Percentage difference and percentage change can produce different answers for the same pair of numbers. That does not mean one calculation is wrong. They use different reference values and answer different questions. Choosing the right formula starts with deciding whether one number is your baseline.
For example, the percentage difference between 100 and 120 is approximately 18.18% using their average. Moving from 100 to 120 is a 20% increase. Moving back from 120 to 100 is a 16.67% decrease. This guide explains why those answers differ and how to choose the right calculation for prices, sales, and performance reports.
Percentage difference compares two values without assigning either one the role of an original value. A common definition divides their absolute difference by their average. This guide uses that definition for positive values, such as two supplier quotes collected at the same time.
Percentage change measures movement from an original value to a new value. Examples include sales growth between months and a price increase over time. The original value is the denominator, so reversing the comparison changes the result.
For two positive values, use:
Percentage difference = absolute difference ÷ average of the two values ×100
- Subtract the smaller value from the larger value.
- Add both values and divide by 2 to find their average.
- Divide the absolute difference by that average and multiply by 100.
For 100 and 120, the absolute difference is 20. Their average is (100 +120) ÷2 =110. The percentage difference is 20 ÷110 ×100 ≈ 18.18%.
This comparison is symmetric: switching the order of 100 and 120 gives the same answer. Neither number serves as the starting point. When writing a report, state that you used the average-based definition because informal uses of “percentage difference” sometimes mean percentage change instead.
When you have a starting value and an ending value, use:
Percentage change = (new value − original value) ÷ original value ×100
Moving from 100 to 120 gives (120 −100) ÷100 ×100 = 20%. A positive result indicates an increase. Moving from 120 to 100 gives (100 −120) ÷120 ×100 ≈ −16.67%, indicating a decrease.
The return trip has a different percentage because its starting point is larger. Likewise, adding 20% and then subtracting 20% does not restore an original amount:100 becomes 120 and then 96. The second percentage applies to 120.
| Question | Reference value | Answer |
|---|---|---|
| What is the percentage difference between 100 and 120? | Average:110 | 18.18% |
| How much did 100 increase to reach 120? | Original:100 | 20% |
| How much did 120 decrease to reach 100? | Original:120 | 16.67% decrease |
Suppose two suppliers quote$800 and$1,000 for equivalent work. Their absolute difference is$200 and their average is$900. The average-based percentage difference is 200 ÷900 ×100 ≈22.22%.
If your question is “How much more expensive is the second quote than the first?”, use$800 as the baseline. The answer is 25%. If your question is “How much would I save by choosing$800 instead of$1,000?”, use$1,000 as the baseline. The saving is 20%. Write the question before choosing the denominator.
Sales rise from$5,000 in one month to$6,500 in the next. The increase is$1,500, and 1,500 ÷5,000 ×100 =30%. This is percentage change, since the earlier month is the baseline. An average-based difference would describe another relationship and should not replace the growth figure. See our sales increase percentage guide for more examples.
A conversion rate moving from 4% to 5% increases by one percentage point. Its relative percentage increase is (5 −4) ÷4 ×100 =25%. Its average-based percentage difference is 1 ÷4.5 ×100 ≈22.22%. These measures describe different aspects of the same numbers, so label them explicitly.
Open the Our Daily Tools Percentage Calculator to calculate an increase or decrease from an original value to a new value. Enter the starting number first and the ending number second, then check the displayed formula.
For an average-based percentage difference, calculate the absolute difference and the average first. Then find what percentage the difference represents of the average. Do not treat the increase/decrease result as a symmetric percentage difference; its denominator is the original value.
- Automatically dividing by the larger number: the correct reference depends on your question.
- Rounding too early: retain precision during the calculation and round the final result.
- Starting from zero: ordinary percentage change is undefined because the formula divides by zero. Report the absolute increase instead.
- Comparing two zeros: their numerical difference is zero, but the average-based formula gives zero divided by zero.
- Using negative numbers without context: losses and comparisons crossing zero need a clearly defined method. The positive-value interpretation in this article does not automatically carry over.
Using the average-based formula, it is approximately 18.18%. The 20% figure is the increase from 100 to 120.
Use it to compare two positive values with no designated baseline. Use percentage change when measuring movement over time or comparing against a reference value.
Yes. Moving from 100 to 250 is a 150% increase. For positive values, the average-based percentage difference does not exceed 200%.
Check your numbers: use the free percentage calculator and identify your reference value before interpreting the result.