The percentage difference calculator will be the most useful in cases when none of the values should be considered the initial or base value. It can be used to compare two different values, such as prices or measurements. In other words, it determines the difference in percentage between the two values.
For instance, the percentage difference between 50 and 75 is 40% based on their average as the reference point. However, an increase from 50 to 75 is equal to 50% since it calculates percentage based on 50 being the original number. The percentage difference calculator shows both results separately so that you can distinguish between them.
To find the percent difference between two values:
- Take one value away from the other.
- Find the absolute value of that subtraction result.
- Find the average of those two values.
- Divide the absolute difference by the average.
- Multiply the division result by 100.
The equation looks like this:
The absolute-value symbols ensure that the result will be a positive number, no matter which order in which you enter the values. The use of the average in the equation prevents any changes to the result when the values are flipped around each other.
How to Use the Tool
Using the online calculator requires just a few seconds.
- Type the first number into the Value A box.
- Type the second number into the Value B box.
- Check the result.
- Look through the step-by-step calculation description to understand how the tool came to the result.
- Click Copy to copy the result, Save to save it, or Reset to start a new computation.
Both input fields accept either integer or decimal values. Input values must be of the same unit type—dollar versus dollar, kilograms versus kilograms, centimeters versus centimeters, etc.
What Does the Result Mean?
In this way, the outcome reveals the size of the difference between two numbers based on their middle point.
A result of:
- 0% indicates the numbers are identical.
- 5% indicates the values are rather close.
- 40% indicates the difference is equal to 40% of the average of those values.
- 100% indicates one positive number is three times bigger than the other.
- 200% occurs when one non-negative value is zero and the other value is bigger than zero.
There is no universal percentage that automatically implies that a comparison is good/bad, big/small. It all depends on the subject under discussion. The gap of 2% might matter for laboratory tests but is not as important while comparing project estimates at the initial stage of development.
Percentage Difference Formula
For two numbers, A and B, use the following formula:
Where:
- A is the first number.
- B is the second number.
- |A − B| is the absolute numerical difference.
- (A + B) ÷ 2 is the average of both numbers.
- Multiplication by 100 transforms the result to a percentage.
We use the average because there is no initial/correct/more important number among them.
How to Calculate Percentage Difference Manually
Let us say that you want to calculate the difference between 50 and 75.
Step 1: Find the Absolute Difference
The absolute numerical difference between the two numbers is 25.
Step 2: Find the Average
The midpoint, or the average of the two numbers, is 62.5.
Step 3: Divide the Difference by the Average
In this step, you are comparing the numerical difference to the average of the two numbers.
Step 4: Convert the Decimal to a Percent
Thus, the percentage difference between 50 and 75 is 40%.
Why Does the Tool Also Show a 50% Increase?
The two percentages provide different information.
Symmetric Comparison
In case of symmetrical comparison of 50 and 75 as two values of equal importance:
Directional Increase
If 50 is the old value and 75 is the new one:
The first percentage describes the relative distance between the two equally important values, while the second provides the percentage increase from a certain initial point.
This differentiation should be clear for you when you are comparing prices, sales, measurements, business performance, etc.
Percentage Difference vs. Percentage Change
People tend to misuse the terms, using them interchangeably, although these are two different types of computation.
| Comparison method | When to use it | Reference value | Shows direction? |
| Percentage difference | Neither value is the baseline | Average of both values | No |
| Percentage change | One value is the original figure | Original value | Yes |
| Percentage increase | The new value is higher | Original value | Yes |
| Percentage decrease | The new value is lower | Original value | Yes |
| Percentage-point difference | Both inputs are percentages | Direct subtraction | Sometimes |
| Percent error | A measured value is compared with an accepted value | Accepted value | Usually no |
| Statistical variance | You are measuring the spread of a dataset | Dataset mean | No |
Apply the current formula where both values have the same weight. Apply the percent change formula where there is an obvious original and updated figure.
Percentage Difference between Two Percentages
In case both figures given are percentages themselves, you may need either a percentage point difference or a relative difference.
Let the first percentage be 45%, and the second one be 60%.
Percentage-Point Difference
Relative Percent Difference
Which concept will give you the right result depends on what question needs to be answered:
- Apply 15 percentage points in order to indicate the absolute difference between two rates.
- Apply 28.57% in order to find out the relative difference between them on average.
