How To Calculate Reverse Percentage

If you have a starting amount and you want to add a percentage, simply multiply the percent by the original amount to find the amount that gets added. For example, if you need to calculate how much sales tax or tip to add to the bill. But if you only have the final amount know the percentage added, you need to work in reverse to find the original amount. For example, if you had the final cost and the percentage of sales tax and you want to know the cost before tax.

1. Convert Percentage to Decimal

Divide the percentage added to the original by 100. For example, if a sales tax of 6 percent was added to the bill to make it $212, work out

\(6 ÷ 100 = 0.06\)

2. Add 1 to Decimal

Add 1 to the percentage expressed as a decimal. In this example,work out

\(1 + 0.06 = 1.06\)

3. Divide Final Amount by Decimal

Divide the final amount by the decimal to find the original amount before the percentage was added. In this example, work out

\(212 ÷ 1.06 = 200\)

The amount before the sales tax was added is $200.

4. Subtract Original Amount From Final Amount

Subtract the original amount from the final amount to find the amount added. In this example, work out

\(212 – 200 = 12\)

You now know that $12 was added.