Successive Discount CalculatorFree online math calculator — instant results, no sign-up
Calculate the combined discount from two successive reductions.
About the Successive Discount Calculator
The Successive Discount Calculator finds the final amount and combined percentage discount when two reductions are applied one after the other. The second discount applies to the already-reduced amount, not the original amount. With an original amount of 100, a first discount of 20%, and a second discount of 10%, the final amount is 72 and the combined discount is 28%.
- Original amount
- The amount before either discount, expressed in your chosen currency or other consistent units, with a default of 100.
- First discount (%)
- The percentage reduction applied to the original amount, with a default of 20%.
- Second discount (%)
- The percentage reduction applied after the first discount, with a default of 10%.
Formula and method
F = A × (1 − d₁/100) × (1 − d₂/100); D = 100 × [1 − (1 − d₁/100) × (1 − d₂/100)] = d₁ + d₂ − d₁d₂/100. With the default inputs: F = 100 × 0.80 × 0.90 = 72; D = 100 × (1 − 0.80 × 0.90) = 28%.
- AOriginal amount before either discount.
- d₁First discount expressed as a percentage number, such as 20 for 20%.
- d₂Second discount expressed as a percentage number, such as 10 for 10%.
- FFinal amount after both discounts, in the same units as A.
- DCombined discount expressed as a percentage of the original amount.
Convert each discount into the fraction of the amount that remains, then multiply the original amount by both remaining fractions. For the default inputs, the first reduction leaves 100 × 0.80 = 80, and the second leaves 80 × 0.90 = 72. The product of the remaining fractions is 0.72, so the combined discount is 100 × (1 − 0.72) = 28%.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Original amount100
- First discount (%)20
- Second discount (%)10
Results
- Final amount72
- Combined discount (%)28
How to use the Successive Discount Calculator
- 1Enter the Original amount before any reductions; use 100 for the worked example.
- 2Enter the First discount (%) as a percentage number; use 20 for the worked example.
- 3Enter the Second discount (%) as a percentage number; use 10 for the worked example.
- 4Run the calculation to apply the first discount and then apply the second discount to the reduced amount.
- 5Read the results: Final amount = 72 and Combined discount (%) = 28 for the default inputs.
Reading your result
Final amount is the amount remaining after both reductions, in the same units as the original amount; the default result is 72. Combined discount (%) is the single percentage reduction equivalent to applying both discounts successively; the default result is 28, meaning the final amount is 28% below the original amount.
Limitations
The calculation assumes two successive percentage discounts, a nonnegative original amount, and discount rates between 0% and 100%. It does not account for taxes, shipping, fixed-amount coupons, discount caps, or retailer-specific stacking rules. Rounding monetary amounts after each discount can produce a slightly different result from rounding only the final amount. If the original amount is zero, the final amount is zero; the combined rate can still be calculated from the discount rates, but it cannot be measured as savings divided by the original amount.
Common questions
Why do a 20% discount and a 10% discount combine to 28%, not 30%?+
The second discount is taken from the reduced amount of 80, so it removes 8 rather than 10. Total savings are 20 + 8 = 28 from the original amount of 100, which is a 28% combined discount.
Does reversing the two discount rates change the final amount?+
Not under the formula without intermediate rounding: multiplying by 0.80 and then 0.90 gives the same result as multiplying by 0.90 and then 0.80. The default final amount remains 72, though retailer rounding rules can affect actual charges.
Does the original amount affect the combined discount percentage?+
No. The combined percentage depends only on the two discount rates. With rates of 20% and 10%, it is 28%; the original amount determines how much that percentage represents in amount units.
What happens if either successive discount is 0% or 100%?+
A 0% discount leaves the amount unchanged at that stage, so the combined discount equals the other rate. A 100% discount makes the final amount zero and the combined discount 100%.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.