Percentage Difference Calculator

Why “percentage difference” exists

When people say “what’s the percentage difference between these two numbers?” they often mean “how far apart are they as a percentage,” without implying that one is the starting point and the other is the ending point. That’s exactly what percentage difference is for: it compares two values symmetrically using a shared baseline, usually the average of the two values. If you swap the values, the answer stays the same.

This is different from percent change, which is directional. Percent change assumes an “original” value and measures how much the new value moved relative to that original. Percent change answers questions like “How much did it increase from last month?” Percentage difference answers questions like “How different are these two measurements?”

Percentage difference formula

The most common definition uses the absolute difference between A and B divided by their average:

However, when values can be negative or cross zero (for example, temperature changes, offsets, gains/losses, or signed sensor readings), the raw average can create confusing baselines. To keep the baseline stable and symmetric, many calculators use the average of the absolute values:

This calculator defaults to the average of magnitudes (|A| and |B|). You can switch the baseline if you need a specific definition for a class, lab, or reporting standard.

What percentage difference tells you

Percentage difference is a distance measure. It is always non-negative because it reports “how far apart,” not “which direction.” If A is 120 and B is 90, the absolute difference is 30 and the raw average is 105, so the percentage difference is about 28.57%. If you swap A and B, the result stays 28.57%.

This symmetric behavior is exactly why percentage difference is popular for comparing two estimates, two measurements, or two observed results where neither is clearly the baseline.

Percent change is a different question

Percent change uses an original value (old) as the baseline:

If old = 90 and new = 120, the change is +33.33%. If you reverse the direction (old = 120, new = 90), the percent change is −25%. Both are valid because they describe different directions. That’s why percent change is not symmetric.

Increase and decrease are just labeled percent change

“Percent increase” and “percent decrease” are simply percent change with a word label. A positive percent change is an increase; a negative percent change is a decrease. The Increase/Decrease tab helps you compute the direction and keeps the interpretation straightforward.

Choosing the right baseline matters

Most confusion about “percentage difference” comes from mixing definitions. People might compute percent change but call it percentage difference, or they might divide by the wrong number. To choose the right approach, ask a simple question:

• If one value is the clear starting point and you care about direction, use percent change.
• If you just want a symmetric “distance in percent,” use percentage difference.

In this tool, you can use A or B as the baseline if that matches a policy or a worksheet requirement. But for “true” percentage difference, the average baseline is the usual choice.

Why the result can exceed 100%

Percentage difference can be greater than 100% when the absolute difference is larger than the average baseline. For example, compare 10 and 100: the difference is 90 and the average is 55, so the percentage difference is 163.64%. That doesn’t mean something is “more than double” in a directional sense; it means the gap is larger than the average of the values.

What happens when values are zero

If one value is zero and the other is not, percentage difference can still be computed because the average baseline is not zero (unless both values are zero). If both A and B are zero, then the absolute difference is zero and the baseline is also zero, so a percent-based comparison is undefined. In practical terms, the values are identical, so the difference is 0, but “percent difference” is not meaningful because there is no scale to compare against.

Negative values and sign-sensitive data

Signed values are common in real life: profit/loss, temperature deviation, electrical signals, directional velocity, and error terms. When signs matter, a raw average baseline can cancel out (for example, A = 10 and B = −10 gives an average of 0). That’s one reason the average of absolute values is often used for a stable denominator.

If you are working in a context where the raw average is required (for example, a specific textbook definition), you can switch the denominator to “Average of A and B (raw)” and the tool will follow that approach.

Practical uses

Comparing two measurements

If you measure the same quantity twice (two instruments, two runs, two labs), percentage difference tells you how close the readings are in relative terms. It’s a quick way to express consistency without choosing a baseline.

Comparing two estimates or quotes

For budgets and planning, you might compare two quotes for the same service. Percentage difference provides a neutral “how far apart” number. If one quote is the official baseline, then percent change from that baseline may be more relevant.

Comparing model scores or experiment results

In data work, you might compare two metrics where neither is inherently “original.” Percentage difference helps express the gap in a way that doesn’t depend on which value you write first.

Common mistakes this calculator helps prevent

• Using percent change when you actually want symmetric percentage difference.
• Dividing by the wrong baseline (A, B, average, or a signed average that can be near zero).
• Forgetting absolute value when you want a non-directional “distance in percent.”
• Interpreting percent change as symmetric when it is not.

Quick guide: which number should go where?

If you’re using the Percent Change tab, put the earlier or baseline value in “Old” and the later value in “New.” If you’re using Percentage Difference, the order doesn’t matter when you use the average baseline. If a worksheet insists on dividing by a particular reference value, switch the baseline in the Percentage Difference tab to “Use A” or “Use B.”