OneTaskBy Tim King · Updated
Discount Calculator
Sale Price and Savings, Plus Stacked Discounts Applied in Sequence
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How the Discount Calculator works
This discount calculator gives the sale price and the saving. Enter the original price and the percentage off to get the sale price and the amount you save. Add a second percentage when a further discount is applied at the till, and the result also shows what the two together actually come to — which is never the two numbers added up.
Enter the ticket price and the percentage off, and the calculator gives the price you pay and the amount you save. Add a further discount and it also shows the real total percentage off, which is never the two figures added together. That last line is the point of the tool: "take an extra 10 % off sale prices" is the most reliably misread sentence in retail.
Percent off calculator: the formula
Sale price = original price × (1 − discount ÷ 100). The saving is the original price minus the sale price. For a second discount, multiply again by (1 − second ÷ 100). Nothing is added.
Worked example. A jacket marked $249 with 35 % off: 249 × 0.65 = $161.85, so you save $87.15. The mental route is to find 10 % ($24.90), triple it for 30 % ($74.70), add half of 10 % for the remaining 5 % ($12.45), and take the $87.15 total from the ticket.
Stacked discount calculator: discounts multiply, they do not add
Take $100 with 20 % off and you pay $80. A further 10 % comes off the $80, not the $100, so it takes $8 rather than $10 and you pay $72. That is 28 % off in total, not 30 %. The effective discount is 1 − (0.80 × 0.90) = 0.28.
The gap grows with the size of the discounts:
| First discount | Further discount | Real total off | Not |
|---|---|---|---|
| 20 % | 10 % | 28 % | 30 % |
| 30 % | 20 % | 44 % | 50 % |
| 50 % | 20 % | 60 % | 70 % |
| 50 % | 50 % | 75 % | 100 % |
| 70 % | 30 % | 79 % | 100 % |
The last two rows show why: added percentages could reach 100 % and make the item free, but multiplying only ever gets closer. Three lots of 10 % are 27.1 %, not 30 %.
The order does not matter for percentages, because multiplication commutes: 20 % then 10 % and 10 % then 20 % both land on $72. It does matter as soon as a fixed amount joins in. On a $100 item, $20 off then 10 % off gives $72, but 10 % off then $20 off gives $70. Coupon terms state the order for exactly this reason, and most tills apply percentage discounts first.
Reading the result
- Final price is what you pay, rounded to the cent.
- Save is the difference from the ticket in dollars. It is the figure to compare against a competitor's price or a cashback offer.
- Off in total, not … appears only when a further discount is entered. It shows the real combined percentage next to the figure the two numbers suggest. Use the real one when comparing, say, "40 % off" in one shop against "25 % plus an extra 20 %" in another. The second is 40 % too, not 45 %.
Where the arithmetic shows up
- Retail sales. "Up to 70 % off" describes the single best-discounted item. To find the real discount on the thing in your hand, divide the sale price by the original and take the result from one: $45 from $60 is 1 − 0.75 = 25 % off.
- Trade and staff discounts. A 15 % trade discount on top of a 10 % promotion is 23.5 %, not 25 %. Businesses budgeting for stacked promotions need the multiplied figure, or margins vanish faster than expected.
- Supplier price lists. Wholesale terms are often quoted as a chain, such as "40/10/5", meaning 40 % then 10 % then 5 %. That is 48.7 % off list, which you can check by running two of the discounts here and the third on the result.
- Tax. When a price includes GST, VAT or sales tax, discounting it discounts the tax with it, and the answer stays tax-inclusive. When a price excludes tax, discount first and add tax to the discounted figure, which is the order point-of-sale systems use.
Tips and pitfalls
- Percent off is not percent more. A jumper reduced from $80 to $60 is 25 % off, yet $80 is 33 % more than $60. Same prices, different base. Shop signs always use the original price as the base.
- Sellers: discount is not margin. Knocking 20 % off a product with a 25 % markup wipes out the entire profit, because the two percentages use different bases. Work out the margin left with the markup calculator and see margin vs markup for why the two numbers disagree.
Sale price calculator: how much do I save?
