How chained percentages are calculated
Turn each percentage into a multiplier, multiply them, then turn the result back into a percentage.
X% of Y% = (X ÷ 100) × (Y ÷ 100) · overall factor = (1 ± a) × (1 ± b)
- X% of Y%: divide both by 100 and multiply. 20% of 50% is 0.20 × 0.50 = 0.10, or 10%.
- Changes in a row: a 10% rise is × 1.10 and a 10% fall is × 0.90. Multiply the factors.
- Stacked discounts: 20% off is × 0.80 and 10% off is × 0.90. Together, × 0.72, so 28% off.
- Subtract 1 from the combined factor and multiply by 100 for the overall change.
- Order does not matter, because multiplication gives the same answer either way.
Worked example — A $100 item at 20% off, then an extra 10% off at the register: $100 × 0.80 × 0.90 = $72. That is 28% off overall, not 30%.
Common percentages of percentages
| Percentage X | Of Y | Result |
|---|---|---|
| 20% | 50% | 10% |
| 50% | 50% | 25% |
| 10% | 30% | 3% |
| 25% | 80% | 20% |
| 15% | 60% | 9% |
Swipe the table sideways to see the rest.
Each row is worked out by this calculator.
Things to consider
- Never add percentages that apply one after another. Multiply the factors instead.
- A rise then an equal fall always leaves you slightly below where you started.
- Two years of growth at 5% is 1.05 × 1.05 = 1.1025, so 10.25%, not 10%.
- When a shop says "extra 10% off", it almost always means off the already reduced price.
Frequently asked questions
How do I work out a percentage of a percentage?
Divide both by 100 and multiply. 20% of 50% is 0.20 × 0.50 = 0.10, which is 10%. For a percentage of a plain number, use the Percentage Calculator.
Why doesn't +10% then −10% get back to zero?
The fall applies to the bigger number. 100 rises to 110, and 10% of 110 is 11, leaving 99. Overall that is −1%.
Do two discounts add up?
No. 20% off then 10% off is 0.80 × 0.90 = 0.72 of the price, so 28% off, not 30%. Two 50% discounts are 75% off, not free.
Does the order of the discounts matter?
No. 0.80 × 0.90 and 0.90 × 0.80 both give 0.72, so the final price is the same.
How do I combine percentage increases over several years?
Multiply the yearly factors. 20% then 30% growth is 1.20 × 1.30 = 1.56, a 56% rise. To find the change between two actual numbers, use the Percentage Increase and Change Calculator.
How does GST work with a discount?
A $100 item plus 10% GST is $110. Take 20% off and you pay $88. Discount first then add GST and you still get $100 × 0.80 × 1.10 = $88.
Results are estimates for general information only, not financial, medical or professional advice.