Discount Calculator — Step-by-Step Solutions
The Discount Calculator helps you work out sale prices, find discount percentages, and calculate stacked (double) discounts. It supports four modes: find the sale price after a discount, determine the discount percentage from original and sale prices, calculate the effective discount when two discounts are stacked, and see how much you save.
The comparison table shows savings at common discount levels, and the visual bar chart breaks down what you pay versus what you save.
Your calculations will appear here
How to Use the Discount Calculator
- Choose a calculation mode. Sale Price calculates the price after a discount. Find Discount % determines the discount percentage from original and sale prices. Stacked Discounts calculates the effect of two successive discounts. Amount Saved shows your total savings.
- Enter the original price and discount percentage (or sale price, depending on the mode). Use the quick-select buttons for common discount percentages. Results update instantly.
- Review the step-by-step working to understand the calculation. The visual bar shows what proportion of the original price you pay versus what you save.
- For stacked discounts, note that applying two discounts sequentially is not the same as adding them together. A 20% discount followed by a 10% discount is not equivalent to a 30% discount.
Formula and Theory
A discount reduces the price of an item by a percentage of the original price. The sale price equals the original price multiplied by (1 minus the discount as a decimal). For example, a 25% discount on $100 gives a sale price of $100 x (1 - 0.25) = $75.
To find the discount percentage when you know the original and sale prices, calculate: discount = (original - sale) / original x 100. This is useful when a shop displays both prices but not the percentage off.
Stacked discounts (also called double or successive discounts) apply one discount after another. The second discount applies to the already-reduced price, not the original. This means two 20% discounts do not equal a 40% discount. Instead: $100 x 0.80 x 0.80 = $64, which is effectively a 36% discount.
The effective discount rate for stacked discounts d1 and d2 is: 1 - (1 - d1/100)(1 - d2/100), multiplied by 100 to express as a percentage. The effective rate is always less than the sum of the individual rates.
Worked Examples
Example 1: Simple percentage discount
Problem: A jacket originally costs $120 and is 25% off. What is the sale price?
Solution: Discount amount = $120 x 25/100 = $30. Sale price = $120 - $30 = $90.
Answer: $90.00 sale price, $30.00 saved
Example 2: Finding the discount percentage
Problem: A shirt was $80 and is now on sale for $56. What is the discount percentage?
Solution: Savings = $80 - $56 = $24. Discount = $24 / $80 x 100 = 30%.
Answer: 30% discount
Example 3: Stacked discounts on a purchase
Problem: A $200 item has a 20% sale. You also have a 10% coupon applied after the sale. What is the final price?
Solution: After 20% off: $200 x 0.80 = $160. After additional 10% off: $160 x 0.90 = $144. Total saved: $200 - $144 = $56. Effective discount: 28%.
Answer: $144.00 final price (28% effective discount)
Example 4: Amount saved at different discounts
Problem: Compare savings on a $250 item at 10%, 20%, and 30% discount.
Solution: 10%: save $25, pay $225. 20%: save $50, pay $200. 30%: save $75, pay $175.
Answer: $25, $50, and $75 saved respectively
Frequently Asked Questions
Why is a 20% + 10% discount not the same as 30%?
Which order should I apply stacked discounts?
How do I calculate what I save during a sale?
What is the formula for the effective discount of stacked discounts?
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