How to Calculate a Discount: Sale Prices, Percentage Off, and Savings
Sales, coupons, clearance events, promotional codes — discounts are everywhere, and knowing how to calculate them quickly puts you in control of your spending. Whether you are standing in a store trying to figure out what 35% off means for your total, stacking a coupon on top of a sale price, or comparing unit prices to find the actual best deal, this guide gives you the formulas, the shortcuts, and the common traps to avoid.
The Basic Discount Formula
Every discount calculation starts from the same core formula. Once you understand it, everything else is a variation.
Savings = Original Price × (Discount Percentage ÷ 100)
Sale Price = Original Price − Savings
Or combined into one step:
Sale Price = Original Price × (1 − Discount Percentage ÷ 100)
A Simple Example
A pair of shoes is originally priced at $120 and is on sale for 25% off. Here is the math:
- Savings = $120 × 0.25 = $30
- Sale Price = $120 − $30 = $90
Using the one-step version: $120 × 0.75 = $90. Both approaches give the same answer. The one-step version is faster because you simply multiply by the complement of the discount (100% − 25% = 75%, or 0.75).
Working Backward: Finding the Discount Percentage
Sometimes you see a sale price tag but not the discount percentage. To calculate it:
Discount Percentage = ((Original Price − Sale Price) ÷ Original Price) × 100
If a jacket was $200 and is now marked at $140:
- Discount = ($200 − $140) ÷ $200 = $60 ÷ $200 = 0.30
- Discount Percentage = 0.30 × 100 = 30% off
Finding the Original Price from a Sale Price
If you only know the sale price and the discount percentage, you can find the original price:
Original Price = Sale Price ÷ (1 − Discount Percentage ÷ 100)
A shirt is on sale for $42 at 30% off. What was the original price?
- Original Price = $42 ÷ (1 − 0.30) = $42 ÷ 0.70 = $60
Our Discount Calculator handles all three variations — finding the sale price, the discount percentage, or the original price — so you never have to do the arithmetic by hand.
How Stacking Discounts Actually Works
Stacking discounts — applying multiple discounts to the same item — is one of the most misunderstood concepts in shopping math. Many people assume that a 20% off coupon combined with a 15% off sale equals 35% off. It does not.
Why Discounts Compound Instead of Add
When you apply the first discount, the price drops. The second discount is then applied to the already-reduced price, not the original. Each successive discount works on a smaller base, so the combined effect is always less than the sum of the individual percentages.
Let's walk through a concrete example. A kitchen appliance costs $200. The store has a 20% off sale, and you also have a 15% off coupon.
Step 1: Apply the First Discount
$200 × (1 − 0.20) = $200 × 0.80 = $160
Step 2: Apply the Second Discount to the Reduced Price
$160 × (1 − 0.15) = $160 × 0.85 = $136
Actual Combined Discount
You paid $136 instead of $200, a savings of $64. The actual discount percentage is $64 ÷ $200 = 32%, not 35%. The formula for the combined discount is:
Combined Discount = 1 − (1 − d1) × (1 − d2)
Where d1 and d2 are the decimal forms of each discount. For 20% and 15%:
Combined = 1 − (0.80 × 0.85) = 1 − 0.68 = 0.32 = 32%
Does the Order Matter?
Mathematically, no. Applying 15% first and then 20% gives the same result: $200 × 0.85 × 0.80 = $136. Multiplication is commutative, so the order of the discounts does not change the final price. Some stores may have policies about which discount is applied first, but the math works out the same either way.
Common Stacking Scenarios
| Discount 1 | Discount 2 | Perceived Total | Actual Total | On $100 Item |
|---|---|---|---|---|
| 10% | 10% | 20% | 19% | $81.00 |
| 20% | 10% | 30% | 28% | $72.00 |
| 20% | 15% | 35% | 32% | $68.00 |
| 20% | 20% | 40% | 36% | $64.00 |
| 25% | 20% | 45% | 40% | $60.00 |
| 30% | 20% | 50% | 44% | $56.00 |
| 50% | 20% | 70% | 60% | $40.00 |
The gap between the perceived total and the actual total gets larger as the discounts increase. Two 50% off discounts do not give you an item for free — they give you 75% off ($100 × 0.50 × 0.50 = $25).
