How to Calculate a Discount

Sales are engineered to make you do arithmetic badly. The signs are large, the maths is just awkward enough to skip, and the discount structure is often designed so the number in your head is bigger than the number on the receipt. Here is how to calculate a discount properly — including the stacked deals that almost everyone gets wrong.

The basic formula

The amount you save is the price times the percentage. The price you pay is what is left. In one step:

Sale price = price × (1 − discount ÷ 100)

So $100 at 20% off is 100 × 0.80 = $80, saving $20.

A $59.99 item at 15% off is 59.99 × 0.85 ≈ $50.99.

The useful mental reframing: do not calculate what you save — calculate what you pay. For 30% off, you pay 70%. For 40% off, you pay 60%. One multiplication instead of a subtraction, and it is the number you actually care about.

Mental shortcuts

Find 10% by moving the decimal point one place left, then build from it:

• 10% of $80 = $8
• 20% = double it → $16
• 5% = half of 10% → $4
• 15% = 10% + 5% → $12
• 25% = a quarter → divide by 4 → $20
• 75% = three quarters → $60

And one genuinely delightful trick: percentages are reversible. 8% of 50 is the same as 50% of 8 — both are 4. When a calculation looks awkward, flip it. 18% of 50 is hard; 50% of 18 is obviously 9.

Working backwards from the sale price

A sign says “was $100, now $80.” What percentage is that? Or you know the final price and want the original.

Discount % = (saving ÷ original) × 100. Saving $20 on $100 = 20% off.

To recover the original price from the sale price, divide — do not add the percentage back:

Original = sale price ÷ (1 − discount ÷ 100)

An item is $80 after 20% off. The original was 80 ÷ 0.80 = $100.

The common error is to take 20% of $80 ($16) and add it back, arriving at $96. That is wrong, because the discount was 20% of the originalprice, not of the reduced one. This mistake is worth knowing about, because it is exactly how a retailer can inflate a “was” price and have the maths appear to check out.

The stacked-discount trap

Here is the big one. “20% off, plus an extra 10% at the till” is not 30% off.

Percentages do not add, because each one applies to a different base:

• Start: $100
• After 20% off: $80
• After a further 10% off that: $72

You saved $28 — an effective 28%, not 30%. The second discount was taken from $80, not from $100, so it was worth only $8 rather than $10.

The general rule: stacked discounts always come out slightly less than their sum, and the gap widens as the discounts get bigger. “50% off plus another 50% off” is not free — it is 75% off. The item still costs a quarter of its original price.

There is a neat formula if you want it: the combined multiplier is 0.8 × 0.9 = 0.72, so you pay 72%. Multiply the “what you pay” fractions together, and the order does not matter — 20% then 10% gives exactly the same result as 10% then 20%.

The same effect, elsewhere

This is not just a shopping curiosity. The identical arithmetic catches people in more serious places:

A 10% pay cut followed by a 10% pay rise does not restore your salary. $100 → $90 → $99. You are permanently 1% down, and it looks like it should have been neutral.

The same applies to investments: a 50% loss requires a 100% gain to break even, not a 50% gain. Losses hurt more than equivalent-sounding gains help — which is one of the most important facts in personal finance, and it is the same maths as the discount stack.

Sale tactics worth seeing through

• Inflated “was” prices. A 60% discount from a price nobody ever paid is not a discount. Check what the item actually sold for before the sale.
• “Up to 70% off.”“Up to” is doing all the work. One item is 70% off; most are 10%.
• Buy one get one 50% off. That is 25% off overall, not 50% — and only if you wanted two.
• Spend $100, save $20. A 20% discount only if you were already going to spend exactly $100. Spending an extra $40 to unlock it is not saving.

And the oldest truth in retail: a 40% discount on something you do not need is not a 40% saving. It is a 60% expense.

Discounts and tax

Discounts are normally applied before sales tax, so calculate the sale price first and add tax to the reduced amount. A pleasant side effect is that a bigger discount also lowers the tax you pay, so your total saving is slightly larger than the discount alone.

Frequently asked questions

How do I calculate 20% off? Multiply by 0.8 — you pay 80% of the price.

Is 20% + 10% the same as 30% off? No. It is 28% off, because the second discount applies to the already-reduced price.

How do I find the original price? Divide the sale price by (1 − discount as a decimal). $80 after 20% off → 80 ÷ 0.8 = $100.

Is 50% off then 50% off free? No — it is 75% off. You still pay a quarter.

Calculate a discount now

Use our Discount Calculator to get the sale price, your saving and the true effective rate — including stacked discounts, which it applies in the correct order. For general percentage maths, see the Percentage Calculator and our guide on how to calculate percentages.