Last updated: 2026-05-17

Percentages

A percentage expresses a number as a fraction of 100. Writing P% means "P per hundred," so 25% is the same quantity as the fraction 25/100 or the decimal 0.25. Every percentage problem is one of three forms of a single relationship between a part, a whole, and a rate.

The three forms

• Find the part — what is P% of X? For example, 20% of 50 is 10.
• Find the rate — A is what percent of X? For example, 34 out of 40 is 85%.
• Find the whole — A is P% of what? For example, 45 is 15% of 300.

Each section of the calculator handles one form. Enter the two known values and the third is computed.

Formula

The three forms are the same equation rearranged for whichever quantity is unknown:

$$\text{Part} = \text{Whole} \times \frac{P}{100} \qquad P = \frac{\text{Part}}{\text{Whole}} \times 100 \qquad \text{Whole} = \frac{\text{Part}}{P / 100}$$

Worked example

An item priced at $45 represents 15% of an original price. To recover the original, divide the part by the rate written as a decimal: 45 ÷ 0.15 = $300. Checking the other direction, 15% of $300 is 300 × 0.15 = $45.

Converting between decimals and percentages

To convert	Operation	Example
Decimal → %	× 100	0.07 → 7%
% → Decimal	÷ 100	7% → 0.07
Fraction → %	divide, then × 100	3/8 → 37.5%

Percent versus percentage points

A percentage point is the arithmetic difference between two percentages, which is distinct from the relative change between them. If a fund's return drops from 8% to 5%, it has fallen by 3 percentage points, and it has also fallen by 37.5% relative to its starting value (3 ÷ 8 × 100). News reports often use the two interchangeably, so a stated "0.2% rise" in an unemployment rate usually means 0.2 percentage points rather than a 0.2% relative increase.

Applying percentages

Two properties affect how percentages combine:

• Successive percentages do not simply add. A 20% increase followed by a 20% decrease does not return to the original value: $100 becomes $120, then $96, because each step applies to a different base.
• Percentages of different bases cannot be added directly. "15% of salary plus 10% of bonus" cannot be combined into 25% without knowing the relative size of the two amounts.

Frequently Asked Questions (FAQ)

What does "percent" mean?

"Percent" comes from the Latin per centum, meaning "per hundred." 25% means 25 out of every 100, or 0.25 as a decimal. To convert a decimal to a percentage, multiply by 100; to convert a percentage to a decimal, divide by 100.

What is the difference between percent and percentage points?

A percentage point (pp) is the arithmetic difference between two percentages. If interest rates rise from 2% to 5%, that is a 3 percentage point increase — but a 150% relative increase. Confusing the two is a common mistake in news reporting.

How do I convert a decimal to a percentage?

Multiply the decimal by 100. For example, 0.375 × 100 = 37.5%. To go the other way, divide by 100: 37.5% ÷ 100 = 0.375.