Discounts Are Everywhere — Here Is How to Calculate Them
Whether you are shopping a Black Friday sale, clipping coupons, comparing e-commerce deals, or negotiating a bulk purchase, discounts are a part of daily life. Yet many people reach for a calculator app without understanding the simple math behind how to calculate discount amounts. Once you learn the basic discount formula, you can instantly figure out the sale price, the amount you save, or even reverse-engineer the original price from a discounted tag.
This guide covers everything you need: the core percentage off formula, step-by-step examples, stacked discounts, tax calculations, a quick-reference table for common discount percentages, and the important difference between markup and discount. Every formula is accompanied by worked examples so you can follow along with your own numbers.
If you prefer to skip the manual math, our free Discount Calculator handles single discounts, stacked discounts, sales tax, multi-currency formatting, and even converts the final amount to words — all in your browser with no signup required.
The Basic Discount Formula
The discount formula has two parts. First, calculate the discount amount. Then subtract it from the original price to get the sale price.
Discount Amount = Original Price x (Discount% / 100)
Sale Price = Original Price - Discount Amount
Or in one step:
Sale Price = Original Price x (1 - Discount% / 100)The one-step version is useful for quick mental math. If something is 20 percent off, you multiply the price by 0.80 (which is 1 minus 0.20). If it is 35% off, multiply by 0.65. The multiplier is simply 1 minus the discount rate as a decimal.
To find the discount percentage when you know both prices, reverse the formula:
Discount% = ((Original Price - Sale Price) / Original Price) x 100This tells you what percentage discount was applied. For example, if a jacket was $120 and is now $90: ((120 - 90) / 120) x 100 = 25% off. Need to calculate percentages for other scenarios? Our Percentage Calculator supports three modes including percentage change, which is exactly this type of calculation.
Step-by-Step Calculation Examples
Let us work through three examples at different discount levels to reinforce the formula.
Example 1: 10% off $80
Discount Amount = $80 x (10 / 100)
= $80 x 0.10
= $8.00
Sale Price = $80 - $8 = $72.00
Quick method: $80 x 0.90 = $72.00You save $8.00 and pay $72.00.
Example 2: 25% off $120
Discount Amount = $120 x (25 / 100)
= $120 x 0.25
= $30.00
Sale Price = $120 - $30 = $90.00
Quick method: $120 x 0.75 = $90.00You save $30.00 and pay $90.00.
Example 3: 40% off $250
Discount Amount = $250 x (40 / 100)
= $250 x 0.40
= $100.00
Sale Price = $250 - $100 = $150.00
Quick method: $250 x 0.60 = $150.00You save $100.00 and pay $150.00. Notice how the "quick method" multiplier (0.60) is just 1 minus the discount decimal (1 - 0.40). This one-step approach is faster for mental math and works for any percentage off calculation.
How to Find the Original Price from a Sale Price
Sometimes you see a sale tag that says "$60 after 25% off" and want to know what the original price was. The reverse formula is:
Original Price = Sale Price / (1 - Discount% / 100)
Example: Sale price is $60 after 25% off.
Original Price = $60 / (1 - 25/100)
= $60 / (1 - 0.25)
= $60 / 0.75
= $80.00The original price was $80.00. This reverse calculation is useful when stores advertise "now only $X" without showing the original price. You can verify: $80 x 0.75 = $60, which confirms the answer.
Here is a quick reference for reverse-calculating original prices at common discount levels:
After 10% off → divide sale price by 0.90
After 20% off → divide sale price by 0.80
After 25% off → divide sale price by 0.75
After 30% off → divide sale price by 0.70
After 50% off → divide sale price by 0.50Stacked Discounts — How Multiple Discounts Work
A common misconception is that two discounts added together give you that combined percentage off. They do not. When you stack a 20% discount and a 10% discount, the total is not 30% off — it is 28% off. This is because the second discount is applied to the already-reduced price, not the original price.