Sales Tax on Discounted Items
After calculating the discounted price, you still need to account for sales tax to know your actual out-of-pocket cost. In the United States, sales tax is almost always applied to the post-discount price at the point of sale.
The formula for the final price with tax is:
Final Price = Sale Price × (1 + Tax Rate ÷ 100)
Example With Discount and Tax
A $150 jacket is 40% off. Your local sales tax is 8.25%.
- Sale Price = $150 × 0.60 = $90
- Tax = $90 × 0.0825 = $7.43
- Final Price = $90 + $7.43 = $97.43
Note that the tax is calculated on $90, not $150. This saves you $4.95 in tax compared to buying at full price ($150 × 0.0825 = $12.38 versus $7.43). The discount reduces both the base price and the tax amount.
Exceptions to Watch For
Some types of discounts do not reduce the taxable amount:
- Mail-in rebates: You pay the full price (and full tax) at the register and receive money back later. The tax was already charged on the pre-rebate price.
- Loyalty point redemptions: Depending on the retailer and jurisdiction, redeeming loyalty points or store credit may not reduce the taxable amount.
- Manufacturer coupons vs. store coupons: In most states, store coupons reduce the taxable price, but some states tax the pre-coupon price for manufacturer coupons because the manufacturer reimburses the store.
When in doubt, look at the receipt. The taxable subtotal line shows the amount on which sales tax was calculated. Use our Discount Calculator to compute sale price, stacked discounts, and tax in one step.
Mental Math Shortcuts for Common Discounts
You don't always have a calculator handy while shopping. These mental math tricks let you estimate discounts quickly in your head.
10% Off
The easiest discount to calculate mentally. Just move the decimal point one place to the left. 10% of $85 is $8.50. The sale price is $85 − $8.50 = $76.50. This is also the building block for most other discounts.
20% Off
Calculate 10% and double it. 10% of $85 is $8.50, so 20% is $17. Sale price: $85 − $17 = $68.
25% Off
Divide by 4. One quarter of $80 is $20, so the sale price is $60. For numbers that are not evenly divisible by 4, calculate 10% twice (20%) and then add half of 10% (5%). On $85: 20% is $17, 5% is $4.25, so 25% is $21.25, and the sale price is $63.75.
15% Off
Calculate 10% and add half of that for the extra 5%. 10% of $60 is $6, half of $6 is $3, so 15% is $9. Sale price: $60 − $9 = $51.
33% Off (One-Third Off)
Divide by 3. One-third of $90 is $30, so the sale price is $60. For awkward numbers, round first: one-third of $85 is approximately $28.33, so the sale price is about $56.67.
50% Off
Simply divide by 2. Half of anything is the fastest discount to calculate. 50% of $75 is $37.50.
The Complement Shortcut
Instead of calculating the discount and subtracting, multiply by the percentage you pay. At 30% off, you pay 70%, so multiply the price by 0.7. At 15% off, you pay 85%, so multiply by 0.85. This single multiplication is faster than the two-step method and less error-prone in your head.
| Discount | You Pay | Multiply By | Mental Trick |
|---|---|---|---|
| 10% | 90% | 0.90 | Subtract 10% (move decimal) |
| 15% | 85% | 0.85 | Subtract 10%, then subtract half of that |
| 20% | 80% | 0.80 | Subtract 10% twice |
| 25% | 75% | 0.75 | Divide by 4, subtract from original |
| 30% | 70% | 0.70 | Subtract 10% three times |
| 33% | 67% | 0.67 | Divide by 3 |
| 40% | 60% | 0.60 | Subtract half, add back 10% |
| 50% | 50% | 0.50 | Divide by 2 |
Comparing Unit Prices: Finding the Real Deal
A discount is only a good deal if the item was reasonably priced to begin with. Retailers frequently inflate the "original" price to make the discount seem larger (a practice sometimes called the anchor-and-discount strategy). The most reliable way to evaluate whether something is truly a good value is to compare unit prices.
