How to Calculate Percentage

What "percent" actually means

Percent comes from the Latin *per centum* — "by the hundred". So 25% means 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25. Once you internalise that, every percentage question becomes a simple multiplication or division.

The trick is working out which number is the "whole" (the 100%) and which is the "part". Getting that the wrong way round is the single most common percentage mistake.

1. Finding a percentage of a number

Divide the percentage by 100, then multiply by the number.

• Formula: result = (percentage ÷ 100) × number
• Example: 25% of 200 = 0.25 × 200 = 50
• Shortcut: to find 10%, move the decimal point one place left. For 20%, double it. For 5%, halve it.

2. Expressing one number as a percentage of another

Divide the part by the whole, then multiply by 100.

• Formula: percentage = (part ÷ whole) × 100
• Example: 50 out of 200 = (50 ÷ 200) × 100 = 25%
• This is the form used for marks, discounts off a list price and completion rates.

3. Working out a percentage change

Subtract the original value from the new value, divide by the original value, then multiply by 100. The key detail: you always divide by the *original*, never by the new value.

• Formula: change = ((new − original) ÷ original) × 100
• Example: a price rising from 100 to 125 = (25 ÷ 100) × 100 = 25% increase
• A negative answer simply means a decrease.

Percentage changes are not reversible. A 50% increase followed by a 50% decrease leaves you 25% below where you started, because the decrease is taken from a larger number.

Common percentage shortcuts

Percentage points vs percent

If an interest rate rises from 4% to 6%, that is a rise of 2 percentage points — but a 50% increase in the rate itself. Mixing the two up is a classic reporting error, so check which one a figure is describing.