Example: $100 item with 20% off, then 10% off
Step 1: Apply first discount (20%)
$100 x 0.80 = $80.00
Step 2: Apply second discount (10%) to new price
$80 x 0.90 = $72.00
Total savings: $100 - $72 = $28.00 (28% off, not 30%)
Combined multiplier: 0.80 x 0.90 = 0.72
Effective discount: 1 - 0.72 = 0.28 = 28%The general formula for stacked discounts is:
Final Price = Original x (1 - D1/100) x (1 - D2/100) x ... x (1 - Dn/100)
Effective Discount% = (1 - product of all multipliers) x 100Interestingly, the order of the discounts does not matter mathematically. Applying 20% then 10% gives the same result as 10% then 20%, because multiplication is commutative. Our Discount Calculator supports stacked discounts and shows you the effective combined percentage automatically.
Discount with Sales Tax
In most places, sales tax is applied after the discount. You first reduce the price by the discount, then calculate tax on the lower amount. This is the standard method and it works in your favor — you pay tax on the sale price, not the original price.
Here is a worked example with a comparison table:
| Step | Calculation | Amount |
|---|---|---|
| Original Price | -- | $200.00 |
| Apply 25% Discount | $200 x 0.25 = $50 | -$50.00 |
| Sale Price (after discount) | $200 - $50 | $150.00 |
| Apply 8% Sales Tax | $150 x 0.08 = $12 | +$12.00 |
| Final Price (you pay) | $150 + $12 | $162.00 |
The combined formula for discount and tax calculation in one step is:
Final Price = Original x (1 - Discount%/100) x (1 + Tax%/100)
Example: $200, 25% off, 8% tax
Final = $200 x 0.75 x 1.08 = $162.00Note: if tax were applied first and then the discount, you would get $200 x 1.08 x 0.75 = $162.00 — the same result due to the commutative property of multiplication. However, the tax amount itself differs: applying discount first means you pay $12 in tax; applying tax first means you pay $16.20 in tax but then get a larger discount. The total is identical, but tax reporting may differ by jurisdiction. Our Discount Calculator handles the discount-first method, which is the standard in most retail environments.
Common Discount Percentages Quick Reference
Here is a handy table showing the most frequently seen percentage discount levels, the multiplier for quick calculation, and what you actually pay on a $100 item:
| Discount % | Multiplier | You Save (per $100) | You Pay (per $100) | Common Usage |
|---|---|---|---|---|
| 5% | 0.95 | $5 | $95 | Early payment, loyalty rewards |
| 10% | 0.90 | $10 | $90 | Newsletter signup, first order |
| 15% | 0.85 | $15 | $85 | Seasonal promotions |
| 20% | 0.80 | $20 | $80 | Holiday sales, member discounts |
| 25% | 0.75 | $25 | $75 | Clearance events, flash sales |
| 30% | 0.70 | $30 | $70 | End-of-season sales |
| 40% | 0.60 | $40 | $60 | Major clearance, outlet pricing |
| 50% | 0.50 | $50 | $50 | Half-price sales, BOGO equivalent |
To use the multiplier: simply multiply any price by the multiplier. A $65 shirt at 30% off: $65 x 0.70 = $45.50. A $249 gadget at 15% off: $249 x 0.85 = $211.65. Memorizing these multipliers makes in-store mental math almost instant.
Markup vs. Discount — Understanding the Difference
People often confuse markup and discount because both involve percentages applied to prices. However, they use different base values and serve opposite purposes:
- Markup is based on the cost price (what the seller paid). It determines the selling price.
- Discount is based on the selling price (what the customer sees). It reduces the selling price.
Markup Formula:
Selling Price = Cost Price x (1 + Markup% / 100)
Discount Formula:
Sale Price = Selling Price x (1 - Discount% / 100)
Example:
Cost price = $40, Markup = 50%
Selling Price = $40 x 1.50 = $60
Now apply 50% discount to that $60:
Sale Price = $60 x 0.50 = $30
Result: $30 ≠ $40 (original cost)This is a critical insight for anyone in retail or business: a 50% markup followed by a 50% discount does not bring you back to the cost price. The markup is calculated on the lower cost ($40), while the discount is calculated on the higher selling price ($60). The same percentage applied to different bases produces different dollar amounts. If you need to run general percentage calculations for business pricing, our Percentage Calculator handles all three common modes — find X% of Y, find what percentage X is of Y, and calculate percentage change.
Real-World Discount Scenarios
Understanding the discount formula helps you make better purchasing decisions in these common situations:
Black Friday and Cyber Monday Sales
Retailers frequently advertise "up to 60% off" during major sales events. The key phrase is "up to" — most items will have smaller discounts (10-30%), with only a few loss leaders at the headline percentage. To calculate the sale price on any item, use the multiplier method: a $350 TV at 35% off costs $350 x 0.65 = $227.50. Compare that to the item's price history, not just the listed "original price," which may be inflated.
