Discount Calculator

The basic discount formula behind the discount calculator

A discount removes a percentage of the original price. To turn a discount percentage into a sale price, first convert the percentage to a decimal fraction by dividing by 100, then subtract that fraction from 1 to get the fraction of the price you actually keep. Multiply the original price by that fraction.

Worked example. An item is listed at 100 with a 20% discount. Convert 20% to a decimal: 20 ÷ 100 = 0.20. The fraction kept is 1 − 0.20 = 0.80. The sale price is 100 × 0.80 = 80. The amount saved is the difference between the two prices, 100 − 80 = 20, which also matches 20% of 100 directly.

Working backward uses the same relationship in reverse. If you know the sale price and the discount percentage, divide the sale price by the fraction kept to recover the original price.

Using the same numbers, 80 ÷ 0.80 = 100, which correctly returns the original price from the example above.

Percent off vs. a fixed amount off

Not every discount is a percentage. A store coupon, a mail-in rebate, or a “$15 off your purchase” promo removes a flat dollar amount instead, regardless of what the item costs. The math is simpler than a percent-off discount, but it behaves very differently as the price changes, which is why this calculator keeps the two as a separate toggle rather than folding one into the other.

Worked example. A $60 item has a $15-off coupon applied. The sale price is $60 − $15 = $45, and the amount saved is exactly the coupon's face value, $15. Expressed as a percentage of the original price for comparison, $15 off $60 works out to 25% off, but that percentage is just a side effect of this particular price; the same $15 coupon on a $150 item would only be a 10% effective discount, since a fixed amount off does not scale with price the way a percentage does.

How to work out percentage off, step by step

To work out percentage off, turn the percentage into a decimal, multiply it by the price to get the amount off, and subtract that amount from the price. That is how to take percentage off any price, and it is the same arithmetic a percent off calculator or a percentage off calculator runs. For 20 percent off 40, the decimal is 0.20, the amount off is 40 × 0.20 = 8, and the sale price is 40 − 8 = 32. Put another way, you pay 80 percent of 40, and 0.80 × 40 is also 32. A 30 percent discount on 50 takes off 15 and leaves 35.

In the calculator above, that example is three entries: the original price 40, the percent-off option, and a discount of 20. The result shows the sale price of 32 and the amount saved of 8, with the substitution written out underneath. Switch to the fixed amount option for a coupon, or fill the second discount field for a stacked offer, and the same panel updates the same way.

Many people search for how do you do percentages off, or how do you figure percentage off, because the wording trips them up. “Percent off” is the share you subtract, not the share you pay: 25 percent off means you pay 75 percent of the price. Keeping that distinction straight removes most of the mistakes.

Finding the percentage off from two prices

When you know both prices and want to calculate the percentage off, subtract the sale price from the original price, divide by the original price, and multiply by 100. A jacket marked down from 80 to 60 is (80 − 60) ÷ 80 = 0.25, which is 25 percent off. This is how to find percent off when all you have is a before and after price, and it is what a discount percentage calculator does.

Always divide by the original price. Dividing the 20 saved by the sale price of 60 instead gives a misleading 33 percent, which is the most common slip when working this out by hand.

Reading bare numbers like 20 off 50.00

Shoppers often type two numbers with no units, such as 20 off 50.00 or 30 off 25, and leave the meaning to context. If a sign says 20% off, the first number is a percentage; if a coupon says $20 off, it is a dollar amount. The table shows both readings side by side, so you can see how far apart the answers can be.

Mental shortcuts for percent off

Ten percent is the anchor: move the decimal point one place left, so 10% of 45 is 4.50. Twenty percent is double that, twenty-five percent is a quarter of the price, thirty percent is three times the ten percent figure, and fifty percent is half. To take 30% off 60, find 10% (6), triple it (18), and subtract: 60 − 18 = 42. The shortcut is accurate enough for checking a price tag before you reach the register, and the calculator above handles anything less tidy.

The reference table applies the same arithmetic to common price points, every cell computed as price × (1 − discount).

Sales tax and discounts: which comes first

In most places sales tax is charged on the discounted price, so a discount also reduces the tax. An item at 100 with 20% off is 80, and at an 8% tax rate the tax is 6.40 and the total 86.40, instead of 108 without the discount. Rules can differ by region and by coupon type, for example when a manufacturer coupon is treated as a payment rather than a price cut, so check the receipt when the exact total matters.

Stacked discounts: why 20% then 10% off is not 30% off

Stores often advertise two discounts applied one after another, such as a seasonal sale plus an extra coupon at checkout. It is tempting to add the two percentages together and assume “20% off, then 10% off” means “30% off”, but that is not how it works. Each discount is applied to whatever price is current at that step, not to the original price a second time, so the second discount ends up acting on a smaller number than the first one did.

Worked example. Start with an original price of 100. Apply the first discount of 20%: 100 × (1 − 0.20) = 100 × 0.80 = 80. Now apply the second discount of 10% to that new price of 80, not to the original 100: 80 × (1 − 0.10) = 80 × 0.90 = 72. The final sale price is 72, and the total amount saved is 100 − 72 = 28. Expressed as a single combined percentage, that is a 28% discount overall, not the 30% you would get by simply adding 20% and 10% together.

The reason the combined discount always comes out a little smaller than the naive sum is that multiplying two “keep” fractions, 0.80 and 0.90 in this case, gives 0.72, while subtracting the two discount fractions directly would give 1 − 0.20 − 0.10 = 0.70. The two numbers are close but not equal, and the gap grows larger as the discounts get bigger. The order the two discounts are applied in does not change the final answer, since multiplication gives the same result either way, but it is still worth calculating the exact combined percentage rather than estimating it by eye.