What Is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." The symbol % is shorthand for "out of 100."

For example, 25% means 25 out of every 100 — or equivalently, one quarter.

The Three Core Percentage Calculations

1. Finding X% of a Number

To find X% of a value Y, multiply Y by X/100:

Result = Y × (X / 100)

Example: What is 20% of 250?

250 × (20 / 100) = 250 × 0.20 = 50

2. What Percentage Is X of Y?

To find what percentage X is of Y, divide X by Y and multiply by 100:

Percentage = (X / Y) × 100

Example: 50 is what percent of 200?

(50 / 200) × 100 = 0.25 × 100 = 25%

3. Percentage Change

To calculate the percentage change from an old value to a new value:

% Change = ((New − Old) / Old) × 100

A positive result is an increase; a negative result is a decrease.

Example: A product price rose from $200 to $250.

((250 − 200) / 200) × 100 = (50 / 200) × 100 = 25%

Why Percentages Matter

Percentages appear everywhere:

• Finance: interest rates, investment returns, inflation
• Retail: sale discounts, tax rates, cashback offers
• Health: body fat percentage, test accuracy, vaccination rates
• Statistics: survey responses, probability, data analysis

Common Percentage Mistakes

1. Reversing the percentage change: A 50% increase followed by a 50% decrease does not return to the original value. (100 → 150 → 75)
2. Confusing percentage points with percentages: If a rate rises from 5% to 7%, that's a 2 percentage point increase but a 40% relative increase.
3. Not anchoring the base: "20% off" depends on the original price; always identify what the percentage is of.