Coupon Stacking
Many stores allow combining a store coupon with a manufacturer coupon. If you have a 20% store coupon and a $10-off manufacturer coupon, the order matters. Most stores apply the percentage discount first: $80 item at 20% off = $64, minus $10 coupon = $54. If the $10 coupon were applied first: $80 - $10 = $70, then 20% off = $56. The first order saves you more. Always apply percentage discounts before fixed-amount coupons when you have the choice.
Loyalty Programs and Tiered Discounts
Some programs offer increasing discounts based on spending tiers — for example, 5% off after $100 spent, 10% off after $500 spent, and 15% off after $1,000 spent. These work as single discounts applied at checkout, not stacked discounts. Track your savings over time with a spreadsheet or use our Savings Calculator to project how much you could save annually at different loyalty tiers.
Bulk Pricing
Bulk discounts follow a simple volume-based model: buy more, pay less per unit. If a single item costs $12 but a pack of 10 costs $96, the per-unit price drops to $9.60 — a 20% discount. To find the discount percentage on bulk pricing: ((12 - 9.60) / 12) x 100 = 20%. This same approach works for any quantity-based pricing comparison.
For any scenario where you need to document discount calculations — client proposals, purchase orders, or expense reports — our Form to PDF Converter lets you generate professional invoices and receipts directly in your browser, complete with line items and totals.
Frequently Asked Questions
How do I calculate a discount percentage from the original and sale price?
Subtract the sale price from the original price, divide the result by the original price, and multiply by 100. For example, if a product originally costs $80 and is on sale for $60: ((80 - 60) / 80) x 100 = 25% discount. The formula is Discount% = ((Original Price - Sale Price) / Original Price) x 100.
Do stacked discounts of 20% and 10% equal 30% off?
No. Stacked discounts are applied sequentially, not added together. A 20% discount followed by a 10% discount gives a total of 28% off, not 30%. The first discount reduces the price, and the second discount is calculated on the already-reduced price. For a $100 item: 20% off = $80, then 10% off $80 = $72. That is $28 off, or 28%.
Should sales tax be calculated before or after the discount?
In most jurisdictions, sales tax is calculated after the discount is applied. You first reduce the original price by the discount amount to get the sale price, then apply the tax rate to the sale price. For example, a $100 item with 25% off and 8% tax: sale price = $75, tax = $75 x 0.08 = $6, total = $81. Always check your local tax laws, as rules can vary.
How do I find the original price if I know the sale price and discount percentage?
Divide the sale price by (1 minus the discount rate as a decimal). The formula is: Original Price = Sale Price / (1 - Discount% / 100). For example, if an item costs $60 after a 25% discount: Original Price = 60 / (1 - 0.25) = 60 / 0.75 = $80. The original price was $80.
What is the difference between markup and discount?
Markup is a percentage added to the cost price to determine the selling price. Discount is a percentage subtracted from the selling price to determine the sale price. They use different base values: markup is based on cost, while discount is based on selling price. A 50% markup on a $40 cost gives a $60 selling price, but a 50% discount on a $60 selling price gives $30 — not $40. This asymmetry is important in retail pricing.
Conclusion
Calculating discounts is straightforward once you know the core formula: Sale Price = Original Price x (1 - Discount% / 100). Whether you are figuring out how to calculate percentage off a single item, stacking multiple coupon codes, adding sales tax to a discounted purchase, or reverse-engineering the original price from a sale tag, the math always follows the same principles.
The key takeaways from this guide: stacked discounts are always less than their sum, sales tax should typically be applied after the discount, the multiplier method (0.80 for 20% off, 0.70 for 30% off) makes mental math fast, and markup and discount percentages are not interchangeable because they use different base values. Memorize the common discount multiplier table and you will never overpay at a sale again.
Ready to crunch your own numbers? Use our free Discount Calculator for instant results with stacked discounts, tax, and multi-currency support. For general percentage math, try the Percentage Calculator. And if you are planning long-term savings from your bargain hunting, our Savings Calculator shows how those saved dollars grow with compound interest over time.