About Discounts
A discount is a reduction applied to the original (list) price of a product or service. Discounts are used in every industry — retail, hospitality, SaaS, B2B contracts — to move inventory, reward loyalty, incentivise volume purchases, or run promotional campaigns. Understanding how to compute them precisely matters whether you are a shopper comparing deals or a business owner setting prices.
The mathematics is simple: a discount of d% means you pay (1 − d/100) of the original price. But the three scenarios below are the ones that come up in practice — and each requires a slightly different rearrangement of the same formula.
The three discount calculations
| You know | You want | Formula |
|---|---|---|
| Original price + discount % | Sale price | Sale = Original × (1 − d/100) |
| Original + sale price | Discount % | d = (Original − Sale) / Original × 100 |
| Sale price + discount % | Original price | Original = Sale ÷ (1 − d/100) |
Worked example
A $120 jacket is on sale at 25% off:
- You pay = 120 × (1 − 0.25) = 120 × 0.75 = $90
- You save = 120 × 0.25 = $30
Working backwards: if the sale price was $90 and the original was $120, the effective discount was (120 − 90) / 120 × 100 = 25%. And if you saw a $90 ticket that said "25% off", the original price was 90 / 0.75 = $120.
Stacked discounts — and the trap
Retailers often advertise stacked discounts like "20% off, plus an extra 10% off at checkout". Many shoppers assume this means 30% off — it does not.
Stacked discounts multiply, not add:
Effective discount = 1 − (1 − d₁)(1 − d₂)
For 20% + 10%: 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28, which is 28% off, not 30%. The gap grows with the size of the discounts — 50% + 50% is only 75% off, not 100%.
| Stacked | Effective discount | Naive sum | Gap |
|---|---|---|---|
| 10% + 10% | 19% | 20% | 1% |
| 20% + 10% | 28% | 30% | 2% |
| 30% + 20% | 44% | 50% | 6% |
| 50% + 50% | 75% | 100% | 25% |
The rule to remember: an additional 10% off is 10% of the already-discounted price, not 10% of the original.
Discount vs markup — not symmetric
A common mistake is to think a 20% discount can be reversed by a 20% markup. It cannot. If a $100 item is discounted 20% to $80, and you then apply a 20% markup, you get $80 × 1.20 = $96 — not $100. You would need a 25% markup to get back to $100, because 20/80 = 25%.
This asymmetry matters for anyone setting prices or negotiating: the discount % and the required recovery % are always different numbers.
Common use cases
Shopping
Compare sale prices at a glance during a sale.
Retail Pricing
Work out the final price after applying a discount.
Promotions
Verify what a "20% + 10% off" offer actually means.
B2B Contracts
Compute volume discounts on purchase orders.
Invoicing
Work backwards from a final price to find the applied discount.
Learning
See the maths of markup, margin and discount clearly.
Privacy and accuracy
This discount calculator runs entirely in your browser. All calculations happen locally in JavaScript with no server calls. Nothing is uploaded, stored or logged — safe for confidential pricing, invoices and business data.