The table gives the sale price for common percentages off on round ticket prices. The saving is the difference from the original.
| Original price | 10% off | 15% off | 20% off | 25% off | 30% off | 40% off | 50% off |
|---|---|---|---|---|---|---|---|
| $10 | $9.00 | $8.50 | $8.00 | $7.50 | $7.00 | $6.00 | $5.00 |
| $15 | $13.50 | $12.75 | $12.00 | $11.25 | $10.50 | $9.00 | $7.50 |
| $20 | $18.00 | $17.00 | $16.00 | $15.00 | $14.00 | $12.00 | $10.00 |
| $25 | $22.50 | $21.25 | $20.00 | $18.75 | $17.50 | $15.00 | $12.50 |
| $30 | $27.00 | $25.50 | $24.00 | $22.50 | $21.00 | $18.00 | $15.00 |
| $40 | $36.00 | $34.00 | $32.00 | $30.00 | $28.00 | $24.00 | $20.00 |
| $50 | $45.00 | $42.50 | $40.00 | $37.50 | $35.00 | $30.00 | $25.00 |
| $60 | $54.00 | $51.00 | $48.00 | $45.00 | $42.00 | $36.00 | $30.00 |
| $75 | $67.50 | $63.75 | $60.00 | $56.25 | $52.50 | $45.00 | $37.50 |
| $80 | $72.00 | $68.00 | $64.00 | $60.00 | $56.00 | $48.00 | $40.00 |
| $90 | $81.00 | $76.50 | $72.00 | $67.50 | $63.00 | $54.00 | $45.00 |
| $100 | $90.00 | $85.00 | $80.00 | $75.00 | $70.00 | $60.00 | $50.00 |
| $120 | $108.00 | $102.00 | $96.00 | $90.00 | $84.00 | $72.00 | $60.00 |
| $150 | $135.00 | $127.50 | $120.00 | $112.50 | $105.00 | $90.00 | $75.00 |
| $180 | $162.00 | $153.00 | $144.00 | $135.00 | $126.00 | $108.00 | $90.00 |
| $200 | $180.00 | $170.00 | $160.00 | $150.00 | $140.00 | $120.00 | $100.00 |
| $250 | $225.00 | $212.50 | $200.00 | $187.50 | $175.00 | $150.00 | $125.00 |
| $300 | $270.00 | $255.00 | $240.00 | $225.00 | $210.00 | $180.00 | $150.00 |
| $400 | $360.00 | $340.00 | $320.00 | $300.00 | $280.00 | $240.00 | $200.00 |
| $500 | $450.00 | $425.00 | $400.00 | $375.00 | $350.00 | $300.00 | $250.00 |
To work backwards from a sale price to the percentage, or to find a percentage change between any two numbers, use the percentage calculator.
Discount worked examples
First example. A $64 jacket at 35% off: 64 × 0.65 = $41.60, a saving of $22.40.
Second example. A $240 chair with 25% off and then a further 10% off: 240 × 0.75 × 0.90 = $162.00, which is 32.5% off in total, not 35%.
How many percent off is a given sale price? Divide the saving by the original: $41.60 on a $64 ticket saves $22.40, and 22.40 ÷ 64 = 35%.
FAQ
Is 20% off then 10% off the same as 30% off?
No. The second discount applies to the already-reduced price, so $100 becomes $80 and then $72 — a total of 28% off rather than 30%. The gap widens as the individual percentages get larger, so 50% plus 20% is 60% off, not 70%.
Does it matter which discount is applied first?
Not when both are percentages, because multiplication gives the same result in either order. It does matter when a fixed dollar amount is involved: taking $20 off before a 10% discount produces a different total from applying the percentage first.
How do I work out the percentage off from two prices?
Divide the sale price by the original price and subtract the result from one. A jumper down from $80 to $60 gives 60 ÷ 80 = 0.75, so the discount is 25%. The percentage calculator will do that division for you if you would rather not do it by hand.
Is the discount applied before or after GST?
Point-of-sale systems discount the pre-tax price and then calculate the tax on the reduced figure. If your price already includes GST, discounting it proportionally reduces the tax component too, so the percentages work out identically either way.
How do I calculate 30% off a price in my head?
Find 10% by moving the decimal point one place left, then multiply by three. On $85, 10% is $8.50, so 30% is $25.50 and the sale price is $59.50. For 15%, take 10% and add half of it again; for 25%, halve the price and halve it again. Working with the amount saved is usually easier than working with the 70% you still pay.
What is the original price if I know the sale price and the discount?
Divide the sale price by (100 − discount) ÷ 100. Something selling for $63 after 30% off was 63 ÷ 0.70 = $90 originally. Adding 30% back onto $63 gives $81.90, which is wrong, because the 30% was taken from the larger original figure, not the smaller sale figure. The percentage calculator has a reverse mode for this.
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