Discount Calculator

How discounts are worked out

The calculator handles the four situations you meet when shopping:

• Percent off — the discount is a share of the price: 25% off $80 takes $20 off.
• Amount off — a fixed sum comes off, such as a $15 coupon. The calculator also shows what percentage that is, so you can compare it with a percent-off offer.
• Stacked — one discount after another, as in “20% off everything, plus an extra 10% at checkout”. The second discount is taken from the already reduced price, so the total is always less than the two percentages added together.
• Reverse — you know the sale price and the percentage and want the original price.

If you enter a sales tax rate, it is added to the price after the discount. Amounts are rounded to the cent at each step, the way a till rounds them.

Discount formulas

P

original price

d

discount as a decimal (25% → 0.25)

t

sales tax rate as a decimal (8.25% → 0.0825)

For a fixed amount off, the sale price is simply the original price minus the amount, and the discount as a percentage is the amount divided by the original price, times 100. For more percentage questions, such as “what percent is 15 of 80?”, use the percentage calculator.

Worked examples

A jacket costs $80.

1. 25% off: $80 × 0.25 = $20 off, so you pay $60.00.
2. $15 off instead: $80 − $15 = $65.00. That is $15 ÷ $80 = 18.75% off — a worse deal than 25%.
3. 20% off, then an extra 10%: $80 × 0.80 = $64.00, then $64.00 × 0.90 = $57.60. You save $22.40, which is 28% of $80 — not 30%, because the extra 10% is taken from $64, not from $80.
4. With 8.25% sales tax on the $60.00 sale price: $60.00 × 0.0825 = $4.95, so the total is $64.95.
5. Reverse: a tag says $60 after 25% off. The original price was $60 ÷ (1 − 0.25) = $60 ÷ 0.75 = $80.00.

Note the trap in the last example: adding 25% back to $60 gives $75, not $80. The 25% was a share of the original price, so you have to divide by 0.75 to undo it.

Things to keep in mind

• Check the “original” price. A discount is only a saving if the price it is taken from was real. In the US, the Federal Trade Commission’s pricing guides say a former price used in a comparison should be one the item was actually offered at, openly and for a reasonably substantial period.
• Tax rules vary. The calculator taxes the price after the discount, which is how a shop’s own discount is usually treated. Manufacturer coupons can be different: Minnesota, for example, charges sales tax on the full price before a manufacturer’s coupon is taken off. Check your state’s rules if your receipt doesn’t match.
• Prices that already include tax. In countries where shelf prices include VAT or GST, leave the tax field blank: the discount already applies to the tax-inclusive price.
• Rounding. Shops round each discount to the cent and may round in different ways, so a receipt can differ from the calculation by a cent.