Sale signs are designed to create urgency and a feeling of value. But the math behind discounts is simple — and understanding it protects you from misleading pricing, lets you compare deals accurately, and is essential for any business setting prices.
The Three Core Discount Formulas
Formula 1: Find the Sale Price from a Discount Percentage
Sale Price = Original Price × (1 − Discount % / 100)
Example: A $120 jacket is on 25% discount. Sale Price = 120 × (1 − 0.25) = 120 × 0.75 = $90
Alternatively: Discount Amount = 120 × 0.25 = $30 → Sale Price = $120 − $30 = $90
Formula 2: Find the Discount Percentage from Two Prices
Discount % = ((Original Price − Sale Price) ÷ Original Price) × 100
Example: An item originally priced at $80 is on sale for $52. Discount % = ((80 − 52) ÷ 80) × 100 = (28 ÷ 80) × 100 = 35% off
Formula 3: Find the Original Price from a Sale Price and Discount %
Original Price = Sale Price ÷ (1 − Discount % / 100)
Example: A dress is $68 after a 20% discount. What was the original price? Original = 68 ÷ (1 − 0.20) = 68 ÷ 0.80 = $85
This formula is essential for verifying whether a "sale" price is actually discounted from a legitimate original price.
Quick Discount Reference Table
How much you pay at different discount levels on a $100 item:
| Discount % | You Save | You Pay |
|---|---|---|
| 10% | $10 | $90 |
| 15% | $15 | $85 |
| 20% | $20 | $80 |
| 25% | $25 | $75 |
| 30% | $30 | $70 |
| 40% | $40 | $60 |
| 50% | $50 | $50 |
| 70% | $70 | $30 |
How Stacked Discounts Work (And Why They Are Not Additive)
If a store advertises "20% off, then an extra 10% off," you might expect to pay 70% of the original price. You will actually pay more:
Step 1: $100 × 0.80 = $80 (after 20% off) Step 2: $80 × 0.90 = $72 (after 10% off)
Effective discount = 28%, not 30%.
Stacked discounts are multiplicative, not additive. The formula: Combined Discount = 1 − (1 − d₁) × (1 − d₂) = 1 − 0.80 × 0.90 = 1 − 0.72 = 28% total discount
Spotting Misleading Deals
"Up to 70% off": The headline discount applies to a tiny fraction of items. Most items may be discounted 10–15%.
Inflated original prices: Retailers sometimes raise the "original" price before a sale to make the discount appear larger. Formula 2 above lets you calculate the real discount percentage and verify it feels reasonable for the product category.
"Buy 2, get 1 free" vs "33% off each": These are mathematically equivalent — you pay for 2 and get 3. But "buy 2 get 1 free" only applies if you buy 3+ units, while a 33% discount applies to any quantity.
Calculate Any Discount Instantly
Use our Discount Calculator to handle all three formulas — find the sale price, find the discount percentage, or reverse-calculate the original price. You can also use the Percentage Calculator for any custom percentage problem.
Frequently Asked Questions
Q: How do I calculate the sale price from a discount percentage? A: Sale Price = Original Price × (1 − Discount % ÷ 100); a $120 jacket at 25% off becomes 120 × 0.75 = $90.
Q: If a store offers "20% off, then an extra 10% off," do I save 30% total? A: No — stacked discounts are multiplicative, not additive; applying 20% then 10% to $100 gives $72, an effective discount of 28%, not 30%.
Q: How can I check whether a "sale" price is a genuine discount? A: Use the reverse formula, Original Price = Sale Price ÷ (1 − Discount % ÷ 100), to back-calculate what the original price should have been and compare it to the retailer's stated original.
