How to calculate percentage
Percentage is a way to express a fraction of 100. The three most common everyday percentage operations are: calculating what a percentage of a value is, finding what percentage one number is of another, and calculating the percentage change between two values (useful for seeing how much something increased or decreased).
Formulas used
Percentage of a value: result = value × (percentage ÷ 100)
What percentage one number is of another: result = (part ÷ total) × 100
Percentage change: result = ((final − initial) ÷ initial) × 100
Practical example
If a product used to cost $80 and now costs $100, the percentage change is +25%, calculated as (100 − 80) ÷ 80 × 100. On the other hand, if you want to find 20% of $250 (for instance, a commission or discount), the result is $50.
How to calculate percentage manually
Without a calculator, the fastest way is to find 10% first: simply divide the value by 10. From there, other percentages can be found by multiplying or adding that 10% base. For example, to find 30% of $90: 10% is $9, so 30% is 9 × 3 = $27. For fractional percentages, such as 5%, divide the 10% value by 2. This mental shortcut solves most everyday calculations without needing the full formula.
How to calculate a percentage discount
To apply a discount, multiply the original price by the complement of the percentage relative to 100: discounted price = value × (1 − discount ÷ 100). A $150 item with a 20% discount comes to 150 × (1 − 0.20) = $120, which is a $30 savings.
How to calculate a percentage increase
To apply an increase, use the same logic, but add instead of subtract: price with increase = value × (1 + increase ÷ 100). A salary of $3,000 with an 8% raise becomes 3000 × (1 + 0.08) = $3,240.
Difference between percentage and percentage point
The two terms are frequently confused, but they are not the same thing. If an interest rate goes from 10% to 12%, there is an increase of 2 percentage points (the simple difference between the two numbers), but the actual percentage increase is 20% (since 2 is 20% of 10). This distinction is especially important in news reports regarding interest rates, inflation, and election polling, where both terms appear side by side with different meanings.