Discount Calculator

Working out a sale price

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

A 1,000 item at 20% off: 1,000 × 80 ÷ 100 = 800.

In your head, work from 10%. Move the decimal one place left to get 10% of the price, then scale it:

Discount	How	On 1,000
10% off	Take away 100	900
20% off	Take away twice that	800
25% off	Take away a quarter	750
33% off	Take away a third	670
50% off	Halve it	500

The stacked-discount trap

“20% off, then an extra 10% at the till” is not 30% off. It is 28%.

The second discount comes off the already reduced price:

1. 1,000 less 20% → 800
2. 800 less 10% → 720
3. You saved 280 out of 1,000 → 28% off

The gap grows as the discounts get bigger:

Stacked offer	Sounds like	Actually is
20% + 10%	30%	28%
30% + 20%	50%	44%
50% + 20%	70%	60%
50% + 50%	100%	75%

Two 50% discounts can never make something free — each one only ever halves what is left. This is legal, standard retail practice, and worth a few seconds of arithmetic before you decide an offer is exceptional.

One small consolation: the order does not matter. 20% then 10% gives exactly the same price as 10% then 20%.

Going backwards: what was it before?

A jacket is 910 in the sale, marked “30% off”. What was the original price?

Divide, do not add.

• Wrong: 910 + 30% = 1,183
• Right: 910 ÷ 70 × 100 = 1,300

Adding 30% fails because the discount was taken from the higher original price, not from the sale price you are holding. The general rule: divide the sale price by (100 − discount), then multiply by 100.

This is also how you check whether an “original price” is real. If the claimed before-price does not match the arithmetic, the discount on the label is not the discount you are getting.

Tax comes after the discount

In practically every system, sales tax applies to what you actually pay, not the ticket price. A 1,000 item at 20% off with 18% tax:

1. Discount: 1,000 → 800
2. Tax: 18% of 800 = 144
3. Total: 944

Taxing first and then discounting would give the same total here, but not once a tax-free allowance or an exempt category is involved — so the order stated on the receipt matters.

Reading a sale honestly

• “Up to 70% off” means one item somewhere is 70% off. The rest are not.
• “Was 2,000, now 1,000” — check whether it ever sold at 2,000. In many countries the before-price must have been charged for a set period, and enforcement is patchy.
• Buy one get one free is 50% off, if you actually want two.
• Buy two get the third free is 33% off, on three items.
• “Extra 10% for members” is usually stacked, so see the table above.

The useful question is never “how big is the discount?” but “what is this costing me, and would I buy it at that price without the sign?”