Mathematics · Percentages
Find the percent difference between two values
A and B are not labeled “before” and “after.” You get the absolute gap, the gap relative to A, relative to B, and the symmetric gap (divided by the average). That is not a percent increase.
Calculate
How the calculator works
Compute |A − B|. Relative to A, divide by |A|; relative to B, by |B|. The symmetric percent divides by the mean of the absolute values, (|A| + |B|) / 2. All three live on the page because they answer different questions. None of them is “the” rise from A to B.
Formula and method
symétrique = |A − B| ÷ ((|A| + |B|) / 2) × 100
For 100 and 150: gap 50, mean 125, 50/125 = 40%. Swapping A and B leaves this number unchanged.
relatif à A = |A − B| ÷ |A| × 100
Same pair: 50/100 = 50% relative to A, and 50/150 ≈ 33.33% relative to B.
Use this when neither figure is a chronological base (two sensors, two quotes, two lab methods). Percent increase would pick a start and refuse a drop. Here both directions are shown, plus the symmetric form common in science writing. Zero on either side is refused so every ratio exists.
Worked example
100 versus 150
A = 100, B = 150
- Absolute gap |100 − 150| = 50.
- Relative to A: 50/100 = 50%.
- Relative to B: 50/150 ≈ 33.33%.
- Symmetric: 50 / 125 = 40%.
50% vs A, 33.33% vs B, 40% symmetric. Do not pick one silently.
Input notes
- First value (A)
- First figure. Relative-to-A uses this as the denominator. Zero is blocked.
- Second value (B)
- Second figure. The symmetric percent does not care which is A or B.
Assumptions and limits
Assumptions
- A and B measure the same kind of quantity.
- You want a relative gap, not a time-ordered increase.
Limits
- Does not choose a “true” percent for you.
- Not a test of statistical significance.
- Tiny values make percents explode; that is the formula, not a bug.
How to read the result
If A is last year’s sales and B is this year’s, percent increase is the cleaner story. If A and B are two assays of the same sample, quote the symmetric gap or report both one-sided percents. A 40% symmetric gap on 100 vs 150 is not “B is 40% higher than A” in the increase sense (that would be 50%).
Common mistakes
Calling the symmetric 40% a 40% increase from 100 to 150.
An increase from 100 to 150 is 50%. The 40% figure uses the midpoint as the base.
Averaging 50% and 33.33% by hand and expecting a new law.
The symmetric formula already uses the average of |A| and |B| as the denominator. It is not the average of the two one-sided percents (which would be 41.67% here).
Comparison
| Reading | Base | Result |
|---|---|---|
| Increase A → B | A = 100 | 50% |
| Relative to B | B = 150 | 33.33% |
| Symmetric difference | mean 125 | 40% |
Related calculations
- PercentageEnter two numbers of the same kind. The tool returns (part ÷ total) × 100 — useful for a test score, a slice of a budget, or a share of a count.
- Percent increaseGive a starting amount and a higher later amount. The tool reports the rise relative to the start, not a “neutral” gap between two figures.
- ROIROI here is a simple ratio of gain (or loss) to cash put in. It does not know whether the outcome took a month or a decade. CAGR is the tool that uses years.
- Percent decreaseEnter an original amount and a smaller later amount. The result is the drop relative to the original — the same idea as a markdown, without applying a sale price formula.
Frequently asked questions
Which percent should I publish?
Name the base. Do not publish a bare “percent difference” without saying which formula.
Journals often want the symmetric form. Finance often wants increase from a start. This page shows all three so you can match the sentence you actually mean.
Why are zeros forbidden?
Every ratio on the page divides by A, B, or their average of absolute values.
Relative-to-A needs |A| ≠ 0. Relative-to-B needs |B| ≠ 0. If one value is zero, a relative gap is not a well-posed percent here.
Does order matter?
Not for the symmetric gap. Yes for the one-sided percents.
Swap 100 and 150 and the 40% stays. The 50% and 33.33% swap roles. Absolute gap is unchanged.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
This calculation uses a standard mathematical identity. See also the methodology.
When there really is a before and after
If A is the start and B is later and higher, percent increase is the sentence most readers expect.
Calculate a percent increaseCategory: Mathematics