A practical guide to percentages

A percentage describes a quantity out of 100. Knowing which number is the starting point is the key to choosing the right calculation. The Percentage Calculator handles a percentage of a value and the percentage change between two values.

Find a percentage of a number

Divide the percentage by 100, then multiply by the number. To find 15% of 240, calculate 15 ÷ 100 × 240 = 36. The answer is an amount, not a percentage.

Calculate an increase or decrease

Subtract the old value from the new value, divide by the old value, then multiply by 100. A change from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%. A negative answer indicates a decrease.

Notice that reversing the same two numbers gives a different percentage. That is because the denominator changes. Always identify the original value before entering the numbers.

Percentage points are different

If a rate moves from 10% to 15%, it rises by 5 percentage points. Relative to the original 10%, that is a 50% increase. These descriptions answer different questions and should not be used interchangeably.

Watch for zero and repeated changes

A percentage change from zero is undefined because the formula would divide by zero. State the absolute change instead. Two successive 10% increases are also not a 20% total increase: starting at 100 gives 110 and then 121, a 21% increase overall.

What percentage is one number of another?

Divide the part by the total, then multiply by 100:

Percentage = (part ÷ total) × 100

For example, if you complete 18 tasks out of 24, the calculation is (18 ÷ 24) × 100 = 75%. You have completed 75% of the tasks.

Use the full total as the denominator. This calculation is undefined when the total is zero.

Find the original price before a discount

If you know the discounted price and the discount percentage, divide the final price by the fraction of the original price that remains:

Original price = final price ÷ (1 − discount percentage ÷ 100)

Suppose an item costs 160 after a 20% discount. You paid 80% of its original price, so the original price was 160 ÷ 0.80 = 200.

Adding 20% to 160 gives 192, which is incorrect because that percentage uses the reduced price as its starting point.

This formula assumes a single discount with no additional fees. A 100% discount leaves a zero price, so the original price cannot be recovered from that result alone.

A quick checking routine

1. Identify whether you need an amount, a percentage change or a final discounted price.
2. Confirm the original value and the direction of change.
3. Keep extra decimal places during intermediate calculations.
4. Round the final result for its intended use.

The calculator displays rounded answers. For complex accounting or official reports, verify the relevant rounding rules independently.