How to Calculate Percentages — With Examples
What a percentage actually is
A percentage is just a fraction whose denominator is always 100. The word comes from Latin per centum — "by the hundred." When you say 25%, you are saying 25 out of every 100, or the fraction 25/100, or the decimal 0.25. That third form is the key: every percentage problem gets easier the moment you turn the percentage into a decimal and multiply.
Percentages are everywhere because they make unlike quantities comparable. A 12% raise on one salary and a 12% raise on another produce different amounts of money, but the same relative change — and it is the relative change people usually want to talk about.
Finding a percentage of a number
This is the most common percentage task: tips, discounts, taxes, interest. The rule is one multiplication:
part = percentage ÷ 100 × totalA 15% tip on a $68 restaurant bill
Convert 15% to a decimal: 15 ÷ 100 = 0.15. Multiply by the total: 0.15 × 68 = 10.2.
15% of $68 = $10.20
A quick mental trick: 10% first
10% of a number is just the number with the decimal point moved one place left: 10% of 68 = 6.8. Then 5% is half of that: 3.4. Adding them gives 6.8 + 3.4 = 10.2 — the same 15% without touching a calculator.
10% + 5% = 15% → $10.20
Percentage change: increases and decreases
Percentage change compares a new value to an old value relative to the old value. The formula always divides by the original number — dividing by the new one is the classic error:
change % = (new − old) ÷ old × 100A price goes from $80 to $100
The difference is 100 − 80 = 20. Divide by the original price: 20 ÷ 80 = 0.25. Multiply by 100.
The price increased by 25%
The same item is discounted from $50 to $40
Difference: 40 − 50 = −10. Divide by the original: −10 ÷ 50 = −0.20.
A 20% decrease (a −20% change)
Reverse percentages: finding the original number
Sometimes you know the number after a percentage was applied, and you need the original. Do not just subtract the percentage from the final number — that computes the percentage of the wrong base. Instead, think in multipliers: increasing by 25% multiplies by 1.25, so recovering the original means dividing by 1.25.
A shirt costs $60 after a 20% discount was applied. Sixty dollars is 80% of the original price, so the original was 60 ÷ 0.80 = $75. Check: 20% of 75 is 15, and 75 − 15 = 60. It works.
| Situation | Multiplier to apply | To undo it |
|---|---|---|
| Increase of 10% | × 1.10 | ÷ 1.10 |
| Decrease of 10% | × 0.90 | ÷ 0.90 |
| Increase of 25% | × 1.25 | ÷ 1.25 |
| Discount of 20% | × 0.80 | ÷ 0.80 |
| Increase of 150% | × 2.50 | ÷ 2.50 |
Percentages vs. percentage points
If an interest rate rises from 10% to 13%, it rose by 3 percentage points. But its relative increase is (13 − 10) ÷ 10 = 30%. Newspapers, banks and politicians mix these up constantly; a "3% increase" of a 10% rate would only bring it to 10.3%. Whenever a percentage itself changes, ask which of the two the speaker means.
One more useful habit: always sanity-check the direction. If a quantity went down, the percentage change must be negative; if your discount calculation makes the price bigger, you divided where you should have multiplied.