The discount formulas
Sale price = Original × (1 − Discount ÷ 100)
Original = Sale price ÷ (1 − Discount ÷ 100)
The third one matters more than people expect. To find what something cost before a 30% discount, divide by 0.70 — do not add 30% back. Adding 30% to a $1,400 sale price gives $1,820, but the true original was $2,000.
Stacked discounts do not add up
"30% off, then an extra 20% off at checkout" sounds like 50% off. It is not. The second discount applies to the already-reduced price.
The gap between the advertised 50% and the actual 44% is $120 on this purchase.
| Advertised | Sounds like | Actually is |
|---|---|---|
| 20% + 10% | 30% | 28% |
| 30% + 20% | 50% | 44% |
| 50% + 20% | 70% | 60% |
| 50% + 30% | 80% | 65% |
| 40% + 25% | 65% | 55% |
| 70% + 20% | 90% | 76% |
Judging whether a discount is real
- Check the reference price. Many jurisdictions require the "was" price to have been genuinely charged for a set period. Price-history tools can verify this.
- Work out the unit price. A "3 for 2" on a larger pack is not always cheaper per unit than the standard size.
- Ignore the percentage, look at the price. 70% off something overpriced is still overpriced.
- Watch the tax interaction. Tax is calculated on the discounted price, so a discount saves you the tax on the discounted portion too.
For the tax side of a purchase, see the sales tax calculator or the GST calculator.
Frequently asked questions
How do I calculate a percentage discount?
Multiply the price by the discount as a decimal to get the saving, then subtract. For 30% off $2,000: 2,000 × 0.30 = $600 saved, leaving $1,400.
Faster: multiply directly by (1 − discount). 2,000 × 0.70 = $1,400.
How do I find the original price from a sale price?
Divide by (1 − discount ÷ 100). A $1,400 item at 30% off originally cost 1,400 ÷ 0.70 = $2,000.
Adding the percentage back gives the wrong answer, because the percentage was taken from the larger original figure.
Is 30% off plus 20% off the same as 50% off?
No. The second discount applies to the reduced price, so the combined effect is 44%, not 50%. On a $2,000 item that is a $120 difference.
The formula is 1 − (1 − d₁) × (1 − d₂).
Is tax calculated before or after a discount?
After. Sales tax and GST apply to the price you actually pay, so a discount also reduces the tax.
This means the true saving is slightly larger than the discount alone — you save the tax on the discounted portion too.