A Discount Calculator
A discount is a percentage taken off the price before tax, so the sale price and the money saved are two separate numbers that the tag never prints. On an original price of 120 with 25 per cent off, the saving is 30.0, the sale price is 90.0, and with 8 per cent tax the bill is 97.2.
Sale price before tax
90
- Amount saved
- 30
- Final price with tax
- 97.2
- Effective discount
- 25.00%
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
sale price = original x (1 - rate); saving = original x rate
- original
- The pre-tax price before any reduction, such as 120
- rate
- Discount percentage as a decimal, so 25 per cent becomes 0.25
- saving
- Money removed from the price, equal to original x rate
- sale
- Price after the discount but before tax, equal to 90.0 here
How to check the result by hand
- 1
Establish the pre-tax price
Start from the price before tax is added, because the discount applies to that figure and not to the final bill. On a 120 item the base is 120, and the 8 per cent tax is not yet in play. If the only number you have already includes tax, divide it out first so the discount is taken from the correct base.
- 2
Turn the percentage into a decimal
25 per cent is 0.25, and the division by a hundred is the step most often skipped under time pressure. Writing 25 into the multiplication instead of 0.25 inflates the discount a hundredfold, turning a 30.0 saving into 3000.0. Convert once, deliberately, before doing any arithmetic.
- 3
Multiply to find the discount amount
120 x 0.25 = 30.0 gives the money removed from the price. This is the figure the tag refers to when it promises a saving, and it is the number to compare against other offers expressed in currency. A discount near a quarter of the price should look like roughly a quarter of the price, so check the magnitude before moving on.
- 4
Subtract to reach the sale price
120 - 30.0 = 90.0 is the price before tax, and it is what the shelf label should show. The sale price is 75 per cent of the original whenever the discount is 25 per cent, which is another quick check. Keeping the discount amount and the sale price side by side makes an arithmetic slip obvious.
- 5
Add tax back to reach the final bill
90.0 x 1.08 = 97.2 is the amount actually paid once 8 per cent tax is applied to the reduced price. The tax is charged on 90.0, so it is 7.2 rather than the 9.6 it would have been on the original 120. The discount reduced both the price and the tax, which is why the final bill sits below the original plus its full tax.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Discount page.