How to calculate a discount
A percentage discount reduces the original price by a fraction. The math is two simple multiplications: find the discount amount, then subtract.
discount = original price × (discount % / 100)final price = original price − discountEquivalently, multiply directly by the "keep" fraction:
final price = original price × (1 − discount % / 100)A 30% off coupon on a $80 item gives a discount of $24 and a final price of $56 — or, in one step, $80 × 0.70 = $56.
Mental math shortcuts
- 50% off — halve the price.
- 25% off — divide by 4, then subtract from full price (or pay 75%).
- 33% off — divide by 3, then subtract (or pay two-thirds).
- 20% off — divide by 5, then subtract (or pay 80%).
- 10% off — move decimal one place left to find the discount.
- 15% off — 10% plus half of 10%.
Stacked discounts
When two discounts apply, they multiply rather than add. A "30% off" coupon on a "20% off" sale gives:
final = price × 0.80 × 0.70 = price × 0.56 → 44% total discount, not 50%Stores sometimes word it as "extra 30% off sale prices" specifically because customers expect the bigger total. Always compute the multiplier explicitly when discounts stack.
Discount vs total saved
The discount percentage describes per-item savings. To calculate total savings on a multi-item purchase, multiply the discount amount by quantity:
total saved = discount × quantityA "buy 5 at 40% off $25 each" deal saves $10 × 5 = $50 — provided you actually needed five.
Reverse calculation — finding the original price
If you only know the sale price and the discount percentage, recover the original price by dividing:
original = sale price / (1 − discount % / 100)A jacket on sale for $112 at 30% off was originally $112 / 0.70 = $160.
Discount math after tax
In most jurisdictions, sales tax applies to the discounted price, not the original. The correct order is:
- Discount first:
$100 − 30% = $70 - Tax on discounted price:
$70 × 1.08 = $75.60
Applying tax before the discount gives the same final answer because multiplication is commutative — but tax is calculated by the register on the post-discount amount in the US, so that is the right mental model.
Is the deal actually good?
A few useful sanity checks before celebrating a discount:
- Reference price check. Is the "original price" the manufacturer's MSRP or an inflated tag chosen for the sale? Sites like CamelCamelCamel show Amazon price history.
- Need test. A 70% discount on something you wouldn't buy at full price still costs 30% of full price for no value.
- Unit price comparison. "10% off the family-size box" may still be more expensive per unit than the standard size at full price.
- Bundling. Quantity discounts often only pay off if you'd consume the full quantity before it expires.