It is important in comparison of interest rates, survey results, conversion rates, polling data, success rates, and other percentage amounts.
How to Calculate Percentage Difference in Excel
Put the first figure in cell A2 and the second figure in cell B2.
Apply the following Excel formula:
=ABS(A2-B2)/AVERAGE(A2,B2)
After this, format the cell with the calculated value as a percentage.
Another way is to use:
=ABS(A2-B2)/AVERAGE(A2,B2)*100
In case you apply the latter formula, do not format the cell that will contain the result as a percentage since the formula itself will multiply the result by 100.
Formula With Zero Handling
Apply this formula to avoid dividing by zero error:
=IF(AVERAGE(A2,B2)=0,"Undefined",ABS(A2-B2)/AVERAGE(A2,B2))
Format any numerical output of this formula as a percentage.
How to Calculate the Difference of Two Percentages in Google Sheets
The formulas used in Google Sheets are the same as in Excel.
Input:
=ABS(A2-B2)/AVERAGE(A2,B2)
Then format the cell with the result as a percentage.
If you want to find the percentage point difference, use:
=ABS(A2-B2)
For instance, if A2 equals 45% and B2 is 60%, the percentage point difference equals 15 percentage points.
Do not multiply the formula by 100 and format the resulting cell as a percentage, since applying both operations to the same cell may result in an incorrect value 100 times bigger than the right one.
Price Difference in Percentage
Price comparison may be useful in case of assessment of two retailers, suppliers’ quotations, subscriptions, packages of services, and current market prices.
For example, the price of one product is $80, and the other one is $100.
Symmetrical Price Comparison
The prices are different by 22.22% considering their average value.
Price Increase From $80 to $100
The new price is 25% greater than the initial price of $80.
Use the former formula when comparing two prices symmetrically. Use the latter when analyzing the increase of price through time.
Relative Percent Difference
Relative percent difference, which may be written as RPD, is usually calculated using the symmetric average-based formula of two values’ comparison:
This notion is widely used when evaluating duplicate measurements, observations, or testing. The smaller the RPD result, the closer the two compared values; the bigger one, the further.
The acceptable RPD level varies in dependence on the industry, methods of testing, accuracy of measurements, and other standards. The calculator gives the mathematical answer, but not the acceptable one.
Practical Examples
Comparing Two Product Prices
The price of a certain product is $24 and $30 in two different stores.
The two prices vary by 22.22% of their average.
Comparing Test Scores
Two students have test scores of 72 and 84.
The two test scores vary by 15.38% of their average.
Comparing Measurements
Two measurements made are 98.5 cm and 101.5 cm.
The two measurements vary by 3%.
Comparing Supplier Quotes
Two suppliers provide quotes of $4,200 and $4,800.
The two quotes vary by 13.33% of their midpoint.
Comparing Production Totals
Two machines produce 940 units and 1,060 units.
The two production totals vary by 12% of their average.
Is This a Variance-Between-Two-Numbers Calculator?
This is not statistically a variance calculator between two numbers.
The difference between two numbers is:
The percentage comparison between the two numbers is expressed as follows:
Variance in statistics calculates how much the values are spread from their mean. It is commonly calculated with an entire dataset but not necessarily two separate figures.
Sometimes people use a difference, gap, or variation as a “variance.” However, formally speaking, in mathematics and statistics, variance implies another calculation.
When Should You Use This Calculation?
Use it when:
- Comparing two prices in the present without choosing a base
- Testing the correspondence between two measurements
- Comparing students’/groups’ grades
- Looking through quotes of your suppliers, contractors, or vendors
- Calculating the gap between two estimates
- Comparing the numbers of production/performance
- Finding relative percent difference
- Comparing two independent numerical values
Don’t apply this formula if:
- There is a clear number indicating the original value.
- You need to show a change over time.
- There is an accepted standard value.
- There is a need to show the difference in percentage points.
- You calculate the variance of your statistic.
Important Edge Cases
Both Values Are Equal
If the two values are the same, then the numerical difference will be zero, which gives 0% in the end.
One Value Is Zero
If you compare zero with some positive number, then the result will be 200%.
This is not the case for 50 being a 200% increase over zero. The percent change from zero is undefined since there will be zero in the denominator.
Both Values Are Zero
The difference between the two numbers is zero, but the average is also zero. Due to the impossibility of division by zero, there will be no finite percentage calculated.
