 100 = 0.085

Decimal to percentage: multiply by 100, or move the decimal point two places right.

0.25 = 25%
1.5 = 150%

Fraction to percentage: divide the numerator by the denominator, then multiply by 100.

3/4 = 0.75 = 75%
5/8 = 0.625 = 62.5%

Converting to a decimal first is the step most mistakes skip: 15% of something is 0.15 times it, not 15 times it.

Finding a Percentage of a Number

What percentage is one number of another? (Number ÷ Total) × 100. What percentage is 45 of 180? (45 ÷ 180) × 100 = 25%.

What is a given percentage of a number? Convert the percentage to a decimal and multiply. 15% of 240 = 0.15 × 240 = 36.

Shopping example: an $80 jacket with a 30% discount. The discount is 0.30 × $80 = $24, so you pay $80 − $24 = $56. The Percentage calculator does this "what is P% of N" step for tips, sales tax and discounts.

Quick tips: 10% of a number is the number with the decimal point moved one place left. For 15%, take 10% and add half of it; for 20%, double the 10% figure.

Percentage Change and Percentage Difference

Percentage change compares a new value with an old one and is relative to the old value:

Percentage change = ((New − Old) ÷ Old) × 100

A stock that rises from $50 to $65: ((65 − 50) ÷ 50) × 100 = 30% increase. A positive result is an increase, a negative one a decrease. The Percentage Change calculator returns this from an original and a new value.

Percentage difference compares two values when neither is the baseline, using their average:

Percentage difference = (|Value 1 − Value 2| ÷ average of the two) × 100

Test scores of 85 and 95: average = 90, difference = 10, so (10 ÷ 90) × 100 ≈ 11.1%.

Use percentage change when there is a before and an after (prices, populations, scores over time). Use percentage difference when comparing two independent measurements or survey results.

Percent vs. Percentage Points

When the quantities being compared are themselves percentages, the two ways of describing a change differ a lot:

An interest rate that goes from 5% to 10% rises by 5 percentage points (10 − 5).
The same change is a 100% increase ((10 − 5) ÷ 5 × 100).

A news report that says a rate "rose 5%" when it rose 5 percentage points understates the change; one that says "rose 100%" when it rose from 5% to 10% may sound alarming without context. Say which one you mean.

Common Mistakes

Stacking discounts. Successive percentages multiply rather than add. A 20% discount followed by a further 10% off leaves 0.80 × 0.90 = 72% of the price, a 28% total discount, not 30%.

Reversing a percentage change. A 50% drop is not undone by a 50% rise: $100 falls to $50, and 50% of $50 only brings it back to $75. You'd need a 100% rise.

Ignoring the base. A 50% increase from 2 to 3 and a 50% increase from 2,000 to 3,000 are the same percentage but very different amounts. Report the base alongside the percentage when the numbers are small.

Simple vs. compound interest. When percentages are applied repeatedly (interest, growth rates), each period's percentage applies to the new total, so the result is larger than the percentage times the number of periods.