The Basic Discount Formula
Calculating a discount requires just two numbers: the original price and the discount percentage. The formula is:
Sale Price = Original Price × (1 − Discount Rate)
Discount Amount = Original Price − Sale PriceUse the free discount calculator above to get instant results, or work through the math yourself using the steps below. The formula works for any discount, from 1% off to 99% off.
Variable Definitions
| Variable | What It Means | Example Value |
|---|---|---|
| P | Original (pre-discount) price | $120.00 |
| d1 | First discount percentage (as a decimal: 30% = 0.30) | 0.30 |
| d2 | Second (stacked) discount percentage | 0.10 |
| t | Sales tax rate (as a decimal: 8% = 0.08) | 0.08 |
| P1 | Price after first discount | $84.00 |
| P2 | Price after stacked discount (before tax) | $75.60 |
| F | Final price after discount and sales tax | $81.65 |
Step-by-Step Worked Examples
Example 1 — Single Discount: Clothing Sale
A jacket is priced at $120.00 and is on sale for 30% off. The local sales tax rate is 7%. What is the final price?
| Step | Calculation | Result |
|---|---|---|
| Price after discount | $120.00 × (1 − 0.30) = $120.00 × 0.70 | $84.00 |
| Discount amount | $120.00 − $84.00 | $36.00 saved |
| Sales tax on discounted price | $84.00 × 0.07 | $5.88 |
| Final price with tax | $84.00 + $5.88 | $89.88 |
| Cost per dollar saved | $84.00 ÷ $36.00 | $2.33 per dollar saved |
You pay $89.88 at the register, saving $36.00 off the original price. The effective discount is 30% (30% × $120 = $36).
Example 2 — Stacked Discounts: Electronics
A laptop is priced at $999.99. The store is running a 15% off sale, and you also have a 10% off coupon that stacks on top. The sales tax rate is 8.25%.
| Step | Calculation | Result |
|---|---|---|
| After first discount (15% off) | $999.99 × (1 − 0.15) = $999.99 × 0.85 | $849.99 |
| After second discount (10% off reduced price) | $849.99 × (1 − 0.10) = $849.99 × 0.90 | $764.99 |
| Total discount amount | $999.99 − $764.99 | $235.00 saved |
| Effective discount rate | $235.00 ÷ $999.99 | 23.5% (not 25%) |
| Sales tax on discounted price | $764.99 × 0.0825 | $63.11 |
| Final price with tax | $764.99 + $63.11 | $828.10 |
The key insight: stacking 15% and 10% discounts produces a 23.5% total discount, not 25%. The second 10% applies to $849.99 (not $999.99), so it saves $85.00 — less than if applied to the full price.
Example 3 — Comparing Two Stores
A coffee brand sells the same 2-lb bag at two stores:
- Store A: Listed at $18.99 with a 20% sale discount
- Store B: Regular price $16.49, no discount
Both stores charge 6% sales tax. Which is the better deal?
| Store A (20% off $18.99) | Store B ($16.49 regular) | |
|---|---|---|
| Price before tax | $18.99 × 0.80 = $15.19 | $16.49 |
| Sales tax (6%) | $15.19 × 0.06 = $0.91 | $16.49 × 0.06 = $0.99 |
| Final price | $16.10 | $17.48 |
Store A wins by $1.38 (about 7.9% cheaper). This example shows why comparing the final after-tax price across stores is more reliable than focusing only on discount percentages. A 20% discount on a high-priced item can still beat a "regular" price at another store — but not always.
Stacked Discounts: The Math Behind the Myth
One of the most common misconceptions in retail math is that stacked discounts add together. They do not. Each discount applies to a progressively smaller base price, so the combined effect is always less than the sum of the percentages.
The formula for the effective combined discount when two percentages are stacked:
Effective Total Discount = 1 − (1 − d1) × (1 − d2)| First Discount | Second Discount | Sum (incorrect) | Actual Effective Discount |
|---|---|---|---|
| 10% | 10% | 20% | 19.0% |
| 20% | 10% | 30% | 28.0% |
| 25% | 15% | 40% | 36.25% |
| 30% | 20% | 50% | 44.0% |
| 50% | 25% | 75% | 62.5% |
The gap between the sum and the actual discount widens as the percentages increase. At 50% + 25%, you might expect 75% off — but you actually get 62.5% off. Knowing this prevents unpleasant surprises at the register.
