Percentages and discounts: How this was calculated
One percent is one hundredth. Choose the mode for your task: the same percentage can require a different calculation.
Percent of a number
Base × percentage ÷ 100
Find the amount corresponding to a given percentage of the base.
12.5% of 240 = 240 × 12.5 ÷ 100 = 30.00.
Percentage change
(New value − original value) ÷ original value × 100
Compare the difference between two values with the original value. The denominator keeps the original sign.
80 → 100: (100 − 80) ÷ 80 × 100 = 25.00%.
Discounted price
Price × (100 − discount) ÷ 100
Find the final price after one percentage discount.
€80 with a 12.5% discount: 80 × 87.5 ÷ 100 = €70.00.
Precision
Two decimal places. Rounded once, at the end; exact halves are rounded away from zero.
Percentage change keeps the original value’s sign in the denominator: −100 to −50 gives −50%.
Limits and special cases
- Up to 15 integer digits and 6 decimal places.
- The share base and the original value for change must not be zero. Even a change from zero to zero is undefined as a percentage.
- Negative values are allowed for percent-of, share and change. With a negative original value, the sign of the percentage change alone does not indicate improvement or decline.
- For a discount, the price must be nonnegative and the discount must be 0–100%. The result is the final price; a separately rounded saving is not added to it.
- This does not calculate compound interest, loans or taxes.
These are ordinary arithmetic operations. No tax year, statutory rates or tax rules apply to this calculator.
Sources and methodology
The method uses the arithmetic formulas and manually derived examples shown here.