How to Calculate a Discount

Updated

To find a sale price, multiply the original price by 1 minus the discount: $80 at 25% off is $80 × 0.75 = $60. To find the original price from a sale price, divide instead: $60 ÷ 0.75 = $80. And two discounts in a row don't add up: 20% off and then 10% off is 28% off, not 30%.

Illustration: price tags marked down from $80 to $60 and from $100 to $72, and a tag reading 28%, not 30%

The three discount questions

1. What's the sale price?

Sale price = price × (1 − discount)

$80 × (1 − 0.25) = $80 × 0.75 = $60.00, saving $20.00.

For a quick estimate in your head, find 10% by moving the decimal point (10% of $80 is $8), then scale: 20% is $16, 25% is $20, 30% is $24. On coolca.lc's main calculator you can type it directly: $80 − 25% gives $60.

2. What was the original price?

If a tag says $60 after 25% off, adding 25% back gives $75, which is wrong: the 25% was taken from the original price, not from $60. Divide by 1 minus the discount:

Original price = sale price ÷ (1 − discount)

$60 ÷ 0.75 = $80.00

3. How much off is it really?

When a store shows two prices, "was $80, now $60", find the percent off by dividing the savings by the original price:

Percent off = (1 − sale ÷ price) × 100

(1 − $60 ÷ $80) × 100 = 25%

It's worth checking. Signs round generously, and "up to 50% off" usually means a few items are 50% off and most are less.

Stacked discounts and coupons

"Take an extra 10% off sale prices" is one of the most misread offers in retail. Each discount is taken from the price after the one before it, so percentages multiply rather than add:

$100 with 20% off is $80.

An extra 10% off $80 is $72.

That's 28% off in all, not 30%.

The order of two percentages doesn't change the result: 20% then 10% and 10% then 20% both come to $72. But the order of a percentage and a dollar coupon does:

Percentage first, then the dollar amount, is better for you, and it's the order most receipts apply them in. The Stacked Discounts Solver uses that order: up to two percentages, then a coupon, with the total percent off and the amount saved spelled out.

Comparing deals

Using the Discount Solver

coolca.lc's Discount Solver has three slots: Price, Off % and Sale. Fill in any two and the third shows SOLVE, so it answers all three questions above.

coolca.lc Discount Solver: $80.00 with 25% ($20.00) off is $60.00
$80 with 25% off is $60, and the line above shows the $20 saved.
  1. Open Discount.
  2. Type the original price, such as 80, and tap Price.
  3. Type the discount, such as 25, and tap Off %.
  4. Tap Sale, which shows SOLVE.

To find the original price, fill in Sale and Off % and tap Price. To find the real percent off, fill in Price and Sale and tap Off %.

Stacked Discounts

The Stacked Discounts Solver has five slots: Price, Off %, Then %, Coupon $ and Sale. Then % and Coupon $ are optional; leave either empty to skip it.

coolca.lc Stacked Discounts Solver: $100 with 20% then 10% off and a $5 coupon is $67.00, 33% ($33.00) off in all
$100 with 20% off, then 10% more, then a $5 coupon: $67, which is 33% off in all.

Questions

Is 25% off the same as paying 75%?

Yes. That's why multiplying by 0.75 gives the sale price directly. 40% off means paying 60%, so multiply by 0.6.

How do I add a percentage back after a discount?

You can't by adding the same percentage. Going from $60 back to $80 is a 33.33% increase, because $20 is a third of $60. To undo a discount, divide by 1 minus the discount, as above.

Is a 50% off coupon on top of 50% off free?

No. 50% off, then 50% off the reduced price, is 75% off in all: you pay a quarter of the original price.

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