These two phrases sound almost identical, and calculators for both are usually just called "percentage calculator" somewhere — but they answer genuinely different questions and use different formulas. Mixing them up gives you a technically wrong number, even though it "looks" like an answer.
Percentage Change: Direction Matters
Percentage change compares a value to where it started. It tells you how much something grew or shrank relative to its original value, and the result can be positive (increase) or negative (decrease).
% Change = ((New − Old) ÷ |Old|) × 100
Example: a stock goes from $40 to $50. ((50−40)÷40)×100 = 25% — a 25% increase. There's a clear "before" and "after," so direction is meaningful.
Run it the other way — the stock falls from $50 back to $40 — and the answer is ((40−50)÷50)×100 = −20%. Same two numbers, different result, because the starting value (the denominator) changed. That asymmetry is a feature: a fall of 20% followed by a rise of 25% really does return you to where you began.
The vertical bars around Old mean "absolute value". They only matter when the starting value is negative. If a company's loss shrinks from −50 to −25 (in thousands), (−25 − (−50)) ÷ |−50| × 100 = +50%, correctly showing an improvement. Without the absolute value the sign would flip and suggest things got worse.
Percentage Difference: No Direction, Just Distance
Percentage difference compares two values that are equally valid, with no "original" or "before" — like comparing two competing products' prices, or two cities' populations. Because neither value is the baseline, the formula divides by their average instead of picking one as the starting point, and the result is always positive.
% Difference = (|v1 − v2| ÷ ((v1 + v2) ÷ 2)) × 100
Example: Product A costs $40, Product B costs $50. The average is $45. (10 ÷ 45) × 100 ≈ 22.2% — notice this is a different number than the 25% you'd get from treating it as a "change," because there's no defined starting point to divide by instead.
How to Tell Which One You Need
- Is there a clear "before" and "after," or an original value being tracked over time? → Percentage change.
- Are you comparing two separate, equally-valid values with no inherent order? → Percentage difference.
Sales growth, salary raises, price drops — all percentage change. Comparing two competitors, two survey results, or two measurements of the same thing from different sources — percentage difference.
Side-by-Side: Same Numbers, Three Answers
The table below runs the same pairs of values through both formulas. Notice that percentage change gives two different answers depending on which value you treat as the start, while percentage difference gives one answer that does not care about order.
| Values | Change A → B | Change B → A | Difference |
|---|---|---|---|
| 40 and 50 | +25% | −20% | ≈ 22.22% |
| 80 and 120 | +50% | ≈ −33.33% | 40% |
| 100 and 150 | +50% | ≈ −33.33% | 40% |
| 200 and 210 | +5% | ≈ −4.76% | ≈ 4.88% |
| 10 and 30 | +200% | ≈ −66.67% | 100% |
For values that are close together, the three figures are similar and the choice barely matters. As the gap widens they drift far apart — 10 and 30 can be described as "+200%", "−66.67%" or "100% different" depending on the formula. That is exactly why it pays to state which one you used.
Worked Scenarios
Salary raise (percentage change)
Your salary rises from $48,000 to $51,600. There is a clear before and after, so use change: (51,600 − 48,000) ÷ 48,000 × 100 = 3,600 ÷ 48,000 × 100 = 7.5%.
Two contractor quotes (percentage difference)
One builder quotes $1,200 and another $1,350. Neither is the "original", so use difference: the gap is $150 and the average is $1,275, giving 150 ÷ 1,275 × 100 ≈ 11.76%. If you specifically want to know how much more the second quote is than the first, that is a change question instead: 150 ÷ 1,200 × 100 = 12.5% more.
Two lab measurements (percentage difference)
Two instruments measure the same sample as 12.4 g and 12.9 g. Neither is known to be correct, so: 0.5 ÷ 12.65 × 100 ≈ 3.95%.
A Close Cousin: Percent Error
When one value is a known or accepted reference, neither formula above is quite right — you want percent error, which divides by the reference value:
% Error = (|Measured − Accepted| ÷ |Accepted|) × 100
A student measures gravitational acceleration as 9.6 m/s² against the accepted 9.81 m/s²: 0.21 ÷ 9.81 × 100 ≈ 2.14%. Structurally this is percentage change with the sign dropped, because the reference acts as the baseline.
Common Mistakes
- Calling a difference an "increase". Percentage difference has no direction, so "Product B is 22.2% more expensive" is wrong; B is 25% more expensive than A, and the two prices are 22.2% apart.
- Picking a baseline at random. If you use change for two equal-status values, someone else can pick the other baseline and get a different, equally "correct" number.
- Mixing up percentages and percentage points. A survey result moving from 40% to 46% is a 6 percentage point rise, but a 15% relative change. More on this in Percentage Increase and Decrease Formula & Examples.
- Dividing by zero. Percentage change from a starting value of 0 is undefined. Report the absolute change instead ("from 0 to 35 sign-ups").
Quick Mental Checks
- For any two positive values, the percentage difference always lands between the "down" change and the "up" change (ignoring signs) — between 20% and 25% for 40 and 50.
- If one value is double the other, the difference is always about 66.67% (for example 50 and 100:
50 ÷ 75). - Percentage difference for positive numbers can never exceed 200%; that only happens when one value is zero.
Our Percentage Difference Calculator and Percentage Calculator (which handles change) are both free — worth bookmarking whichever one matches your situation. See also How to Calculate a Discount Percentage for a common real-world example of percentage change.
Frequently Asked Questions
Can percentage difference be more than 100%?
Yes. It exceeds 100% whenever one value is more than three times the other — for example 10 and 50 give 40 ÷ 30 × 100 ≈ 133.3%. For non-negative values, it reaches its maximum of 200% when one of the two values is zero.
Which one do newspapers and reports usually mean?
When a report says a figure was "X% higher than last year", it is describing percentage change, even if it uses the word "difference". The symmetric percentage difference formula is more common in science, engineering and product comparisons.
Does it matter which value I enter first in a percentage difference calculator?
No. The formula uses the absolute gap and the average of the two values, so swapping them gives the same result. In a percentage change calculation the order does matter, so make sure the original value goes in the "from" field.
What should I use when one of the values is negative?
Percentage difference becomes unreliable when the two values have opposite signs, because their average can be close to zero. In that case report the absolute gap, or use percentage change against a clearly defined baseline.
Try it yourself: take two prices you are comparing this week and run them through the Percentage Difference Calculator, then enter the same pair as a before-and-after in the Percentage Calculator and compare the two answers.