Percentages and discounts: the reference table
Almost every percentage question is one of three, and mixing them up is where the mistakes come from. Both tables are below; the section under them is the part worth reading once.
Open the percentage calculator →Common percentage calculations
| Question | Answer |
|---|---|
| 3% of 100 | 3 |
| 5% of 100 | 5 |
| 8% of 100 | 8 |
| 10% of 100 | 10 |
| 12% of 100 | 12 |
| 15% of 100 | 15 |
| 20% of 100 | 20 |
| 25% of 100 | 25 |
| 30% of 100 | 30 |
| 33% of 100 | 33 |
| 40% of 100 | 40 |
| 50% of 100 | 50 |
| 60% of 100 | 60 |
| 70% of 100 | 70 |
| 75% of 100 | 75 |
| 80% of 100 | 80 |
| 90% of 100 | 90 |
| 10% of 50 | 5 |
| 15% of 50 | 7.5 |
| 20% of 50 | 10 |
| 25% of 50 | 12.5 |
| 50% of 50 | 25 |
| 10% of 75 | 7.5 |
| 20% of 75 | 15 |
| 25% of 75 | 18.75 |
| 10% of 150 | 15 |
| 15% of 150 | 22.5 |
| 20% of 150 | 30 |
| 25% of 150 | 37.5 |
| 5% of 200 | 10 |
| 10% of 200 | 20 |
| 15% of 200 | 30 |
| 20% of 200 | 40 |
| 25% of 200 | 50 |
| 50% of 200 | 100 |
| 10% of 250 | 25 |
| 20% of 250 | 50 |
| 25% of 250 | 62.5 |
| 10% of 300 | 30 |
| 15% of 300 | 45 |
| 20% of 300 | 60 |
| 25% of 300 | 75 |
| 50% of 300 | 150 |
| 10% of 400 | 40 |
| 20% of 400 | 80 |
| 25% of 400 | 100 |
| 5% of 500 | 25 |
| 10% of 500 | 50 |
| 15% of 500 | 75 |
| 20% of 500 | 100 |
| 25% of 500 | 125 |
| 50% of 500 | 250 |
| 10% of 600 | 60 |
| 20% of 600 | 120 |
| 25% of 600 | 150 |
| 10% of 700 | 70 |
| 20% of 700 | 140 |
| 10% of 800 | 80 |
| 20% of 800 | 160 |
| 25% of 800 | 200 |
| 10% of 900 | 90 |
| 20% of 900 | 180 |
| 5% of 1000 | 50 |
| 10% of 1000 | 100 |
| 15% of 1000 | 150 |
| 20% of 1000 | 200 |
| 25% of 1000 | 250 |
| 50% of 1000 | 500 |
| 10% of 1500 | 150 |
| 20% of 1500 | 300 |
| 25% of 1500 | 375 |
| 5% of 2000 | 100 |
| 10% of 2000 | 200 |
| 15% of 2000 | 300 |
| 20% of 2000 | 400 |
| 25% of 2000 | 500 |
| 50% of 2000 | 1000 |
| 5% of 5000 | 250 |
| 10% of 5000 | 500 |
| 20% of 5000 | 1000 |
| 25% of 5000 | 1250 |
| 5% of 10000 | 500 |
| 10% of 10000 | 1000 |
| 20% of 10000 | 2000 |
Discount prices
| Discount | Original | You save | You pay |
|---|---|---|---|
| 10% off | $25.00 | $2.50 | $22.50 |
| 10% off | $50.00 | $5.00 | $45.00 |
| 10% off | $75.00 | $7.50 | $67.50 |
| 10% off | $100.00 | $10.00 | $90.00 |
| 10% off | $150.00 | $15.00 | $135.00 |
| 10% off | $200.00 | $20.00 | $180.00 |
| 10% off | $300.00 | $30.00 | $270.00 |
| 10% off | $500.00 | $50.00 | $450.00 |
| 15% off | $50.00 | $7.50 | $42.50 |
| 15% off | $100.00 | $15.00 | $85.00 |
| 15% off | $200.00 | $30.00 | $170.00 |
| 15% off | $300.00 | $45.00 | $255.00 |
| 15% off | $500.00 | $75.00 | $425.00 |
| 20% off | $25.00 | $5.00 | $20.00 |
| 20% off | $50.00 | $10.00 | $40.00 |
| 20% off | $75.00 | $15.00 | $60.00 |
| 20% off | $100.00 | $20.00 | $80.00 |
| 20% off | $150.00 | $30.00 | $120.00 |
| 20% off | $200.00 | $40.00 | $160.00 |
| 20% off | $250.00 | $50.00 | $200.00 |
| 20% off | $300.00 | $60.00 | $240.00 |
| 20% off | $500.00 | $100.00 | $400.00 |
| 20% off | $1000.00 | $200.00 | $800.00 |
| 25% off | $50.00 | $12.50 | $37.50 |
