Percent Off Calculator

How to use the percent off calculator

The calculator has two modes, chosen with the Calculate switch at the top.

• Discount amount (the default). Type the percent off in the left box and the original price in the right box, so the sentence reads "20 % off 50". You get the final price and how much you save.
• Percent off & Discount. Type the original price and the sale price. You get the amount you save and the percentage discount, which is handy for checking whether a "big sale" really is one.

Prices are shown with a dollar sign, but the arithmetic does not depend on the currency, so you can use the results for euros, pounds or any other money. Amounts are rounded to cents, and whole amounts are shown without the decimals. If a box is empty or zero there is nothing to work out, so the calculator asks you to fill in the numbers instead of showing a result.

How percent off is calculated

A percent off always refers to the original price. The saving is that percentage of the original, and you pay what is left.

saving = original price × percent off ÷ 100

final price = original price − saving = original price × (1 − percent off ÷ 100)

To work backwards from two prices, divide the saving by the original price:

percent off = (original price − sale price) ÷ original price × 100

Worked examples

20% off $50. The saving is 50 × 20 ÷ 100 = $10, so you pay 50 − 10 = $40. A quick way to do this in your head: 10% of $50 is $5 (move the decimal point one place), and 20% is twice that.

35% off $129.99. The saving is 129.99 × 0.35 = 45.4965, which rounds to $45.50. The final price is 129.99 − 45.4965 = 84.4935, shown as $84.49. The two rounded figures still add up to the original, 45.50 + 84.49 = 129.99.

From two prices. A jacket was $80 and now costs $60. The saving is $20, and 20 ÷ 80 = 0.25, so the discount is 25% off. With less tidy numbers, $19.99 reduced to $14.50 saves $5.49, and 5.49 ÷ 19.99 gives 27.46%.

The table shows common discounts applied to a $60 item.

Stacked discounts and sales tax

Two discounts in a row do not add up. If a shop takes 20% off and then offers an extra 10% off the new price, the second discount applies to the already-reduced amount.

combined factor = (1 − 0.20) × (1 − 0.10) = 0.72

On a $100 item you pay $72, a total discount of 28%, not 30%. The order does not matter, but you must multiply the factors rather than add the percentages.

Sales tax and VAT are normally added after the discount, because they are charged on the price you actually pay. The $50 item at 20% off costs $40; with 8% tax added the total is 40 × 1.08 = $43.20. To add or remove tax on a price, use the VAT calculator.

Common percent off tasks

• Checking a sale. Enter the old and new prices in the second mode to see the real percentage. A claim of "up to 50% off" only applies to some items.
• Comparing offers. "$15 off $60" is the same as 25% off, because 15 ÷ 60 = 0.25. Converting both offers to a percentage makes them comparable.
• Finding the original price. If you know the sale price and the percent off, divide the sale price by (1 − percent off ÷ 100). A $48 price after 20% off means the original was 48 ÷ 0.8 = $60.
• Marking prices down in your own shop. Use the first mode to set a clearance price, then check the margin with the profit margin calculator.

For a wider set of discount questions, including a discount in money terms, see the discount calculator. When the price has dropped and you simply want the size of the fall, use the percent decrease calculator.

Percent off, discount and markdown

In everyday shopping the words mean the same thing: the price is lowered by some share of the original. "Percent off" names that share, "discount" is the money you save, and retailers call the reduction a markdown.

Be careful about reversing a discount. After 25% off, a $100 item costs $75. To get back to $100 the price must rise by 25 ÷ 75, which is 33.3%, not 25%, because the increase is measured against the smaller number.

Rules about advertised reductions vary. In the European Union, for example, a price reduction announcement must refer to the lowest price the trader charged in the previous 30 days. Check the rules that apply where you shop or sell.