How to Calculate a Percentage

What a percentage represents

A percentage describes an amount per hundred. The symbol 25% means 25 out of 100, or the decimal 0.25. Converting a percentage to a decimal is often the simplest first step: divide the percentage by 100.

Percentages are relative, so the reference value matters. Saying that a price rose by 10% is incomplete unless the original price is known. The same 10% can represent very different absolute amounts.

Find a percentage of a number

Use percentage of value = (percentage ÷ 100) × value. To find 18% of 250, divide 18 by 100 to get 0.18, then multiply 0.18 × 250 = 45.

This formula is useful for tips, discounts, taxes, commissions, and allocations. The answer keeps the unit of the starting value: 18% of $250 is $45, while 18% of 250 kg is 45 kg.

Find what percentage one value is of another

Use percentage = (part ÷ whole) × 100. If 42 of 60 tasks are complete, (42 ÷ 60) × 100 = 70%, so 70% of the tasks are complete.

The denominator must be the whole or reference amount. Reversing the values answers a different question, and a zero denominator makes the comparison undefined.

Calculate percentage increase or decrease

Use percentage change = ((new value − original value) ÷ |original value|) × 100. A positive result is an increase and a negative result is a decrease.

If a price moves from $80 to $100, the change is $20 and the percentage increase is 20 ÷ 80 × 100 = 25%. Going back from $100 to $80 is a 20% decrease because the new baseline is $100. Percentage changes are not symmetric.

Common percentage mistakes

Do not add or subtract percentage points as though they were percentage changes. Moving from 20% to 25% is an increase of 5 percentage points, but a relative increase of 25% because 5 ÷ 20 = 0.25.

Avoid rounding too early. Keep several digits through intermediate steps, then round the final answer to the precision your situation needs. For money, two decimal places are usually practical.

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