How to calculate percentages, discounts and percentage change
Understand the core percentage formulas with worked examples for discounts, increases, reverse percentages and comparisons.
Tervix · practical guide
Write down what represents the whole before calculating. Most percentage mistakes come from dividing by the wrong base, not from multiplication.
Percentages express a quantity relative to one hundred. The arithmetic is usually short; the difficult part is identifying the base value. A discount, an increase, a share of a total and a percentage change use related formulas, but they do not answer the same question.
1. Find a percentage of a number
Convert the percentage to a decimal by dividing it by 100, then multiply by the base value. To find 18% of 250, use 0.18 × 250 = 45. The base is 250 because the question asks for a portion of that amount.
This formula is useful for tips, taxes, commissions and allocations. Keep extra decimal places during the calculation and round money only at the end according to the required currency rules.
Formula
- part = base × percentage ÷ 100
- 18% of 250 = 250 × 18 ÷ 100 = 45
3. Calculate a discount or increase
First calculate the percentage amount, then subtract it for a discount or add it for an increase. A 20% discount on 80 is 16, so the final price is 64. A 20% increase on 80 produces 96.
A decrease and an equal increase do not cancel. Reducing 100 by 20% gives 80; increasing 80 by 20% gives 96 because the second percentage uses a different base. To return from 80 to 100 requires a 25% increase.
Two-step method
- discount amount = original × rate
- final price = original − discount amount
4. Measure percentage change
Subtract the old value from the new value, divide the difference by the old value, and multiply by 100. Moving from 50 to 65 is an increase of 15; 15 ÷ 50 × 100 = 30%. Moving from 65 back to 50 is a decrease of about 23.08%, not 30%, because 65 is now the base.
If the old value is zero, ordinary percentage change is undefined because division by zero is impossible. Report the absolute change and explain that no finite percentage change can be calculated from a zero baseline.
Formula
- change % = (new − old) ÷ old × 100
- (65 − 50) ÷ 50 × 100 = 30%
5. Recover the original value
When a final value already includes an increase, divide by one plus the rate. If 120 includes a 20% increase, the original is 120 ÷ 1.20 = 100. When a final price reflects a 20% discount, divide by 0.80.
Do not simply subtract 20% from the final value. That uses the final value as the base and answers a different question. Translate the situation into a multiplier: 100% + 20% becomes 1.20; 100% − 20% becomes 0.80.
Final checklist
- ✓Identify the whole or original value.
- ✓Convert the rate to a decimal or divide by 100.
- ✓Use the old value as the base for percentage change.
- ✓Treat increases and decreases as different multipliers.
- ✓Keep precision until the final step.
- ✓Check whether a result above 100% is logically possible.
Open the Tervix percentage calculator
Calculate parts, shares, increases, decreases and percentage change with visible formulas.
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Reviewed July 29, 2026 using standard percentage identities and independently checked worked examples.