Discount calculator

The sale price is the original price times the share you still pay:

sale price = original price × (1 − discount / 100)

Your savings are the original price minus the sale price. The calculator shows both to the cent.

When two discounts are stacked, such as 30% off the ticket price and then an extra 10% off at the register, the second discount applies to the already reduced price. So the multipliers are multiplied, not the percentages added:

sale price = original × (1 − d₁/100) × (1 − d₂/100)

The calculator handles this automatically and tells you the true combined discount.

A pair of headphones costs $79.99 and is 20% off.

1. Multiplier: 1 − 20 / 100 = 0.8.
2. Sale price: 79.99 × 0.8 = $63.99 (63.992, rounded to the cent).
3. You save: 79.99 − 63.99 = $16.00.

Mental math shortcut: 10% of $79.99 is about $8, so 20% is about $16. Sales tax, if any, is added to the sale price, not the original, so the discount also lowers the tax you pay.

A jacket is $120, marked 30% off, with an extra 10% off at checkout.

1. After the first discount: 120 × 0.7 = $84.
2. After the second: 84 × 0.9 = $75.60.
3. You save $44.40, which is 37% of the original price.

The combined discount is 37%, not 40%, because the extra 10% only applies to $84. The order doesn't matter: 10% first and then 30% gives the same $75.60. Retailers know that "30% + 10%" sounds like 40%, so it pays to run the numbers.

If you only see the original and the sale price, the discount percentage is:

percent off = (original − sale) / original × 100

For example, a $120 item on sale for $90: (120 − 90) / 120 × 100 = 25% off. This is handy when a store shows "was $120, now $90" without a percentage, or when you want to compare two sales that use different wording, such as "$30 off" and "25% off" on items with different prices.

To work backwards from a sale price to the original, divide: $63.99 / 0.8 = $79.99.

Quantity deals can be turned into a percentage too, as long as you need all the items:

Deal	Effective discount per item
Buy one, get one free (BOGO)	50%
Buy one, get one 50% off	25%
Buy two, get one free	33.33%
Buy three, get one free	25%

If you didn't need the extra item, your real discount on the one you wanted is 0%, and a smaller straight discount would have been the better deal.

Coupons come in two flavors: a percentage ("20% off") and a fixed amount ("$15 off a purchase of $75 or more"). To compare them, turn the fixed amount into a percentage of what you'll actually spend. $15 off a $75 order is 20% off; on a $100 order it is only 15%. In general, a percentage coupon is worth more on a large purchase and a fixed-amount coupon on a small one. The break-even point is where the two give the same savings: for 20% versus $15, that's a $75 order.

When a store allows both, apply the percentage discount first if you get to choose: 20% off $100 is $80, then $15 off is $65. The other way round, $15 off first gives $85, then 20% off gives $68.

• Check the reference price. A big percentage off an inflated "compare at" price may not be a real saving. Comparing with the price the item actually sold for recently, or at other stores, tells you more.
• Mind sales tax. In the US, sales tax is calculated on the discounted price in most cases. A manufacturer's coupon can be treated differently from a store discount in some states, so check your receipt.
• Round at the end. Registers round each line to the cent, so a stacked discount can differ by a cent from this calculator.

The values you enter are saved in the link, so the Share button lets you send a deal to someone else with the math already done.

For a price list in Excel or Google Sheets, with the original price in A2 and the discount percentage in B2 (entered as 20 for 20%):

• Sale price: =A2*(1-B2/100)
• Savings: =A2*B2/100
• Two stacked discounts in B2 and C2: =A2*(1-B2/100)*(1-C2/100)
• Percent off from two prices (original in A2, sale in B2): =(A2-B2)/A2*100

Round to the cent with ROUND(…, 2) if the result goes onto price tags. For a store-wide sale, putting the discount in a single cell and referring to it with an absolute reference (such as $E$1) lets you change every price at once.