How Sales Tax Interacts with Discounts
In most US states, sales tax is applied to the final discounted price, not the original price. This works in the buyer's favor: you only pay tax on the money you actually spend.
Final Price with Tax = Discounted Price × (1 + Tax Rate)For example, a $200 item discounted 40% to $120 with an 8% tax rate:
- Tax amount: $120 × 0.08 = $9.60
- Final price: $120 + $9.60 = $129.60
- You save $80 on the item price — and also avoid paying tax on that $80
Note: Tax laws vary by state and item type. Some categories (groceries, prescription drugs) may be exempt from sales tax in certain states. The discount calculator includes a tax field so you can model the exact final cost in your area.
Understanding Cost Per Dollar Saved
The "cost per dollar saved" metric is a practical way to evaluate whether a discount is worth acting on — especially if the purchase requires going out of your way or taking on unnecessary spending.
Cost Per Dollar Saved = Price After Discount ÷ Total Discount Amount| Discount % | Original Price | You Spend | You Save | Cost Per $ Saved |
|---|---|---|---|---|
| 10% | $100 | $90 | $10 | $9.00 |
| 25% | $100 | $75 | $25 | $3.00 |
| 40% | $100 | $60 | $40 | $1.50 |
| 50% | $100 | $50 | $50 | $1.00 |
| 70% | $100 | $30 | $70 | $0.43 |
At a 50% discount, you spend exactly one dollar for every dollar you save — a true 2-for-1 deal. At a 10% discount, you spend nine dollars for every dollar you save, which may not be worth the effort of a special trip. Use this metric to prioritize which sales deserve your attention and which can be skipped.
Common Discount Scenarios and How to Calculate Them
Reverse Calculation: Finding the Original Price
When you know the sale price and the discount rate but want to find the original price:
Original Price = Sale Price ÷ (1 − Discount Rate)Example: A sweater costs $49 after a 30% discount. What was the original price?
$49 ÷ (1 − 0.30) = $49 ÷ 0.70 = $70.00. Verify: $70 × 0.70 = $49. ✓
Finding the Discount Percentage from Two Prices
When you know the original and sale prices and want to calculate the discount rate:
Discount % = (Original Price − Sale Price) ÷ Original Price × 100Example: An item dropped from $85 to $59.50. What is the discount?
($85 − $59.50) ÷ $85 × 100 = $25.50 ÷ $85 × 100 = 30% off.
BOGO (Buy One Get One) Deals
A "buy one get one free" (BOGO) deal is effectively a 50% discount when buying two items of equal price. "Buy one get one 50% off" means you pay full price for the first item and half price for the second — an effective combined discount of 25%. Always calculate the per-unit cost to assess BOGO deals accurately.
Practical Tips for Evaluating Sales
- Compare the final price, not the discount percentage. A 50% off deal on an inflated "original" price may cost more than a 10% off deal at a competitor with honest pricing.
- Check the pre-sale price history. Some retailers temporarily raise prices before a sale to make the discount look larger. If the "original" price seems unusually high, research what the item normally costs.
- Factor in shipping costs. A 20% discount can be offset entirely by shipping charges. Always include shipping in your final price comparison.
- Consider whether you would buy at full price. Buying something on sale that you would not have purchased at full price is spending, not saving. The best discount is on something you already planned to buy.
- Use the cost per dollar saved metric for high-value purchases. For items over $100, the cost per dollar saved helps you decide if a special trip or early purchase is worth the effort.
How to Use the Discount Calculator
Enter the following values into the discount calculator to see your results instantly:
- Original Price: The full retail price before any discounts. Use the sticker or listed price — not a previously marked-down price — for accurate results.
- Discount Percentage: The primary discount being offered (e.g., 25 for 25% off). Leave the second discount field at 0 if there is only one discount.
- Second Discount (optional): Enter any additional stacked discount, such as a coupon code or loyalty member reduction applied after the first discount.
- Sales Tax Rate: Your local or state tax rate. Common US rates range from 0% (Oregon, Montana, New Hampshire, Delaware) to around 10% in some cities. Sales tax is applied to the discounted price.
The calculator shows five results: total discount amount, price after discounts before tax, final price with tax, effective total savings percentage, and cost per dollar saved. Use these to compare deals across stores or decide whether a sale is worth acting on.