This guide will show you how you can compute reverse percentages in Google Sheets using basic arithmetic operations.
Reverse percentages, or inverse percentages, are useful when you have the final value and the percentage or percentage change, and you need to work “backward” to get the original number.
There are two possible ways we can compute for the reverse percentage. First, we can find the original value given the final number and the percentage of the original number that made it. Second, we can find the original value given the final value, and the percentage increased or decreased. Both of these have their own formulas, which we will explore later.
Let’s look at a scenario where we might need to solve for a reverse percentage.
In this example, let’s say you want to buy the latest iPhone. According to their website, it is currently on sale for $524. The website also mentions that the iPhone is currently at 75% of its original price. You want to know how much money you saved, so you want to know the original price. How can we do this?
We can easily solve for the original price by using the following formula:
final_price / percentage = original_price
Using this formula, we can see that the original price of the iPhone is about $698. We can confirm this by solving for the discount. Seventy-five percent of $698 is $524. This means that we would have saved $174 on the sale.
Alternatively, you might have a different set of given values: the final price and the percentage that increased or decreased. For example, you bought a shirt that cost you $12 that was said to be 20% off its original price. To get the original price, we can use the following formula:
final_price / (1-percentage) = original_price
Similarly, if the price has increased by a certain percentage, we can use the following formula to get the original price:
final_price / (1+percentage) = original_price
For example, let’s say that we know that a certain brand’s internet speed is 20% quicker than one of their competitors. We know that the current internet speed is 95Mbps. We can use the reverse percentage formula above to get the speed of their competitor.
Now you have an idea of when to use reverse percentages. Let’s now look at an application of it working on an actual Google Sheet.
A Real Example of Calculating the Reverse Percentage
Let’s look at a real example of solving for reverse percentages used in a Google Sheets spreadsheet.
In the table below, we have a column that computes the original price of a product given its final price and the discount.
To get the values in Column C, we just need to use the following formula:
In the example below, we have a Reverse Percentage Calculator. We add our discounted value in cell B2 and our percentage in cell B3. Our calculator will then return the original value.
In this next example, we have a list of cities in the United States and their growth rate and current population. Using the reverse percentage formula, we can infer what the population was last year, assuming the given growth rate. For example, using this table, we can see that Buckeye City had an estimated population of 95,238 last year, assuming a yearly growth rate of 5%.
You can make your own copy of the spreadsheet above using the link attached below.
If you’re ready to try computing reverse percentages in Google Sheets, let’s begin writing it ourselves!
How to Calculate Reverse Percentages in Google Sheets
In this section, we will go through each step needed to start computing the reverse percentages in Google Sheets. This guide will show you how to find the original price of an item given its discounted price and the discount.
Follow these steps to start calculating for reverse percentages:
- First, make sure that you have both the discounted price and discount available. In the table below, we have both variables in their indicated columns.
- Select a cell to place our formula. In this example, we’ll start with cell C2.
- Write down the formula using cell references to the discounted price and discount. For the first price, we used the formula
=A2/(1-B2). Note that we used a subtraction in the denominator. This is because we know that this is a percentage decrease.
- Once you get the right result, we can drag the formula down to fill out the rest of the column.
Frequently Asked Questions (FAQ)
- Can you use decimals for percentage increases and decreases?
As an alternative to subtracting or adding to 1, you can also use decimals to represent increases and decreases. For example, 0.75 represents a 25% decrease, and 1.35 represents a 35% increase.
- Why does my formula return an error?
Make sure that the values are all numerical. Do also make sure that the denominator does not equal to 0 otherwise, the formula will return a
#DIV/0!error. For example, a final price of $25 with a 100% discount is mathematically invalid because that would mean that the denominator would equal zero =25/(1-100%) = 25/(1-1) = 25/0.
That’s all you need to remember to start solving reverse or inverse percentages problems in Google Sheets. This step-by-step guide shows how to use basic arithmetic operators to find the original value before a percentage change.
You can now use this reverse percentage formula together with the various other Google Sheets formulas available to easily create great worksheets that just work for your use case.
Stay notified of new Google Sheets guides like this by subscribing to our newsletter!