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How to Calculate Discount and Sale Prices
The discount formula is:
\[\text{Sale Price} = \text{Original Price} \times \left(1 - \frac{\text{Discount\%}}{100}\right)\]A 30% discount on an $89.99 item gives you $89.99 x 0.70 = $62.99. That is the entire concept. The rest of this post covers variations, stacking, and mental math shortcuts.
The basic discount formula
To find the sale price, multiply the original price by (1 minus the discount as a decimal). A 25% discount means you pay 75% of the original price. A 40% discount means you pay 60%. The discount percentage tells you what is removed; the remainder is what you pay.
For example, 25% off $149.95 gives $149.95 x 0.75 = $112.46. And 40% off $64.00 gives $64.00 x 0.60 = $38.40. The discount calculator runs this formula for any combination of price and percentage.
Here is another example with a rounder number. A $250 jacket at 35% off costs $250 x 0.65 = $162.50. The discount itself is $87.50. When the numbers are clean, you can verify this by checking that the discount amount plus the sale price equals the original: $87.50 + $162.50 = $250. This is a useful sanity check when doing discount math by hand.
Stacking discounts: why 20% + 10% is not 30%
Stores sometimes offer stacked discounts like “take 20% off, then an extra 10% off.” This is not the same as 30% off, and the reason is that the second discount applies to the already-reduced price, not the original.
Start with a $100 item. Take 20% off first: $100 x 0.80 = $80. Then take 10% off the $80: $80 x 0.90 = $72. The final price is $72, not $70. The general formula for stacked discounts is:
\[\text{Final Price} = \text{Original} \times (1 - d_1) \times (1 - d_2)\]The combined effective discount is 28%, not 30%. This difference gets larger with bigger discounts.
Consider a more extreme example: 50% off plus an additional 50% off. Many shoppers would expect to get the item for free. The actual math is $100 x 0.50 x 0.50 = $25. The effective discount is 75%, not 100%. Each successive discount operates on a smaller base, so the total discount is always less than the sum of the individual percentages.
The order of stacking does not matter mathematically. A 20% discount followed by 10% gives the same final price as 10% followed by 20%, because multiplication is commutative. $100 x 0.80 x 0.90 = $100 x 0.90 x 0.80 = $72 either way.
Finding the original price from a sale price
If a shirt is marked “$45 after 25% off,” the original price was $45 / (1 - 0.25) = $45 / 0.75 = $60. A common mistake is to add 25% of the sale price back: $45 + $11.25 = $56.25. That is wrong because 25% of $45 is not the same as 25% of the original $60. The percentage calculator can reverse-calculate this, or you can use the formula:
\[\text{Original Price} = \frac{\text{Sale Price}}{1 - \frac{\text{Discount\%}}{100}}\]This error is worth understanding more closely. When you see “$45 after 25% off,” the $45 represents 75% of the original. Adding 25% of $45 back gives you 25% of 75% of the original, which is only 18.75% of the original. You end up short every time. The correct method is always to divide by the complement of the discount.
Another example: a pair of shoes is $68 after a 15% discount. The original price is $68 / 0.85 = $80. Check: 15% of $80 is $12, and $80 - $12 = $68. The numbers confirm the answer.
Mental math shortcuts for common discounts
You do not need a calculator for most common discounts. The approach is the same 10%-anchor method used in all percentage calculations. Here are the shortcuts for an $85 item:
| Discount | Mental math method | Discount amount | Sale price |
|---|---|---|---|
| 10% off | Move decimal left | $8.50 | $76.50 |
| 15% off | 10% + 5% | $12.75 | $72.25 |
| 20% off | Double the 10% | $17.00 | $68.00 |
| 25% off | Divide price by 4 | $21.25 | $63.75 |
| 33% off | Divide price by 3 | $28.33 | $56.67 |
| 50% off | Divide price by 2 | $42.50 | $42.50 |
| 75% off | Pay 25% (divide by 4) | $63.75 | $21.25 |
For prices that are not round numbers, approximate first and adjust. If a $47.99 item is 20% off, treat it as $48. 10% of $48 is $4.80, so 20% is $9.60. The sale price is approximately $38.39, which is close enough for deciding whether to buy it. You can always confirm the exact number with the discount calculator before checkout.
Comparing “percent off” to “dollars off”
Retailers sometimes offer a choice between a percentage discount and a flat dollar amount. A $20 coupon versus 25% off sounds like it requires math, but the comparison is simple: calculate what 25% off gives you in dollars and compare it to $20. On an $60 purchase, 25% off saves $15, so the $20 coupon is better. On a $100 purchase, 25% off saves $25, so the percentage is better. The breakpoint is the price where both discounts give the same savings. In this case, $20 / 0.25 = $80. Below $80, take the flat coupon. Above $80, take the percentage.
Do not forget sales tax
A sale price is the price before tax. If your state has 8% sales tax, an item marked 30% off at $89.99 costs $62.99 + ($62.99 x 0.08) = $62.99 + $5.04 = $68.03 at the register. When comparing deals across stores or online, always calculate the final out-of-pocket cost including tax.