The Average Is Zero
Pairs of opposite signed values, such as -10 and 10, will have an average value of 0. As such, the usual average method of calculating percentages cannot yield a finite percentage.
Negative Values
The negative numbers can represent temperature readings, bank account balance, coordinates, losses, signed differences, and others. The exact meaning of negative numbers depends on a particular situation. In general, non-negative numbers should be used for comparisons for normal quantities.
Common Calculation Mistakes
Dividing by the Larger Number
Dividing by the larger number will not give a neutral comparison between the two numbers. Furthermore, switching the order of the two numbers will give different answers.
Dividing by the Smaller Number
The division where the smaller number is used as the denominator normally causes a directional effect instead of comparing the two numbers equally.
Forgetting the Absolute Value
Omission of the absolute value may lead to the negative result, especially when the smaller number is placed at first.
Confusing Percent With Percentage Points
A transition from 30 percent to 40 percent is a difference of 10 percentage points, but it is not just a 10 percent increase.
Formatting an Excel Result Twice
Applying a multiplication by 100 and also using the percent format on a spreadsheet formula may give an incorrect answer of 4,000 percent for what should have been 40 percent.
Mixing Units
Remember to compare values in the same unit. Never compare dollars to kilograms or feet to meters until you convert them to the same units.
Frequently Asked Questions
What is a percentage difference calculator?
It is an online calculator that calculates the ratio of the relative difference between two numbers by dividing the absolute difference by their average value.
How to find the percentage difference between two numbers?
Calculate the difference between two numbers, take out the minus sign, average the two numbers, and then divide the difference by their average.
How to calculate the percentage difference between two numbers?
Find the absolute difference between two numbers and then compare the difference with their average. The two numbers must be similar in magnitude and units.
What is the formula for calculating percentage difference?
A simple formula is used in calculating the percentage difference where the absolute difference between two numbers is divided by their average.
What is the percentage difference between 50 and 75?
The answer is 40%. The numbers are 25 units apart, and their average is 62.5.
Is 75 40% or 50% more than 50?
The first number is 50% higher than 50 since the latter is the base number. But the comparison of these two numbers gives the result of 40% due to using their average.
Is there any difference between the two numbers' order?
Not really, in case of positive values, swapping these numbers will not affect the result due to using the absolute difference and mean of these numbers.
Could the percentage difference be negative?
The result cannot be negative because of using the absolute numerical difference. But for the negative values, the situation might need additional analysis depending on the context.
Could the result be higher than 100%?
Yes, for the nonnegative numbers, the percentage difference could be anywhere between 0% and 200%. The figure higher than 100% indicates that the difference is greater than the average of two numbers.
What happens if one of the values is zero?
A comparison of zero with the positive value gives a 200% symmetric difference. The percentage change calculation from zero is another thing, and it is not possible because of the absence of any denominator other than zero.
What if both numbers are equal to zero?
It's undefined, because the numerator (numerical difference) and the denominator (average) are both zeros, and the fraction is divided by zero.
Are percentage difference and percentage change equal?
No, they're not. While the former is based on equal treatment of the two compared numbers, the latter is calculated relative to the old value and shows either increase or decrease.
How do I find the percentage difference in Excel?
Insert both values into two different cells, and use the subtraction formula for them and the average formula. Then just divide the difference by average.
How do I find the percentage difference between two numbers in Google Sheets?
The method is the same as in Excel. You need to divide the difference of two cells by the average.
How do I calculate the difference between two percentages in Sheets?
Subtract one percentage from another and take the absolute value of the percentage point difference. Calculate their relative difference using the average-based formula when necessary.
How do I calculate a price difference in percentage?
The absolute price difference should be compared to the average price in case the two prices have the same importance. When one price is the initial price, calculate the percentage difference of change.
What is an RPD calculator?
It is an instrument which calculates the relative percent difference between two figures. It is widely used in case of duplicate measurements/tests/observations.
Are percentage variations the same?
The term “percentage variation” can be either percentage difference or percentage change. It depends if the formula used the average of both numbers or the original number.
Is this different from the general percentage calculator?
Yes, the general percentage calculator is a general tool that will let you find the percentage of a number, the percentage of one number to another, or the percentage added to a number.
How many decimal places do I have to show?
Two decimal places are acceptable for most practical purposes. More decimal places may be necessary for scientific, financial, engineering, or contractual purposes.
