The basic discount formula
Calculating a sale price requires three core numbers:
- Original price ($P$): The regular listing price before any discount.
- Discount percentage ($D$): The markdown rate expressed as a percentage.
- Final sale price ($S$): The net price you pay before tax.
The foundational formulas:
Discount Amount = Original Price × (Discount % / 100)
Final Sale Price = Original Price − Discount Amount
Or solved in a single mathematical operation:
Final Sale Price = Original Price × (1 − Discount % / 100)
Example: A 25% off clothing sale
A winter coat has an original price tag of $160.00 and is marked at 25% off:
- Discount Amount: $160.00 × 0.25 = $40.00
- Final Price: $160.00 − $40.00 = $120.00
You save $40.00 and pay $120.00.
Factoring in Sales Tax or VAT
A frequent point of confusion when shopping is whether sales tax is calculated before or after the discount is subtracted.
- Standard Retail Rule: Legally, sales tax is assessed on the discounted sale price, not the original sticker price.
- Formula with Tax:
Price After Tax = (Original Price × (1 − Discount % / 100)) × (1 + Tax % / 100)
Example: 30% discount with 8.5% sales tax
A laptop originally costs $800.00 with a 30% discount and an 8.5% sales tax rate:
- Calculate discounted subtotal:
- $800.00 × (1 − 0.30) = $800.00 × 0.70 = $560.00
- Calculate sales tax:
- $560.00 × 0.085 = $47.60
- Calculate total out-of-pocket cost:
- $560.00 + $47.60 = $607.60
Stacked discounts: Why 40% + 10% is NOT 50%
Retailers often run promotions such as "Take 40% off clearance items, plus an extra 10% off at checkout."
Many shoppers assume 40% + 10% = 50%. In reality, stacked discounts are applied sequentially, not additively:
Final Price = Original Price × (1 − D1) × (1 − D2)
Worked comparison on a $100 item:
- First discount (40% off):
- $100.00 × (1 − 0.40) = $60.00
- Second discount (10% off the remaining $60):
- $60.00 × (1 − 0.10) = $54.00
- Total savings:
- $100.00 − $54.00 = $46.00 (an effective discount of 46%, not 50%)
The Universal Stacked Discount Formula
To find the exact effective discount rate of any two promotions:
Effective Discount Rate = 1 − (1 − D1) × (1 − D2)
For 40% and 10%:
- Rate = 1 − (0.60 × 0.90) = 1 − 0.54 = 0.46 = 46%
Retail promotions decoded: "Buy One, Get One 50% Off"
Another classic retail strategy is BOGO promotions:
- Buy 1, Get 1 Free (Same item): You get two identical items for the price of one. The real discount across both items is 50%.
- Buy 1, Get 1 50% Off (Same price items): You pay 100% + 50% = 150% for two items that normally cost 200%. The real discount is 50 / 200 = 25% off each item.
Reverse discount calculation: Finding the original price
If you know what you paid and the discount rate, how do you find the original price before the sale?
Original Price = Sale Price / (1 − Discount % / 100)
Example: You bought a pair of running shoes on clearance for $68.00 after a 15% discount. What was the original price?
- Calculation: $68.00 / (1 − 0.15) = $68.00 / 0.85 = $80.00
How to calculate discounts in Microsoft Excel & Google Sheets
If you are managing e-commerce inventories, retail spreadsheets, or budgeting sheets, use these formulas:
| Task | Formula in Cell |
|---|---|
Find Sale Price (Original in A2, Discount % in B2) | =A2 * (1 - B2) |
| Find Discount Amount | =A2 * B2 |
Find Discount Percentage (Original in A2, Sale in B2) | =(A2 - B2) / A2 (format cell as %) |
Price After Tax (Sale in C2, Tax Rate in D2) | =C2 * (1 + D2) |
Quick Reference Discount Table
| Original Price | 10% Off | 20% Off | 30% Off | 40% Off | 50% Off |
|---|---|---|---|---|---|
| $25.00 | $22.50 | $20.00 | $17.50 | $15.00 | $12.50 |
| $50.00 | $45.00 | $40.00 | $35.00 | $30.00 | $25.00 |
| $100.00 | $90.00 | $80.00 | $70.00 | $60.00 | $50.00 |
| $150.00 | $135.00 | $120.00 | $105.00 | $90.00 | $75.00 |
| $200.00 | $180.00 | $160.00 | $140.00 | $120.00 | $100.00 |
| $500.00 | $450.00 | $400.00 | $350.00 | $300.00 | $250.00 |
Frequently Asked Questions
Does a coupon apply before or after manufacturer discounts?
In most retail checkout systems, store-wide percentage markdowns apply first, and manufacturer coupons or fixed-dollar vouchers ($10 off) deduct from the remaining subtotal.
What is the fastest mental shortcut for 20% off?
Divide the price by 10 (shift the decimal point left one space), then double that number to find your savings. Subtract that savings from the price. (e.g., $90 / 10 = $9; $9 × 2 = $18 savings; $90 − $18 = $72).
What is price anchoring?
Price anchoring is a psychological marketing technique where a high "original" manufacturer suggested retail price (MSRP) is displayed next to a sale price to make the savings seem dramatic. Always evaluate the final price against current market competitors rather than the sticker markdown alone.
Summary
- Calculate single discounts by multiplying the original price by (1 − Discount Rate).
- Stacked promotions multiply remaining fractions rather than adding percentages.
- For immediate calculations with optional sales tax rates, use our free client-side Discount Calculator. For other percentage problems, refer to our How to Calculate a Percentage guide.