Math & Science · Guide
Percentage Difference vs Percentage Change
If one number came first, use percent change. If they are just being compared, use percentage difference.
Want the answer for your own numbers? Use the free Percentage Calculator — it does every step below for you.
Which one do you need?
| Question | Use |
|---|---|
| My rent went from $1,200 to $1,320. By how much? | Percent change |
| Sales fell from 500 to 420 units. By how much? | Percent change (decrease) |
| Shop A charges $40, shop B $50. How different are they? | Percentage difference |
| Two lab measurements: 9.8 and 10.2. How far apart? | Percentage difference |
Percent change (increase or decrease)
Percent change = (new − old) ÷ old × 100
A positive answer is an increase. A negative answer is a decrease.
Example: increase
Rent from $1,200 to $1,320: (1,320 − 1,200) ÷ 1,200 = 120 ÷ 1,200 = 0.10.
A 10% increase
Example: decrease
Sales from 500 to 420: (420 − 500) ÷ 500 = −80 ÷ 500 = −0.16.
A 16% decrease
Percentage difference
When neither number is the "starting point", divide by their average. That way the answer is the same whichever order you put them in.
% difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Example: $40 vs $50
|40 − 50| = 10. Average = 45. 10 ÷ 45 = 0.222.
Percentage difference = 22.2%
Why the two give different answers
Take the same pair, 40 and 50:
- Change from 40 to 50: (50 − 40) ÷ 40 = +25%
- Change from 50 to 40: (40 − 50) ÷ 50 = −20%
- Percentage difference between them: 22.2%
Percent change depends on which number you start from. Percentage difference does not. That is the whole reason both exist.
Percent error: a third formula
Science classes add one more. Percent error compares a measurement with a known true value, so it divides by the true value:
Percent error = |measured − true| ÷ true × 100
Example: measuring gravity as 9.6 m/s² (true value 9.81)
|9.6 − 9.81| = 0.21. 0.21 ÷ 9.81 = 0.0214.
Percent error = 2.1%
So: change divides by the old value, difference divides by the average, error divides by the true value. Pick the one that matches your question.
Percentage points are something else
If an interest rate goes from 4% to 5%, it rose by 1 percentage point — but by 25 percent (1 ÷ 4). News stories mix these up all the time. When the numbers are already percentages, say which one you mean.
A trap: up and down are not symmetric
A 50% rise followed by a 50% fall does not get you back to the start. $100 → $150 → $75. To undo a 50% rise you need a 33.3% fall. The bigger the swing, the bigger the gap.
Work any of these out in the percentage calculator using "Percentage change from X to Y".
Changes over several periods
Percent changes in a row multiply; they do not add. A 10% rise followed by a 20% rise is a 32% rise in total, not 30%: 1.10 × 1.20 = 1.32.
To find the average yearly growth over several years, use this:
Average growth = (end ÷ start)1 ÷ years − 1
Rent going from $1,200 to $1,500 over 3 years grew 25% in total, but about 7.7% a year — not 8.3%, which is what simple division gives.
Reversing a percent change
To find the value before a rise, divide — do not subtract. If rent is $1,320 after a 10% increase, the old rent was 1,320 ÷ 1.10 = $1,200. Taking 10% off $1,320 gives $1,188, which is wrong, because the 10% was worked out on the smaller number.
In Excel or Google Sheets
With the old value in A2 and the new value in B2:
- Percent change:
=(B2-A2)/A2, then format the cell as a percentage. - Percentage difference:
=ABS(A2-B2)/AVERAGE(A2,B2) - Percent error, with the true value in C2:
=ABS(B2-C2)/C2
Frequently asked questions
Divide the absolute difference by the average of the two numbers and multiply by 100. For 40 and 50: 10 ÷ 45 × 100 = 22.2%.
Subtract the old value from the new, divide by the old value and multiply by 100. From 1,200 to 1,320 is a 10% increase; from 500 to 420 is a 16% decrease.
Percent error measures how far a measured value is from a known true value: |measured − true| ÷ true × 100. Measuring 9.6 when the true value is 9.81 gives a percent error of about 2.1%.
Yes, for increases. Going from 50 to 150 is a 200% increase, because the rise of 100 is twice the starting value. A decrease can never go past −100%, since that would mean falling below zero.