To work out a discount you need two numbers: how much the price drops and what you actually pay. A percent-off deal links them with one formula: sale price = original price × (1 − discount ÷ 100). Learn it once and you can price any deal, in a shop or in a spreadsheet.
The two formulas you need
- Sale price = original × (1 − rate ÷ 100)
- Amount saved = original × (rate ÷ 100)
Worked example: 30% off a $120 jacket
- Convert the discount to a decimal: 30 ÷ 100 = 0.30.
- Find the multiplier: 1 − 0.30 = 0.70.
- Multiply the original price: 120 × 0.70 = $84.
- Amount saved: 120 × 0.30 = $36. Check: 84 + 36 = 120, so the numbers agree.
The clever part is the multiplier. Once you know that 30% off means "pay 70%", the whole calculation is a single multiplication instead of two steps.
Quick mental shortcuts
- 10% off: move the decimal point one place left, then subtract it. $80 → $8 off → $72.
- 25% off: divide by 4 to get the saving. $200 → $50 off → $150.
- 50% off: halve the price. $36 → $18.
- 20% off: take 10%, double it (20% of $45 = $9 off), then subtract.
Common discounts at a glance
| Original | Discount | Multiplier | Sale price | Saved |
|---|---|---|---|---|
| $50 | 10% | 0.90 | $45.00 | $5.00 |
| $80 | 25% | 0.75 | $60.00 | $20.00 |
| $120 | 30% | 0.70 | $84.00 | $36.00 |
| $60 | 40% | 0.60 | $36.00 | $24.00 |
| $249 | 15% | 0.85 | $211.65 | $37.35 |
Stacked discounts are not added together
"Extra 20% off an already 30%-off item" is not 50% off. Apply the discounts one after the other. A $100 item drops to $70, then to $56 — a real total discount of 44%. The reason is that the second discount is taken from the already reduced price, not the original.
Reverse it: find the original price
If you know the sale price and the discount but not the original, divide instead of multiply: original = sale price ÷ (1 − rate ÷ 100). A $84 sale price at 30% off reverses to 84 ÷ 0.70 = $120. This is handy for checking whether a "was" price on a tag is honest.
Don't forget tax and rounding
A discount is applied before sales tax, not after. If the $84 jacket sits in a region with 8% tax, tax is 84 × 0.08 = $6.72, for a final $90.72. Round only at the end; rounding the discount mid-way can shift the total by a cent or two.
Enter the original price and the discount rate in our percent off calculator to get the sale price and the saving instantly, and read how to calculate a discount percentage for the reverse direction.