| 25% off | $100.00 | $25.00 | $75.00 |
| 25% off | $200.00 | $50.00 | $150.00 |
| 25% off | $300.00 | $75.00 | $225.00 |
| 25% off | $400.00 | $100.00 | $300.00 |
| 25% off | $500.00 | $125.00 | $375.00 |
| 30% off | $50.00 | $15.00 | $35.00 |
| 30% off | $100.00 | $30.00 | $70.00 |
| 30% off | $200.00 | $60.00 | $140.00 |
| 30% off | $300.00 | $90.00 | $210.00 |
| 30% off | $500.00 | $150.00 | $350.00 |
| 40% off | $50.00 | $20.00 | $30.00 |
| 40% off | $100.00 | $40.00 | $60.00 |
| 40% off | $200.00 | $80.00 | $120.00 |
| 40% off | $500.00 | $200.00 | $300.00 |
| 40% off | $1000.00 | $400.00 | $600.00 |
| 50% off | $50.00 | $25.00 | $25.00 |
| 50% off | $100.00 | $50.00 | $50.00 |
| 50% off | $200.00 | $100.00 | $100.00 |
| 50% off | $500.00 | $250.00 | $250.00 |
| 50% off | $1000.00 | $500.00 | $500.00 |
| 60% off | $100.00 | $60.00 | $40.00 |
| 60% off | $200.00 | $120.00 | $80.00 |
| 60% off | $500.00 | $300.00 | $200.00 |
| 70% off | $100.00 | $70.00 | $30.00 |
| 70% off | $200.00 | $140.00 | $60.00 |
| 70% off | $500.00 | $350.00 | $150.00 |
| 75% off | $100.00 | $75.00 | $25.00 |
| 75% off | $200.00 | $150.00 | $50.00 |
The three questions
"What is 20% of 80?" is multiplication: 0.20 × 80 = 16. "16 is what percent of 80?" is division: 16 ÷ 80 = 0.20, so 20%. "80 increased by 20%" is a third thing: 80 × 1.20 = 96. The same two numbers give 16, 20% and 96 depending on which question you are asking.
When a result looks wrong, it is almost always because the wrong one of these three was applied. Say the question aloud before reaching for the arithmetic.
Percentage increase and decrease are not symmetric
A price that rises 20% and then falls 20% does not return to where it started. £100 rises to £120, then 20% of £120 is £24, leaving £96. The second percentage is taken against a larger base, so you lose more than you gained.
This is why a 50% loss needs a 100% gain to recover, and it is the single most useful thing on this page for anyone reading investment or sales figures.
Stacked discounts do not add
"An extra 20% off sale prices" where the sale is already 30% off is not 50% off. It is 0.70 × 0.80 = 0.56, so 44% off. Each discount applies to what is left after the previous one.
The same arithmetic works in your favour with stacked interest or repeated growth — which is compounding, and it is the reason it outruns intuition over long periods.
Percentage points are a different unit
If a rate moves from 4% to 5%, that is a rise of one percentage point and also a rise of 25%. Both are correct and they describe the same change. Headlines routinely pick whichever sounds larger, so it is worth checking which is meant.
Common questions
How do I work out X% of Y?
Divide the percentage by 100 and multiply. 15% of 60 is 0.15 × 60 = 9.
Why do two 20% discounts not make 40%?
The second applies to the already-reduced price. 0.80 × 0.80 = 0.64, so 36% off, not 40%.
What's the difference between 1% and one percentage point?
Percentage points measure the gap between two percentages. 4% to 5% is one percentage point, and also a 25% increase.