Finance
Discount calculator
Two discounts of 20% and 10% are not 30% off. They are 28%, and the difference is why stacked offers are advertised the way they are.
The shortcut worth learning
Instead of calculating the saving and subtracting it, calculate what you pay directly. An item at 30% off costs 70% of the original, so multiply by 0.70. One operation instead of two, and no chance of subtracting from the wrong number.
For mental arithmetic, 25% off is three quarters of the price, 33% off is two thirds, and 40% off is the price minus 40% — or 60% of it, which is easier: take 10%, multiply by six.
Why stacked discounts disappoint
Percentage discounts apply in sequence, each to the reduced price left by the last. Take 20% off $100 and you have $80; take a further 10% and you take it from $80, not from $100. The result is $72 — a 28% total discount rather than 30%.
Order does not matter: 10% then 20% gives the same $72. What matters is that the second percentage is applied to a smaller base. Retailers advertising "extra 20% off sale prices" are relying on the fact that shoppers add the numbers.
A fixed dollar amount behaves differently — it is subtracted rather than multiplied, so the order does change the outcome. Applying a $20 coupon before a 30% discount saves you less than applying it afterward. Most retailers apply percentage discounts first for exactly this reason.
Reversing a discount
To find the original price from a sale price, divide rather than multiply back up. An item marked down 40% now costing $60 was originally $60 ÷ 0.60 = $100. Adding 40% to $60 gives $84, which is wrong by a wide margin.
The same asymmetry is why a 50% loss requires a 100% gain to recover, and it is one of the most reliably misunderstood pieces of everyday arithmetic.
The reference price problem
A discount is only meaningful relative to a price someone actually paid. Practices vary, but the pattern of a brief high-price period followed by a long "sale" is common enough that consumer protection regulators in several jurisdictions require the reference price to have been charged for a minimum period before it can be used in advertising.
The practical defence is to compare the sale price against other retailers rather than against the crossed-out number, and to check price history where a tool exists for the category.
Common questions
How do I calculate 15% off in my head?
Take 10% by moving the decimal one place left, then add half of that to get the discount. On $60: $6 plus $3 is $9 off, so you pay $51. Alternatively, multiply by 0.85 directly if you have a calculator.
Is tax charged before or after the discount?
After, in essentially all jurisdictions — you are taxed on what you actually pay. Manufacturer coupons are the usual exception in some US states, where the tax may be calculated on the pre-coupon price because the retailer is reimbursed for the difference.
What does "up to 70% off" mean?
That at least one item somewhere in the sale carries a 70% reduction. It says nothing about the rest, and the deepest discounts typically apply to the least popular sizes and colours.