Math & Science · Guide
How to Calculate a Discount Percentage
Three questions cover every sale: what do I pay, how much do I save, and what percentage was that?
Want the answer for your own numbers? Use the free Percentage Calculator — it does every step below for you.
1. What will I pay? (taking a percentage off)
Sale price = original price × (1 − discount ÷ 100)
Example: 30% off $85
1 − 0.30 = 0.70. $85 × 0.70 = $59.50.
You pay $59.50 and save $25.50
2. How much do I save?
Saving = original price × discount ÷ 100
25% off $120 saves $120 × 0.25 = $30.
3. What percentage off was it? (from two prices)
Sometimes you only see a "was" price and a "now" price.
Discount % = (original − sale) ÷ original × 100
Example: was $80, now $56
$80 − $56 = $24. $24 ÷ $80 = 0.30.
That is 30% off
Always divide by the original price, not the sale price. Dividing $24 by $56 gives 43%, which is wrong.
Discount chart
Sale prices for common discounts:
| Original | 10% off | 20% off | 25% off | 30% off | 40% off | 50% off |
|---|---|---|---|---|---|---|
| $20 | $18.00 | $16.00 | $15.00 | $14.00 | $12.00 | $10.00 |
| $50 | $45.00 | $40.00 | $37.50 | $35.00 | $30.00 | $25.00 |
| $100 | $90.00 | $80.00 | $75.00 | $70.00 | $60.00 | $50.00 |
| $200 | $180.00 | $160.00 | $150.00 | $140.00 | $120.00 | $100.00 |
4. What was the original price?
If you only know the sale price and the discount, divide — do not add the percentage back on:
Original price = sale price ÷ (1 − discount ÷ 100)
A $59.50 item marked 30% off was $59.50 ÷ 0.70 = $85. Adding 30% to $59.50 gives $77.35, which is wrong, because the 30% was taken from the higher price.
Mental maths shortcuts
- 10% off: move the decimal one place left and subtract. 10% of $67 is $6.70.
- 20% off: find 10% and double it.
- 25% off: divide by 4. 25% of $96 is $24.
- 15% off: 10% plus half of 10%.
- 50% off: halve it.
- Swap trick: x% of y equals y% of x. 8% of 50 is the same as 50% of 8 — 4.
Stacked discounts do not add up
"An extra 20% off sale prices" on top of 30% off is not 50% off. Each discount applies to the new, lower price.
Example: $100 item, 30% off then an extra 20% off
$100 × 0.70 = $70. Then $70 × 0.80 = $56.
Total discount: 44%, not 50%
Combined discount = 1 − (1 − d1) × (1 − d2)
Discounts and sales tax
In the US, sales tax is usually added after the discount. On a $59.50 sale price with 8% tax, you pay $59.50 × 1.08 = $64.26. Coupons that are "$ off" rather than "% off" are also usually taken off before tax. In countries with VAT, the shelf price already includes the tax — see the VAT calculator to split it out.
Is the "discount" real?
A big percentage off an inflated "was" price is not a real saving. Compare the sale price with what other shops charge, not just with the crossed-out number.
Do any of these in a click with the percentage calculator: "X decreased by Y%" for sale prices, and "Percentage change from X to Y" for the discount rate.
Buy-one-get-one deals
- Buy one, get one free is 50% off both items together.
- Buy one, get one half price is 25% off both items together.
- 3 for 2 is a third off — about 33% — across all three.
These only save money if you wanted the extra items anyway.
Dollars off vs percent off
Is “$20 off” better than “20% off”? It depends on the price. They are equal at $100. Below that, $20 off wins: on a $60 item you pay $40 instead of $48. Above it, 20% off wins: on a $150 item you pay $120 instead of $130.
Frequently asked questions
Multiply the price by (1 minus the discount as a decimal). 30% off $85 is $85 × 0.70 = $59.50. The saving is $85 × 0.30 = $25.50.
Subtract the sale price from the original, divide by the original, and multiply by 100. From $80 to $56 is $24 ÷ $80 × 100 = 30% off.
No. A 30% discount followed by an extra 20% is a 44% total discount, because the second discount applies to the already reduced price.
Divide the sale price by one minus the discount as a decimal. A $59.50 price after 30% off was $59.50 ÷ 0.70 = $85.
On items under $100, $20 off saves more. On items over $100, 20% off saves more. At exactly $100 they are the same.