Choose the initial price, discount, or final price to solve for, then enter the four displayed values. Discounts apply sequentially, with one final rounding to cents.
Triple Discount Formula
A triple discount applies three discounts one after another. Each discount is applied to the reduced price from the previous step, not to the original price each time.
To solve for the initial price:
To solve for one missing discount:
- FP = final price after all three discounts
- IP = initial price before any discount
- D1 = first discount percentage
- D2 = second discount percentage
- D3 = third discount percentage
Select Final price to multiply the initial price by all three discount factors.
Select Initial price to divide the final price by the three discount factors. A known 100% discount makes the inverse nonunique or impossible.
Select the missing discount to rearrange the same formula. Enter the four displayed values. A zero price or another 100% discount can prevent a unique solution.
Triple Discount Multipliers and Equivalent Discounts
These examples show how separate discounts combine. The equivalent single discount is the one discount that would give the same final price.
| Discounts | Multiplier | Equivalent single discount | Final price on $100 |
|---|---|---|---|
| 10%, 10%, 10% | 0.729 | 27.10% | $72.90 |
| 20%, 10%, 5% | 0.684 | 31.60% | $68.40 |
| 25%, 15%, 10% | 0.57375 | 42.63% | $57.38 |
| 50%, 20%, 10% | 0.36 | 64.00% | $36.00 |
Price After Each Discount
This table shows the step-by-step price for a $200 item with three discounts.
| Step | Discount | Calculation | Price |
|---|---|---|---|
| Starting price | None | $200.00 | $200.00 |
| After first discount | 20% | 200 × 0.80 | $160.00 |
| After second discount | 10% | 160 × 0.90 | $144.00 |
| After third discount | 5% | 144 × 0.95 | $136.80 |
Examples
Example 1: Find the final price
You have an initial price of $150 with discounts of 20%, 15%, and 10%.
The final price is $91.80.
Example 2: Find a missing third discount
An item starts at $200. The first discount is 25%, the second discount is 10%, and the final price is $121.50.
The third discount is 10%.
FAQ
Are three 10% discounts the same as one 30% discount?
No. Three 10% discounts are applied one after another. The combined multiplier is 0.90 × 0.90 × 0.90 = 0.729. That means the equivalent single discount is 27.10%, not 30%.
Does the order of the three discounts matter?
No. For percentage discounts only, the order does not change the final price. For example, 20%, 10%, and 5% give the same result in any order because the same three multipliers are being multiplied together.
Why can the calculator reject a missing discount result?
A missing discount must be between 0% and 100%. If the numbers imply a negative discount or a discount greater than 100%, the inputs are not consistent. Check the initial price, final price, and the other two discounts.
