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Discount Calculator — Free Online ToolThe three discount formulas
All discount problems reduce to one of three calculations. Here are the formulas and worked examples for each.
Formula 1: Find the sale price
If you know the original price and the discount percentage, the sale price is:
Sale Price = Original Price × (1 − Discount% / 100)
Example: A jacket originally priced at $120 is on sale with a 30% discount.
Sale Price = $120 × (1 − 30/100) = $120 × 0.70 = $84
You can also express this as: the discount amount is $120 × 0.30 = $36, so the sale price is $120 − $36 = $84. Both approaches give the same result.
Formula 2: Find the discount percentage
If you know both the original price and the sale price, the discount percentage is:
Discount% = (Original Price − Sale Price) / Original Price × 100
Example: A smartphone originally priced at $800 is now selling for $680. What is the discount?
Discount% = ($800 − $680) / $800 × 100 = $120 / $800 × 100 = 15%
This formula is useful for comparing deals across different stores when you know both price points.
Formula 3: Find the original price
If you know the sale price and the discount percentage, the original price is:
Original Price = Sale Price / (1 − Discount% / 100)
Example: A pair of shoes is on sale for $75 after a 25% discount. What was the original price?
Original Price = $75 / (1 − 25/100) = $75 / 0.75 = $100
This reverse calculation is especially useful when retailers show only the sale price and the discount percentage without stating the original price clearly.
How to calculate stacked discounts
Retailers sometimes offer multiple discounts applied in sequence — for example, "20% off, then an extra 10% off". A common mistake is to add the percentages together and assume the combined discount is 30%. It is not.
Stacked discounts must be applied sequentially, not added:
- Start with the original price: $100
- Apply the first discount (20%): $100 × 0.80 = $80
- Apply the second discount (10%) to the already-reduced price: $80 × 0.90 = $72
The final price is $72, which represents a total saving of $28 — equivalent to a single discount of 28%, not 30%.
The formula for the combined effective discount rate of two sequential discounts is:
Combined Discount% = 1 − (1 − D1/100) × (1 − D2/100), expressed as a percentage.
For 20% and 10%: 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28 = 28% combined discount.
Reverse-engineering original prices
A common retail practice is to advertise a product at a "sale price" without clearly stating what the original price was. If you see a product labelled "was $X, now $Y", verify the maths using Formula 2 above to confirm the stated discount percentage is accurate.
In some cases, original prices are inflated artificially before a sale to make the discount appear larger than it is. Cross-checking prices against historical pricing data or competing retailers helps you identify genuine deals.
Tips for spotting misleading retail pricing
- Verify the original price. Check whether the item was actually sold at the stated "original" price before the sale, or whether the price was artificially raised shortly before the promotion.
- Compare across retailers. A 40% discount from one retailer may still be more expensive than the regular price at another. Always check the absolute price, not just the percentage.
- Watch for stacked discount confusion. "Up to 50% off — plus an extra 20% off" is not 70% off. Apply the formulas above to find the real combined discount.
- Check the unit price for bulk deals. "Buy 2, get 1 free" is effectively a 33% discount per unit. Compare the per-unit cost against the regular single-unit price to assess the value.
- Use our Discount Calculator. Enter any two known values — original price and percentage, or original and sale price — to get the third instantly without manual arithmetic.
Frequently asked questions
How do I calculate a discount percentage?
Use the formula: Discount% = (Original Price − Sale Price) / Original Price × 100. For example, if an item costs $80 after a $20 reduction from $100: ($100 − $80) / $100 × 100 = 20%. This formula works for any currency and any price pair.
How do I find the sale price after a discount?
Sale Price = Original Price × (1 − Discount% / 100). A $100 item with a 25% discount: $100 × (1 − 0.25) = $100 × 0.75 = $75. You save $25. Use our Discount Calculator to skip the arithmetic entirely.
How do I find the original price from the sale price?
Original Price = Sale Price / (1 − Discount% / 100). If the sale price is $75 after a 25% discount: $75 / 0.75 = $100. This reverse calculation is useful when a retailer shows only the sale price and discount percentage.
Can I stack multiple discounts?
Yes, but you must apply them sequentially, not add them together. A 20% discount followed by a 10% discount on $100 gives: $100 × 0.80 = $80, then $80 × 0.90 = $72. The combined effect is a 28% total discount, not 30%. Adding percentages overstates the benefit.
Conclusion
Discount calculations reduce to three simple formulas: finding the sale price, finding the discount percentage, and finding the original price. Once you understand these formulas, you can verify any advertised deal, calculate stacked discounts accurately, and make smarter purchasing decisions. Use our free Discount Calculator to perform any of these calculations instantly — no maths required.
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