How to Find Percentage Difference Between Two Numbers
To find the percentage difference between two numbers, take the absolute difference between them, divide it by their average, and multiply by 100. In formula form: |A − B| / ((A + B) / 2) × 100. This tells you how far apart two values are relative to their midpoint, which makes it useful when neither number is a natural “starting point.” Using the average as the base — not one of the values — is the single biggest source of errors.
What Is Percentage Difference
Percentage difference is a measure of how far apart two values are, expressed as a percentage of their average. It answers the question “how different are these two numbers?” without assuming one came first or one is “correct.”
That last point is what separates it from two lookalike measures:
- Percentage change compares an old value to a new value, so there is a clear before-and-after. Dividing by the original value tells you how much something grew or shrank.
- Percentage error compares an experimental or measured value to an accepted or true value. There, the “correct” number is known, so you divide by it.
Percentage difference is the right tool when the two numbers are peers — two measurements of the same thing, two prices for the same item, two results from the same test. Neither is a baseline, so the average becomes the fair reference point. Khan Academy’s lessons on ratios and proportions cover the underlying idea that a percentage is just a fraction with 100 as the denominator.
Percentage Difference Formula
The standard formula is:
Percentage difference = |A − B| / ((A + B) / 2) × 100
Each piece does a specific job:
- |A − B| is the absolute difference between the two values. The vertical bars mean you drop any negative sign, so the result is always zero or positive. This matters because percentage difference is directionless — 40 and 60 differ by the same amount as 60 and 40.
- (A + B) / 2 is the average, or midpoint, of the two values. It is the shared base you divide by.
- × 100 converts the decimal into a percentage.
Math is Fun explains absolute value the same way: it is the distance from zero, so it never comes out negative. Note that the order of A and B does not change the answer, because the absolute difference and the average are both symmetric.
Step-by-Step Calculation
Here is a worked example. Suppose two bags of coffee beans are weighed on the same scale: Bag A is 500 grams, Bag B is 450 grams.
Step 1 — Subtract to find the difference. 500 − 450 = 50. Apply the absolute value: |50| = 50.
Step 2 — Add the two values. 500 + 450 = 950.
Step 3 — Divide the sum by 2 to get the average. 950 / 2 = 475.
Step 4 — Divide the difference by the average. 50 / 475 = 0.1053 (rounded to four decimal places).
Step 5 — Multiply by 100 to convert to a percentage. 0.1053 × 100 = 10.53%.
So the two bags differ by about 10.5%. If you swapped the order — 450 first, 500 second — you would get the same 10.53%, which is the built-in check that you used the formula correctly rather than the percentage change formula.
A quick way to sanity-check your answer
If both numbers were identical, the difference would be zero and so would the percentage. If one value were zero and the other were 100, the average would be 50 and the percentage difference would be 200% — the largest relative gap this formula can produce for non-negative numbers. If your result is far outside that range or comes out negative, you have likely divided by the wrong base or dropped the absolute value.
Comparing the three formulas side by side
| Measure | Formula | Base you divide by | When to use it |
|---|---|---|---|
| Percentage difference | |A − B| / ((A + B) / 2) × 100 | Average of the two values | Neither value is a baseline |
| Percentage change | (New − Old) / Old × 100 | The original (old) value | Tracking growth or decline over time |
| Percentage error | |Measured − True| / True × 100 | The accepted or true value | Checking an estimate against a known value |
The only thing that changes across these formulas is the denominator — and that single choice is what makes each one appropriate for a different situation.
Common Mistakes to Avoid
- Dividing by one of the values instead of the average. This is the most frequent error. If you divide the difference by A or by B, you have quietly switched to percentage change or percentage error, and your answer will be wrong for a difference comparison.
- Ignoring the absolute value. Without the bars, subtracting in the “wrong” order gives a negative percentage. Direction is meaningless here, so always take the positive difference.
- Confusing the formula with percentage change. Percentage change has a strict order (old, then new) and can exceed 100% or fall below −100%. Percentage difference is symmetric and, for non-negative values, tops out at 200%.
- Mixing up the base when a true value exists. If a measurement is being checked against an accepted standard, percentage error is the correct measure, not percentage difference.
- Rounding too early. Keep at least four decimal places through the division step, then round the final percentage. Rounding the average to a whole number first can shift the answer noticeably.
For financial, medical, or scientific decisions where a small gap matters — dosage calculations, lab tolerances, price comparisons — treat these as quick estimates and confirm with a qualified professional or the governing standard.
Key Takeaways
- Percentage difference is |A − B| / ((A + B) / 2) × 100: the absolute gap divided by the average, times 100.
- Use it when the two numbers are peers; use percentage change when there is an old and a new value, and percentage error when one value is a known standard.
- The answer is always non-negative and does not depend on the order of the two numbers.
- The most common error is dividing by one value instead of the average — that turns the calculation into a different formula entirely.
