The basic discount formula
When something is on sale, you need three numbers:
- Original price — the full price before the discount.
- Discount percentage — how much is being taken off, expressed as a percentage.
- Final price — what you actually pay.
The relationship between them:
Discount amount = Original price × (Discount % / 100)
Final price = Original price − Discount amount
Or combined into one step:
Final price = Original price × (1 − Discount % / 100)
Example 1: A clothing sale
A jacket has an original price of 120 and is on sale for 25% off.
Discount amount = 120 × (25 / 100)
Discount amount = 120 × 0.25
Discount amount = 30
Final price = 120 − 30 = 90
You save 30 and pay 90.
Example 2: Verify a "was/now" price
You see a sofa advertised at "Was 800, Now 600." Is that really a 25% discount?
Discount amount = 800 − 600 = 200
Discount percentage = (200 / 800) × 100 = 25%
Yes — it is exactly 25% off.
This is useful for checking whether advertised savings are accurate, especially during sale events where "original" prices may be questionable.
Example 3: Finding the original price from a discounted price
You know the sale price is 85 and the discount was 15%. What was the original price?
Original price = Sale price / (1 − Discount % / 100)
Original price = 85 / (1 − 0.15)
Original price = 85 / 0.85
Original price ≈ 100
The original price was 100.
Stacked discounts
Some promotions combine discounts. For example, "20% off, then an extra 10% off at checkout."
These do not add up to 30%. Each discount is applied to the price after the previous discount.
Starting price: 100
After 20% off: 100 × 0.80 = 80
After an extra 10% off the already-reduced price: 80 × 0.90 = 72
Total saving: 100 − 72 = 28 (not 30).
Effective discount rate: (28 / 100) × 100 = 28%
To calculate the effective rate of any two stacked discounts:
Effective rate = 1 − (1 − D1/100) × (1 − D2/100)
For 20% and 10%:
Effective rate = 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28 = 28%
Reverse calculation: what percentage off?
You find a pair of shoes at 65 that were originally 95. What is the discount percentage?
Discount % = ((Original − Sale) / Original) × 100
Discount % = ((95 − 65) / 95) × 100
Discount % = (30 / 95) × 100
Discount % ≈ 31.6%
Quick reference
| Original | Discount | You save | You pay |
|---|---|---|---|
| 50 | 10% | 5 | 45 |
| 100 | 20% | 20 | 80 |
| 200 | 15% | 30 | 170 |
| 350 | 30% | 105 | 245 |
| 80 | 50% | 40 | 40 |
Practical tips
- Always verify claimed discounts. Calculate the actual percentage from the original and sale price, especially during major sale events.
- Stack carefully. Two separate discounts are not additive — they multiply.
- Watch for VAT/tax. Discounts are usually applied to the pre-tax price. Check whether the final price shown includes tax.
- Price anchoring. A high "original" price makes a discount look impressive. If the item was sold at that price for only a short period, the discount may be misleading.
Use the Discount Calculator to compute any discount scenario instantly. For understanding the percentage maths behind it, see How to Calculate a Percentage.