Discount calculator

The math behind a sale price

Three short formulas give all the answers:

• Price after discount = price × (1 − discount ÷ 100)
• You save = price × discount ÷ 100
• You pay = price after discount × (1 + tax ÷ 100)

Take an $80 jacket at 25% off where sales tax is 8%. The discount is 80 × 0.25 = $20, so the price after discount is $60. Tax adds 60 × 0.08 = $4.80, and you pay $64.80. You save shows $20, the discount alone; tax is not counted as a saving there.

A quick check in your head: 25% off means paying 75%, so multiply by 0.75. 30% off a $120 item is 120 × 0.7 = $84. Thinking “what share do I pay” instead of “what comes off” turns every discount into one multiplication.

Why two discounts do not add up

“20% off, plus an extra 10% at the register” is not 30% off. The second discount is taken from the already reduced price:

• $100 − 20% = $80
• $80 − 10% = $72

That is 28% off in total. The rule is to multiply the shares you pay at each step: 0.8 × 0.9 = 0.72, so you pay 72% and save 28%. A “50% off, then a further 20% off” clearance sale is 0.5 × 0.8 = 0.4, or 60% off, not 70%.

The order of two percentage discounts does not matter, but a fixed-amount coupon and a percentage do. On a $100 item, $10 off and then 20% off leaves $72; 20% off and then $10 off leaves $70. Stores decide which comes first, so read the fine print.

To stack discounts in Octoolo, run the first one, then type the Price after discount back in as the new Price with the second percentage. Or type 100 − 20% − 10% into the calculator, which takes each percentage from the running total and shows 72.

Tax, VAT and the order of things

With a percentage discount and a percentage tax, the order makes no difference to the total. 20% off $100 and then 8% tax is $86.40, and 8% tax first and then 20% off is $86.40 too, because multiplication does not care about order. Octoolo adds tax last because receipts usually show the discount first and the tax on the reduced price.

What does matter is whether tax is in the price at all. In the US and Canada, shelf prices usually leave sales tax out, so enter your rate in Tax. In the UK, the EU, Australia and many other places, prices shown to shoppers include VAT or GST; enter 0 and the answer is already what you pay.

One more case: a sale price you only know after the fact. If you paid $60 after 25% off, the original was 60 ÷ 0.75 = $80. Dividing gets you there; adding 25% back to $60 gives only $75.

Is it really a deal?

Different offers phrase the same discount in different ways. Turning each into one percentage makes them comparable:

• Buy one, get one 50% off on two $20 items: you pay $30 for $40 of goods, 25% off overall.
• Buy one, get one free: 50% off, but only if you wanted two.
• Buy 3, pay for 2: a third off, about 33%.
• $15 off orders over $75: 20% off at exactly $75, and a smaller share as the order grows.
• Spend $50, save $10: if your basket is $35 and you add a $15 item just to qualify, you pay $40 instead of $35.

The percentage calculator turns any before-and-after pair into a percent change, so you can check a “was $80, now $60” label in a second: −25%.