The Unit Price Formula
Unit Price = Total Price ÷ Quantity (or Weight)
This works for anything sold in variable sizes: groceries, cleaning supplies, beverages, personal care products, or bulk items.
Example: Which Box of Cereal Is Cheaper?
- Brand A: 12 oz box for $3.48 → $3.48 ÷ 12 = $0.29 per oz
- Brand B: 18 oz box for $4.86 → $4.86 ÷ 18 = $0.27 per oz
- Brand A (24 oz "family size"): $5.76 → $5.76 ÷ 24 = $0.24 per oz
The family size box has the lowest unit price, but only if you will actually consume 24 ounces before it goes stale. The "best deal" should factor in waste. A lower unit price is not a bargain if half the product expires unused.
Discount Plus Unit Price: The Complete Picture
When a discounted item competes with a non-discounted alternative, combine the discount calculation with a unit price comparison. A 20% off coupon on a 16 oz bottle of olive oil priced at $9.99 makes it $7.99, or $0.50 per ounce. A store-brand 32 oz bottle at $11.99 full price is $0.37 per ounce. Despite the coupon, the store brand is 26% cheaper per ounce.
Our Percentage Calculator is useful for quick comparisons like this when you want to know the percentage difference between two unit prices.
Common Discount Traps to Watch For
Retailers are sophisticated in how they present discounts. Knowing these traps helps you spend wisely.
Inflated Original Prices
A common tactic is to set a high "regular" price that the item rarely or never sells at, then permanently offer a "sale" that brings it to the intended market price. If every item in the store is perpetually 40% off, the "original" price is not the real price. Compare against the unit prices of competitors to judge whether the sale price is genuinely good.
Buy One Get One (BOGO) Math
"Buy one, get one free" sounds like 50% off, but only if you actually wanted two. If you only needed one, you are paying full price for the item you wanted and getting something you might not use. BOGO is truly 50% off only when you need both items. "Buy one, get one 50% off" is only 25% off the total when you buy two.
Minimum Purchase Requirements
"$20 off when you spend $100" is a 20% discount, but only if you were already planning to spend $100. If you add items to your cart just to reach the threshold, you might spend more in total than you would have without the coupon. Always ask: would I buy this without the discount?
Percentage Off vs. Dollar Off
A $10 off coupon sounds less exciting than 20% off, but on a $40 item, $10 off (25% savings) is better than 20% off ($8 savings). Always convert to the same terms before comparing. On high-priced items, percentage discounts tend to be worth more. On low-priced items, a flat dollar amount can be the better deal.
Free Shipping Thresholds
Adding a $12 item to your cart to qualify for "free" shipping on a $35 minimum order only saves money if the shipping cost would have been more than $12. Check the shipping cost first before adding filler items. Often, paying for shipping on the smaller order costs less than buying something you do not need.
Putting It All Together: A Real Shopping Scenario
Let's walk through a complete example that combines everything in this guide. You are shopping for a new blender during a department store sale. Here are the details:
- Original price: $149.99
- Store sale: 30% off all kitchen appliances
- You have a 10% off coupon (stacks with the sale)
- Sales tax rate: 7.5%
Step 1: Apply the Store Discount
$149.99 × (1 − 0.30) = $149.99 × 0.70 = $105.00 (rounded)
Step 2: Apply the Coupon to the Reduced Price
$105.00 × (1 − 0.10) = $105.00 × 0.90 = $94.50
Step 3: Calculate the Combined Discount
Combined discount = 1 − (0.70 × 0.90) = 1 − 0.63 = 37% (not 40%)
Your savings: $149.99 − $94.50 = $55.49
Step 4: Add Sales Tax
$94.50 × 1.075 = $101.59
Step 5: Compare to Alternatives
Before buying, check whether the same blender is available elsewhere at a lower total price. A competing store might sell it for $109.99 with no sale but free shipping and no tax (if online and out of state). That is $109.99 vs. your $101.59 — the stacked discount wins in this case. But if the competitor had it for $89.99, paying full price there would be cheaper than your "37% off" deal at the department store. Always compare the final out-of-pocket cost, not just the discount percentage.
