Discount Calculator

Calculate savings, final sale prices, and effective discounts for stacked promotions, flat coupons, sales tax, or Buy X Get Y deals.

Math Audited
Original Price$100.00
$
$0$1000
Discount Percentage20%
%
0%100%
Sales Tax0%
%
0%25%
Final Sale Price (with Tax)
$80.00

You save $20.00 (20% off the total value).

Original retail value$100.00
Total savings amount-$20.00
Discounted subtotal (pre-tax)$80.00
Sales tax (0%)+$0.00
20%
Saved
Price Components
Total Savings: $20.00 (20%)
Net Price Paid: $80.00 (80%)
How is this calculated?
Sale Price Subtotal = $100.00 ร— (1 - 20%) = $80.00 Sales Tax = $80.00 ร— 0% = $0.00 Final Price = $80.00 + $0.00 = $80.00
Mathematical Audit LogVerified against Corporate Finance Institute markdown standards & NIST Handbook retail pricing guidelines.Last Audited: 2026-07-10
Mathematical Formulas
Single Discount: S = P ร— (1 - d/100)
Stacked Discount: S = P ร— (1 - d1/100) ร— (1 - d2/100)
Flat Discount: S = max(0, P - F)
BOGO: S = G ร— (XยทP + YยทPยท(1 - Z/100)) + RยทP
Reverse Discount: P = S / (1 - d/100)
Core Assumptions
  • Stacked discounts are applied sequentially (compounded) matching store coupon guidelines.
  • Promo items in multi-buy (Buy X Get Y) are identical in retail price.
  • Sales tax is calculated on the net discounted subtotal at checkout.
Limitations & Exclusions
  • Does not account for loyalty points, store credit, or specific manufacturer mail-in rebates.
  • Reverse discount is mathematically undefined when stated discount rate is 100% or greater.

About the Discount Calculator

A discount is a price reduction offered on a product or service, widely used in retail and commercial sales campaigns to accelerate inventory turnover, attract customers, and clear seasonal stock. In consumer mathematics, calculating discounts involves converting percentage discounts into decimal multipliers and applying them to original prices. To prevent accounting errors, it is vital to distinguish between a single primary discount and stacked (or double) discounts. Stacked discounts (e.g., "an additional 20% off already discounted clearance items") are applied sequentially, meaning each subsequent discount is calculated based on the declining subtotal rather than the initial original price. After establishing the final discounted sale price, sales tax must be computed on that net sale subtotal. By mastering these formulas, consumers can verify markdown accuracy, compute their total savings, and make sound budgeting decisions during retail shopping cycles.

Mathematical Formula & Logic

The calculations for markdown savings, sequential discounts, and sales tax are defined as follows: 1. Discounted Price (Single Discount): Sale_price = Price_original ร— (1 - Discount_primary / 100) 2. Discounted Price (Stacked/Sequential Discounts): Sale_price = Price_original ร— (1 - Discount_primary / 100) ร— (1 - Discount_stacked / 100) 3. Total Saved: Saved_total = Price_original - Sale_price 4. Sales Tax and Final Price: Tax_amount = Sale_price ร— (Tax_rate / 100) Price_final = Sale_price + Tax_amount 5. Effective Discount Percentage: Discount_effective = (Saved_total / Price_original) ร— 100

Step-by-Step Example

Calculate the sale price, total savings, sales tax, and final price for a $200 jacket with a primary discount of 25%, an additional stackable discount of 10%, and a sales tax of 8%: 1. Compute price after primary discount: $200 ร— (1 - 0.25) = $200 ร— 0.75 = $150 2. Compute price after stacked discount: $150 ร— (1 - 0.10) = $150 ร— 0.90 = $135 3. Calculate total savings: $200 - $135 = $65 4. Compute effective discount: ($65 / $200) ร— 100 = 32.5% (note: this is less than the additive sum of 25% + 10% = 35%) 5. Calculate sales tax: $135 ร— 8% = $135 ร— 0.08 = $10.80 6. Calculate final price: $135 + $10.80 = $145.80 7. The final price to be paid is $145.80, with a total savings of $65 (an effective 32.5% discount).

Reference Data & Values

primarystackedeffective offsale price
20%10%28.0% OFF$144.00
30%15%40.5% OFF$119.00
40%20%52.0% OFF$96.00
50%25%62.5% OFF$75.00

Frequently Asked Questions

To calculate a 20% discount, convert the percentage to a decimal (0.20) and multiply it by the original price to find the savings amount. Then, subtract the savings amount from the original price to get the final sale price.
This is a sequential stacked discount. You first deduct 30% from the original price. Then, you deduct 20% from that new lower price. It does not equal 50% off; instead, it yields a net discount of 44% off the original retail price.
Buy One Get One Free represents a 50% discount only if you buy exactly two items of equal value. If you buy a different quantity or the items have unequal prices, the overall percentage savings will be less than 50%.
To reverse calculate the original price when you know the final sale price and the discount percentage, divide the sale price by (1 minus the discount rate as a decimal). For example, a $60 sale price at 40% off yields $60 / 0.60 = $100 original price.
Stacked discounts are compounding: the store applies the primary discount first, and then applies the secondary discount to that reduced price. This sequential calculation benefits the retailer, as it yields a slightly smaller discount than adding the percentages together.
Sales tax is almost always computed on the final discounted sale price rather than the original list price. If you buy a $100 item on sale for $80 in a state with 10% tax, the tax is $8.00 (10% of $80) for a final total of $88.00.
A flat percentage off is generally more flexible as it does not require buying a specific volume. A Buy One Get One Free (BOGO) deal requires purchasing at least two items to receive any benefit, which can encourage unnecessary spending.
Subtract the flat dollar discount directly from the original price of the item. For example, if you have a '$15 off' coupon on an $80 item, you subtract $15 to get a sale price of $65.