Calculators
Percentage Difference vs Percentage Change: Which One to Use
When to use percentage change and when percentage difference, both formulas on the same numbers, a decision table, percent error and the edge cases where each breaks.
By TooleemPublished Facts checked
Short answer
Use percentage change when one value comes first and the other after it (a price rise, growth over a year): (new − old) ÷ old × 100. Use percentage difference when two values are compared side by side and neither is the starting point (two shops, two measurements): |a − b| ÷ ((a + b) ÷ 2) × 100. For 40 and 50 the change is +25% going up and −20% going down, but the difference is 22.2% either way.
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Percentage Calculator
Work out percentage change, percentage difference, what percent one number is of another, or a percentage of a number.
On this page
The two formulas side by side
Percentage change (has a direction)
(new − old) ÷ old × 100
Percentage difference (no direction)
|a − b| ÷ ((a + b) ÷ 2) × 100
Change divides by the starting value, so it depends on which value you start from and has a sign. Difference divides by the average of the two, so swapping them gives the same answer and it is never negative.
| Values | Change, first to second | Change, second to first | Difference |
|---|---|---|---|
| 40 and 50 | +25.00% | −20.00% | 22.22% |
| 100 and 120 | +20.00% | −16.67% | 18.18% |
| 250 and 240 | −4.00% | +4.17% | 4.08% |
| 10 and 30 | +200.00% | −66.67% | 100.00% |
| 3 and 1,000 | +33,233.33% | −99.70% | 198.80% |
Which one to use
| Situation | Use | Why |
|---|---|---|
| A price went from 40 to 50 | Change: +25% | There is a before and an after |
| Sales this year against last year | Change | Last year is the base |
| The same item costs 40 at one shop and 50 at another | Difference: 22.2% | Neither shop is the starting point |
| Two lab measurements of the same sample | Difference | Both are estimates of the same thing |
| A measurement against a known true value | Percent error | The true value is the base (see below) |
| “Shop B is how much more expensive than shop A?” | Change from A: +25% | The question makes A the base |
The last row is the trap: the wording of the question decides. “How much more expensive is B than A” puts A in the denominator, so it is a change. “How different are the two prices” has no base, so it is a difference.
One example, step by step
Worked example
A monthly subscription costs $12 at one service and $15 at another
Difference = |12 − 15| ÷ ((12 + 15) ÷ 2) × 100 = 3 ÷ 13.5 × 100 = 22.2%
Change from 12 to 15 = 3 ÷ 12 × 100 = +25% Change from 15 to 12 = −3 ÷ 15 × 100 = −20%
If you switch from the $15 service to the $12 one, you save 20% of what you were paying. If you switch the other way, you pay 25% more. In a comparison table with no “from”, quote the 22.2% difference.
Limits and edge cases
- Percentage difference never exceeds 200%. It reaches 200% only when one value is zero, which is why it hides very large gaps: 3 against 1,000 is “198.8%”.
- Percentage change from zero is undefined. Going from 0 to 5 cannot be expressed as a percentage of 0; report the absolute change instead.
- Negative values make both formulas misleading (a loss of −10 moving to a profit of +5). Report the absolute change.
- A rise and an equal fall do not cancel. +20% then −20% leaves you at 96% of the start, because the fall is taken from the higher value.
For discounts in a shop, the discount calculator works out the final price and the saving directly.
Do the calculation
Percentage Calculator
Work out percentage change, percentage difference, what percent one number is of another, or a percentage of a number.