Calculating a discount means finding how much you save and what you actually pay after a percentage reduction. The core formula is straightforward, but stacking multiple discounts, adding tax, and comparing deals introduce subtleties that trip people up.
This guide covers the exact formulas, worked examples, and the most common mistakes.
The Basic Discount Formula
A percentage discount reduces a price by a fraction of the original:
Savings = Original Price × (Discount % ÷ 100)
Final Price = Original Price − Savings
Or in one step:
Final Price = Original Price × (1 − Discount % ÷ 100)
Example
A $120 pair of headphones is 25% off.
- Savings = $120 × 0.25 = $30
- Final price = $120 − $30 = $90
Or: $120 × 0.75 = $90
Mental Math Shortcuts
You don't always need a calculator. These shortcuts handle most common discounts:
| Discount | Shortcut | Example ($80 item) |
|---|---|---|
| 10% | Move decimal left one place | $8.00 off → $72.00 |
| 20% | Find 10%, double it | $16.00 off → $64.00 |
| 25% | Divide by 4 | $20.00 off → $60.00 |
| 33% | Divide by 3 | $26.67 off → $53.33 |
| 50% | Halve it | $40.00 off → $40.00 |
| 5% | Find 10%, halve it | $4.00 off → $76.00 |
| 15% | Find 10% + 5% | $12.00 off → $68.00 |
For other percentages, break them into parts. 35% = 25% + 10%. Calculate each and add the savings together.
Stacked Discounts: Why 20% + 10% ≠ 30%
Stores sometimes offer multiple discounts—a clearance sale plus an extra coupon. These are called stacked discounts, and they are applied sequentially.
The second discount is calculated on the already-reduced price, not the original. This always produces a smaller total reduction than simply adding the percentages.
Formula
Final Price = Original × (1 − d₁/100) × (1 − d₂/100) × …
Effective total discount = (1 − Final Price ÷ Original) × 100
Example: 30% off + 15% coupon on $200 shoes
- After 30%: $200 × 0.70 = $140
- After 15%: $140 × 0.85 = $119
- Total saved: $200 − $119 = $81
- Effective discount: ($81 ÷ $200) × 100 = 40.5% (not 45%)
Does the order matter?
No. Multiplication is commutative. Applying 30% then 15% gives the same result as 15% then 30%:
- $200 × 0.70 × 0.85 = $119
- $200 × 0.85 × 0.70 = $119
How far off is the simple sum?
The gap between stacked and summed percentages grows as the discounts increase:
| Discount 1 | Discount 2 | Stacked total | Simple sum | Difference |
|---|---|---|---|---|
| 10% | 10% | 19.0% | 20% | 1.0% |
| 20% | 10% | 28.0% | 30% | 2.0% |
| 20% | 20% | 36.0% | 40% | 4.0% |
| 30% | 20% | 44.0% | 50% | 6.0% |
| 50% | 50% | 75.0% | 100% | 25.0% |
The last row makes it obvious: two 50% discounts don't make something free. You pay 25% of the original.
Discount + Sales Tax
In most retail scenarios, sales tax is applied after the discount, not before.
Example
$90 jacket, 20% off, 8.25% sales tax:
- After discount: $90 × 0.80 = $72.00
- Tax: $72.00 × 0.0825 = $5.94
- Total: $72.00 + $5.94 = $77.94
If tax were incorrectly applied to the original price: $90 × 0.0825 = $7.43, total = $79.43. That's $1.49 more than it should be.
Reverse Discount: Finding the Original Price
Sometimes you know the sale price and the discount percentage, and need the original.
Original Price = Sale Price ÷ (1 − Discount% ÷ 100)
Example
A shirt costs $45 after 40% off. What was the original price?
$45 ÷ (1 − 0.40) = $45 ÷ 0.60 = $75
Comparing Deals: Percentage Off vs. Fixed Amount
To compare "25% off" vs. "$15 off," convert both to dollars saved:
- 25% of the item price in dollars
- Compare to $15
The percentage deal is better when the item price is high enough that the percentage exceeds the fixed amount:
Breakpoint = Fixed Amount ÷ (Percentage ÷ 100)
Example: $15 off vs. 25% off. Breakpoint = $15 ÷ 0.25 = $60. Above $60, take the 25%. Below $60, take the $15.
BOGO Deals: What's the Real Discount?
"Buy one get one" deals are discounts in disguise:
| Deal | Per-item discount |
|---|---|
| Buy 1 get 1 free | 50% off each |
| Buy 1 get 1 50% off | 25% off each |
| Buy 2 get 1 free | 33.3% off each |
| Buy 3 get 1 free | 25% off each |
Formula: Per-item discount = (Free/discounted items ÷ Total items) × Discount on free item
Common Mistakes
-
Adding stacked percentages. 20% + 10% ≠ 30%. It's 28%. Always apply sequentially.
-
Applying tax to the pre-discount price. Tax goes on the final discounted price in standard retail.
-
Confusing "% off" with "% of." 25% off $80 = you pay $60. 25% of $80 = $20 (the savings, not the price).
-
Rounding between steps. When chaining discounts, keep full decimal precision until the final result, then round to two decimal places.
-
Assuming BOGO = 50% off everything. "Buy one get one 50% off" is 25% off per item, not 50%.
Try It Yourself
Use our discount calculator to apply single or stacked discounts with optional sales tax. It shows a step-by-step breakdown so you can verify the math.
For related calculations:
- Percentage Calculator — find any percentage of a number
- Percentage Change Calculator — compute percent increase or decrease
- Markup Calculator — calculate selling price from cost and markup
- Margin Calculator — find profit margins