Discount Formula
A jacket priced at $120 is marked 35% off during a seasonal sale. Before you reach the register, you can already figure out your exact savings and final price with one simple formula – no guesswork required.
What is the discount formula?
A discount is a reduction applied to an original (list) price. The discount formula calculates either the amount saved or the final price after the reduction:
- Discount amount = Original Price × Discount Rate
- Sale Price = Original Price − Discount Amount
These two lines can be combined into a single expression:
Sale Price = Original Price × (1 − Discount Rate)
The discount rate is expressed as a decimal: 20% becomes 0.20, 35% becomes 0.35, and so on. This is the core formula used in retail, wholesale, finance, and everyday budgeting.
How to calculate a discount step by step
Follow these three steps to find the sale price of any item:
- Convert the percentage discount to a decimal by dividing by 100.
- Multiply the original price by that decimal to find the discount amount.
- Subtract the discount amount from the original price.
Example. A laptop costs $899 and is offered at 15% off.
- Discount amount: $899 × 0.15 = $134.85
- Sale price: $899 − $134.85 = $764.15
Or in one step: $899 × 0.85 = **$764.15**.
How to find the original price from the discounted price
Sometimes you know only the sale price and the discount percentage. To reverse the formula:
Original Price = Sale Price ÷ (1 − Discount Rate)
Example. A pair of shoes sells for $63 after a 10% discount.
- Original price = $63 ÷ 0.90 = **$70**
The customer saved $70 − $63 = $7.
How do successive discounts work?
Retailers sometimes stack two or more discounts – for instance, “20% off, then an additional 10% off.” These are successive discounts, and they are not simply additive.
For two discounts of a% and b%, the combined (effective) discount is:
Effective Discount = a + b − (a × b ÷ 100)
| Discount 1 | Discount 2 | You might expect | Actual effective discount |
|---|---|---|---|
| 20% | 10% | 30% | 28% |
| 30% | 20% | 50% | 44% |
| 25% | 15% | 40% | 36.25% |
| 40% | 10% | 50% | 46% |
Why the gap? The second discount applies to the already reduced price, not the original.
Full example. An item costs $200, with successive discounts of 20% and 10%.
- After the first discount: $200 × 0.80 = $160
- After the second discount: $160 × 0.90 = $144
- Total savings: $200 − $144 = $56, which is 28% – not 30%.
Discount formula in finance: present value and NPV
In corporate finance, the discount rate has a different meaning. It is the interest rate used to calculate the present value (PV) of future cash flows:
PV = FV ÷ (1 + r)ⁿ
Where:
- FV – future value (the amount to be received later)
- r – discount rate per period (as a decimal)
- n – number of periods
Example. You expect to receive $10,000 in 3 years. The annual discount rate is 8%.
- PV = $10,000 ÷ (1.08)³ = $10,000 ÷ 1.2597 = $7,938.32
This means $7,938.32 today is equivalent to $10,000 in three years at an 8% rate. This formula is the foundation of Discounted Cash Flow (DCF) analysis and Net Present Value (NPV) calculations.
Types of discounts
| Type | Where it’s used | How it works |
|---|---|---|
| Percentage | Retail sales, e-commerce | A % off the listed price (e.g., 25% off) |
| Fixed amount | Coupons, clearance | A flat dollar amount off (e.g., $15 off orders over $100) |
| Trade | B2B / wholesale | Deducted from the manufacturer’s list price before invoicing |
| Cash | Invoicing (“2/10 net 30”) | Small % off if the buyer pays within a set number of days |
| Volume / Bulk | Wholesale, subscriptions | Price per unit drops as order quantity increases |
| Seasonal | End-of-season clearance | Deep percentage cuts to move inventory |
Common mistakes when using the discount formula
- Adding percentages. Two discounts of 20% and 10% do not equal 30% off. Always apply them sequentially or use the successive discount formula.
- Confusing markup and discount. If a price is marked up by 25% and then discounted by 25%, you do not return to the original price. A $100 item marked up to $125, then discounted 25%, becomes $93.75.
- Ignoring the base. A “50% off plus an extra 20% off” means the 20% applies to the half-price amount – so the real combined discount is 60%, not 70%.
Quick reference: discount formulas at a glance
| Goal | Formula |
|---|---|
| Discount amount | Original Price × (Discount % ÷ 100) |
| Sale price | Original Price × (1 − Discount % ÷ 100) |
| Original price from sale price | Sale Price ÷ (1 − Discount % ÷ 100) |
| Two successive discounts (effective rate) | a + b − (a × b ÷ 100) |
| Present value (finance) | FV ÷ (1 + r)ⁿ |
This article is for educational purposes. When working with financial discount rates, consult a qualified advisor for investment decisions.