Discounts look simple until the maths goes the wrong way. When you are a seller, you need to know what the sale price will be. When you are a buyer, you might only know what you paid and want to verify the original price. And when a coupon stacks on a sale, neither 20% + 10% = 30% — it equals 28%. Here is how all three work.
Mode 1: Find the sale price
The standard calculation. Given an original price and a discount %, what is the final price?
Sale Price = Original Price × (1 − Discount% ÷ 100)
Savings = Original Price − Sale Price
Savings% = Discount% (same as the input)
Example: $120 item at 25% off
Sale Price = $120 × (1 − 0.25) = $120 × 0.75 = $90.00
Savings = $120 − $90 = $30.00Mode 2: Find the original price (reverse calculation)
You know the price you paid and the discount that was applied. What was the original price? This is the formula retailers do not advertise.
Original Price = Sale Price ÷ (1 − Discount% ÷ 100)
Example: you paid $67.50 and know it was 25% off
Original = $67.50 ÷ (1 − 0.25) = $67.50 ÷ 0.75 = $90.00This is useful for verifying inflated "original" prices in clearance sales, or for calculating the pre-discount cost when you only have the invoice showing the discounted amount.
Mode 3: Find the discount percentage
You know both prices but want the exact discount rate — useful for comparing across different products or negotiations.
Discount% = (Original − Sale) ÷ Original × 100
Example: original $120, you pay $84
Discount% = ($120 − $84) ÷ $120 × 100 = $36 ÷ $120 × 100 = 30%How stacked discounts actually work
When two discounts apply to the same item — a seasonal sale and a loyalty coupon, for example — they are applied sequentially, not added together.
20% sale + 10% loyalty coupon on a $100 item:
Step 1: Apply 20% → $100 × 0.80 = $80.00
Step 2: Apply 10% to new price → $80 × 0.90 = $72.00
Effective discount = ($100 − $72) ÷ $100 = 28%
NOT 20% + 10% = 30%The effective discount from stacking is always less than the sum of the two discounts. The formula is: 1 − (1 − D1) × (1 − D2). For 20% + 10%:1 − 0.80 × 0.90 = 1 − 0.72 = 28%.
Retailers use sequential discounting deliberately — "extra 20% off sale prices" sounds like 40% off but delivers less. The stacked discount calculator shows both the effective rate and the mathematically correct sum for comparison.
Worked examples for sellers
| Scenario | Original | Discount | Sale Price | Effective % |
|---|---|---|---|---|
| Flash sale | $199.99 | 30% | $139.99 | 30.0% |
| Bundle (5 units) | $49.99 × 5 | 10% + 5% | $213.71 | 14.5% |
| Clearance | $89.00 | 40% | $53.40 | 40.0% |
| VIP + sale | $250 | 25% + 15% | $159.38 | 36.25% |
Frequently asked questions
Is 30% off the same as 10% off applied three times? No. Three sequential 10% discounts give 1 − 0.9³ = 27.1% effective discount, not 30%.
How do I find the original price after a sale has ended? Switch to "Find Original Price" mode, enter the sale price you paid and the percentage that was applied. The formula works regardless of when the sale happened.
What is markup vs discount? A markup increases a cost price to a retail price. A discount reduces a retail price for a sale. They use different base values — markup uses cost, discount uses original retail price.
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