How to calculate a discount: sale price, percent off, original price

To find a sale price, multiply the original price by 1 minus the discount written as a decimal: 80 with 20% off is 80 × 0.80 = 64. To find the percentage off, take the sale price from the original and divide by the original. To find the original price from a sale price, divide by 1 minus the discount, not multiply by 1 plus it.

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The three directions at a glance

In each formula, d is the discount as a percentage, so 20% off gives d = 20.

You know	You want	Formula	Example	Answer
Price and % off	Sale price	Price × (1 − d ÷ 100)	80 with 20% off	64
Original and sale price	% off	(Original − Sale) ÷ Original × 100	120 and 84	30% off
Sale price and % off	Original price	Sale ÷ (1 − d ÷ 100)	90 after 25% off	120

How do I work out a sale price from a percentage off?

Multiply the price by 1 minus the discount. For 80 at 20% off, the multiplier is 0.80, so the sale price is 80 × 0.80 = 64, and the saving is 16.

The mental shortcut is to find the discount and subtract it. 10% of 80 is 8, so 20% is 16, and 80 − 16 = 64. For 25% off 120, a quarter of 120 is 30, so the sale price is 120 − 30 = 90.

In the discount calculator, enter the price and the discount percentage in Sale price mode. It shows the sale price and the amount you save.

How do I work out the percentage off from two prices?

Subtract the sale price from the original, divide by the original and multiply by 100. From 120 to 84, the saving is 36, and 36 ÷ 120 × 100 = 30%. The mental shortcut is to find 10% of the original first: 10% of 120 is 12, and 36 is three lots of 12, so 30%.

The common mistake is dividing by the sale price. 36 ÷ 84 is 42.9%, which uses the wrong base. The discount is a share of what the item cost before the sale.

In the discount calculator, switch to % off, enter the original price and the sale price, and read the percentage and the amount saved. If the sale price is higher than the original, the calculator shows the change as a percentage more and an extra cost.

How do I find the original price from a sale price?

Divide the sale price by 1 minus the discount. A sale price of 90 after 25% off gives 90 ÷ 0.75 = 120. Check it by taking 25% off 120: 120 × 0.75 = 90.

The mistake is to add the discount back on: 90 × 1.25 = 112.50. That is wrong, because the 25% was taken from the original 120, not from the sale price. The table shows the divisor for common discounts, using a sale price of 72:

Discount	Multiplier (1 − d ÷ 100)	Original = 72 ÷ multiplier
10%	0.90	80
20%	0.80	90
25%	0.75	96
50%	0.50	144

The discount calculator works forward from an original price, and backward from two prices. It does not start from a sale price and a percentage, so use the formula here. To check your answer with the percentage calculator, enter 25 and 120 in What is X% of Y. The result is 30, and 120 less 30 is 90, the sale price.

Two discounts and sales tax

Two discounts in a row multiply rather than add. 20% off and then 10% off is 0.80 × 0.90 = 0.72, which is 28% off, not 30%. The stacked discounts guide covers the full sum, and the discount calculator's second discount option works it out in one step.

Sales tax is a separate step, and the calculator adds it after the discount. Take 80 with 20% off and 20% tax. The sale price is 64, the tax is 12.80, and the total to pay is 76.80.

A percentage off is the same before and after a tax that applies at a fixed rate. 100 net with 20% off is 80 net, and with 20% VAT added that is 96. A 120 price that already includes 20% VAT, with 20% off, is 96 as well. The percentage is 20% either way, but the cash saving is 20 before tax and 24 with it. For how to take VAT out of a shelf price, see how to add or remove VAT from a price, or use the VAT calculator.

Steps for any discount question

1. Write down the numbers you have: the original price, the sale price or the discount percentage.
2. Pick the direction that matches what you need, using the table above.
3. Use that formula, and work in the order shown.
4. Check by reversing. Apply the discount to the answer you got, or take the percentage from the price and see whether you get the other number back.

How to do it with fixmint

1. Under What to find, choose Sale price to find a price, or % off to find the discount.
2. For Sale price, type the Price and the Discount %. For % off, type the Original price and the Sale price.
3. Tick Second discount, taken off the sale price or Add sales tax after the discount if the offer has them.
4. Read the sale price and the amount saved. A sale price above the original shows as a percentage more.

Edge cases

• Discounts over 100%. A discount above 100% would make the price negative, so the discount calculator accepts 0 to 100%.
• Sale price above the original. That is a negative discount, which is a price increase. The calculator reports it as an amount more.
• Rounding. The discount calculator works out the sale price in one step and rounds it to the cent once. Do the same by hand: calculate the full answer first, and round at the end.
• Reference prices. A "was" price is only useful if the item really sold at it. Compare the sale price with the price you saw before the sale, and check the rules where you shop.

Frequently asked questions

What is 25% off 120?

120 × 0.75 = 90, so you pay 90 and save 30.

How do I work out the original price before a discount?

Divide the sale price by 1 minus the discount. A sale price of 90 after 25% off came from 90 ÷ 0.75 = 120.

Is 50% off then 50% off the same as 100% off?

No. 0.50 × 0.50 = 0.25, so the final price is a quarter of the original, which is 75% off. From 100, the first half-off gives 50 and the second gives 25.

Is sales tax worked out before or after the discount?

The discount calculator adds the tax after the discount. Shops can apply the discount and the tax in different orders, so check the receipt for the final figure.