Discount Calculator

How discounts work

A discount calculator tells you the sale price and how much you save when a percentage is taken off the original price. It is handy for working out whether a "30% off" sticker is really the bargain it looks like, and for comparing deals that are advertised in different ways.

How to use this calculator

1. Enter the original price of the item, such as \(80\).
2. Enter the discount percent, such as \(25\).
3. Use the formula to multiply the original price by the remaining fraction after the discount.
4. Read the sale price and savings, then compare the result with the original price.

The formula explained

The formula \(\text{Sale Price} = \text{Original} \times \left(1 - \frac{\text{Discount}}{100}\right)\) computes the final price after a percent discount. The saved amount is the original price minus the sale price.

• \(\text{Sale Price}\) = the final price after the discount is applied
• \(\text{Original}\) = the starting price before any discount
• \(\text{Discount}\) = the discount percent
• \(\frac{\text{Discount}}{100}\) = the discount written as a decimal fraction

Step by step method

1. Convert the discount percent to a fraction of \(100\).
2. Subtract that fraction from \(1\) to find the part of the price you still pay.
3. Multiply the original price by that remaining part.
4. If needed, subtract the sale price from the original price to find the savings.

Worked example

Problem. A jacket costs \(80\) dollars and is discounted by \(25\%\). Find the sale price and the savings.

1. Compute the remaining fraction, \(1 - \frac{25}{100} = 1 - 0.25 = 0.75\).
2. Multiply by the original price, \(80 \times 0.75 = 60\).
3. Find the savings, \(80 - 60 = 20\).

Tips and common mistakes

• A \(25\%\) discount means you pay \(75\%\) of the original price, not \(25\%\) of it.
• Be careful to use the original price before tax, if you want the discount alone.

Frequently asked questions