Reverse Percentage Calculator: Find the Original Number Before Change
ByMuhammad Ali•Founder of KruskalCode
15:21
6 min read
Have you ever seen a sale price and wondered what the item cost originally? Or perhaps you've been given a final figure after a percentage increase and need to work backwards? This is where a reverse percentage calculation comes in handy. It's a common problem in school maths, personal finance, and even business, helping you uncover the starting value before any percentage adjustments.
Explanation
A reverse percentage calculation is about undoing a percentage change. Instead of finding a percentage of a number, you're finding the number that a given percentage was taken from or added to. The key is to understand that the final number represents a different percentage of the original. For an increase, the final number is more than 100% of the original. For a decrease, it's less than 100% of the original. Our calculator simplifies this process, allowing you to quickly find that elusive original number.
Formula
The general formula for a reverse percentage is: Original Number = Final Number / (1 ± Percentage / 100) Here's how it breaks down: * **For a percentage increase:** You use the '+' sign. The final number is divided by (1 + the percentage as a decimal). * Example: If a number increased by 20%, it became 120% of its original value. So, you divide by 1.20. * **For a percentage decrease:** You use the '-' sign. The final number is divided by (1 - the percentage as a decimal). * Example: If a number decreased by 20%, it became 80% of its original value. So, you divide by 0.80.
Example
Let's say you bought a new gadget for $240, and you know this price included a 20% sales tax. What was the price of the gadget before tax? Here, the final number is $240, the percentage change is 20%, and it was an increase (sales tax added). Using the formula: Original Price = $240 / (1 + 20/100) Original Price = $240 / (1 + 0.20) Original Price = $240 / 1.20 Original Price = $200 So, the gadget cost $200 before the sales tax was applied.
How to use the related calculator
Using our Reverse Percentage Calculator is straightforward. First, enter the 'Final Number' – this is the value you have after the percentage change. Next, input the 'Percentage Change' (just the number, e.g., '20' for 20%). Finally, select whether the original number was subjected to an 'Increase' or a 'Decrease'. Hit calculate, and the tool will instantly display the 'Original Number' for you.
Try the related calculator
Open toolFAQ
What is a reverse percentage?
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.
How do you calculate the original number after a percentage increase?
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.
How do you calculate the original number after a percentage decrease?
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.
Can I use this calculator for sales tax or discounts?
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.
Related articles
About the author
Muhammad Ali. Muhammad Ali is a full-stack developer and founder of KruskalCode. He builds SaaS platforms and automation systems with React and Laravel, and helps teams ship fast, scalable tools.
Need a custom calculator, dashboard, or automation workflow? Reach out to KruskalCode.