For instant calculations like this, use our Discount Calculator, which handles single discounts, stacked discounts, and sales tax in one step.
Quick Reference: Discount Formulas
Here is a summary of every formula covered in this guide for quick reference:
| What You Need | Formula |
|---|---|
| Sale price | Original × (1 − Discount%/100) |
| Savings amount | Original × (Discount%/100) |
| Discount percentage | ((Original − Sale) ÷ Original) × 100 |
| Original price | Sale Price ÷ (1 − Discount%/100) |
| Stacked discounts | Original × (1 − d1) × (1 − d2) |
| Combined discount % | 1 − (1 − d1) × (1 − d2) then × 100 |
| Price with tax | Sale Price × (1 + Tax%/100) |
| Unit price | Total Price ÷ Quantity |
The Bottom Line
Calculating discounts is basic arithmetic, but the way discounts are presented can make even simple savings confusing. The key takeaways are: use the complement shortcut (multiply by what you pay, not what you save) for fast mental math; remember that stacking discounts compounds rather than adds, so two 20% discounts give you 36% off, not 40%; sales tax is applied after the discount in most U.S. jurisdictions; and always compare the final out-of-pocket price or unit price across alternatives, not just the discount percentage.
If you want to skip the math entirely, our Discount Calculator handles everything from simple percentage-off calculations to stacked coupons with tax. For broader percentage problems beyond discounts, our Percentage Calculator covers percentage of, percentage change, percentage difference, and more.
Frequently Asked Questions
How do you calculate a percentage off?
To calculate a percentage off, multiply the original price by the discount percentage divided by 100, then subtract that amount from the original price. The formula is: Sale Price = Original Price × (1 − Discount% ÷ 100). For example, a $80 item at 25% off: $80 × (1 − 0.25) = $80 × 0.75 = $60 sale price. Your savings are $80 − $60 = $20. Alternatively, calculate the savings first: $80 × 0.25 = $20 savings, then subtract from the original: $80 − $20 = $60.
Do discounts stack by adding the percentages together?
No, stacked discounts do not add together. Each discount is applied to the already-reduced price, not the original price. A 20% off coupon plus a 10% off coupon does not equal 30% off. Instead, the first discount reduces the price by 20%, and the second discount reduces the new price by 10%. On a $100 item: 20% off gives $80, then 10% off $80 gives $72. The total discount is 28%, not 30%. The order of application does not matter mathematically — 10% then 20% also gives $72 — but the combined discount is always less than the sum of the individual percentages.
Is sales tax calculated before or after a discount?
In the United States and most jurisdictions, sales tax is calculated on the discounted price, not the original price. If a $100 item is 30% off, you pay tax on $70, not on $100. So with an 8% sales tax: $70 × 0.08 = $5.60 in tax, making the total $75.60. However, some promotions like mail-in rebates or loyalty points may not reduce the taxable amount because the seller still receives the full price. The key distinction is whether the discount reduces the transaction price at the point of sale (tax applies to the reduced price) or whether you receive money back after the transaction (tax applies to the full price).
How do you compare unit prices to find the best deal?
To compare unit prices, divide the total price of each option by the quantity or weight. For example, a 24-ounce bottle of shampoo for $7.20 has a unit price of $0.30 per ounce ($7.20 ÷ 24). A 32-ounce bottle for $8.96 has a unit price of $0.28 per ounce ($8.96 ÷ 32). The larger bottle is the better deal per ounce. Many stores display unit prices on shelf tags, but when they do not — or when comparing across stores — doing this division yourself reveals the true cost. Always compare the same units (price per ounce, price per count, price per pound) for an accurate comparison.
Is a double discount the same as a single discount of the same total percentage?
No, a double discount gives you slightly less savings than a single equivalent discount. Two successive 20% discounts are not the same as one 40% discount. On a $100 item: a single 40% discount gives you $60. Two successive 20% discounts give you $100 × 0.80 × 0.80 = $64. The double discount saves you $36, while the single discount saves you $40. This happens because the second percentage is applied to a smaller base. The mathematical relationship is: combined multiplier = (1 − d1) × (1 − d2), which is always less than (1 − d1 − d2) when both discounts are positive.