Reverse Percentage Calculator – ProMathTools

Reverse Percentage

This calculator helps you find the original number or amount before a percentage increase or decrease was applied. It's super handy for figuring out prices before sales tax or discounts, or for understanding previous values in data analysis.

Final Number

The number or amount after the percentage change.

Percentage Change (%)

The percentage that was added or subtracted.

Type of Change

Was the percentage an increase or a decrease?

How it works

This calculator helps you find the original number or amount before a percentage increase or decrease was applied. It's super handy for figuring out prices before sales tax or discounts, or for understanding previous values in data analysis.

The Formula

Original Number = Final Number / (1 ± Percentage / 100) Use '+' for an increase and '-' for a decrease.

Worked Example

Finding an Original Price
Imagine a jacket is on sale for £80 after a 20% discount. To find its original price, you'd enter: Final Number: 80 Percentage Change: 20 Type of Change: Decrease The calculator will show the original price was £100.

Tips, Assumptions & Limitations

Always double-check if the percentage was an increase or a decrease, as this changes the formula significantly.
Be careful with percentages over 100% for decreases; a 100% decrease would mean the original number was 0, which might not make sense for your problem.
This tool is great for checking your homework on percentage problems or verifying sale prices.

FAQ

A reverse percentage is when you know a number after a percentage change (either an increase or a decrease) and you want to find the original number before that change happened. For example, finding the price of an item before sales tax was added.

To find the original number after an increase, you divide the final number by (1 + percentage / 100). For instance, if a number increased by 10% to become 110, the original number was 110 / (1 + 10/100) = 110 / 1.1 = 100.

To find the original number after a decrease, you divide the final number by (1 - percentage / 100). For example, if a number decreased by 20% to become 80, the original number was 80 / (1 - 20/100) = 80 / 0.8 = 100.

Absolutely! This calculator is perfect for those situations. If you know the final price including sales tax, you can use the 'increase' option to find the price before tax. If you know the discounted price, use the 'decrease' option to find the original price before the discount.