Percent Discount

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Percent Discount Calculation:

  • i$ =

    Price of item in dollars or currency

  • d% =

    Percent of discount

  • p$ =

    Final price of item in dollars or currency after percent discount

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Discount Percent Visualization

Percent Discount Formula

When calculating the final price of an item after a percent discount the application of the discount can be applied in two different but equal ways. In the first formula the percent discount is converted into the percent of the price that will be paid in the end. In the second formula we calculate the discount and subtract it from the price.

First consider the problem by calculating the percent that will be paid rather than the percent discount, 100% minus the discount percent.

p = i * (1-d/100)

Alternatively, find the amount of the discount and subtract it from the price.

p = i - i * (d/100)

Percent Discount Variables

To find the final price (p) after some percent discount (d) we need the input of some initial price (i).

Initial Price (i)
Initial price of the item in dollars or currency. The final price will be in the same units as the input price. Technically the dimension do not need to be currency at all and this could be used as a percent reduction calculator.
Percent Discount (d)
Percent that the initial input price or value will be reduced by.
Final Price (p)
Final price or value after applying the discount. Final value will be in the same units as the input value be they dollars, currency, or some other dimensions.

Percent Discount Solution

An item is marked down for sale. If the initial price is $85 and the reduction is 15% what is the final price.

  • p = i * (1-d/100)
  • Use the formula of finding the percent of the price that will be paid for the item
  • p = 85 * (1-15/100)
  • Substitute in the price of $85 and the discount of 15%
  • p = 85 * (1-0.15)
  • Divide the percent by 100 to get the decimal fraction of percent
  • p = 85 * (0.85)
  • Subtract the percent discount from 1 (100%, of the price) to get the percent that represents the fraction of the price that will be paid
  • p = 72.25
  • Multiply the price by the percent that will be paid
  • $72.25

If an item listed at $85 is discounted at 15% that means 85% (100%-15%) of the price will be paid. The final price that will be paid is $72.25.

Percent Discount Example

If a $20 item is listed as 25% off calculate the final price by calculating the dollars that will be saved and subtracting them from the initial price.

  • p = i - i * (d/100)
  • p = 20 - 20 * (25/100)
  • p = 20 - 20 * 0.25
  • p = 20 - 5
  • 15

If a $20 item is listed at 25% off the savings will be $5, which makes the final price $15 ($20-$5).

Other Percent Calculations

Percent change

Percent increase

Percent decrease