Percentage Difference — the symmetric way to compare two values
Core idea
Percentage difference compares two values without choosing a baseline. It uses the average of both values in the denominator, so swapping the order doesn’t change the result.
How it works
Formula: |A − B| ÷ ((A + B) ÷ 2) × 100.
- Find the absolute difference |A − B|
- Find the mean (A + B) ÷ 2
- Divide and convert to %
Sanity checks
- A = B → 0%
- Swap A and B → same result
- A = 0, B > 0 → 200%
- A = 0 and B = 0 → undefined (mean is 0)
Shortcuts
- Approximate quickly: 100 × |Δ| ÷ mean
- Close numbers? Mean ≈ either value → 100 × |Δ| ÷ value
- Compare with % change by computing both for context
Pitfalls
- Using % change when there’s no clear baseline
- Mean near 0 (e.g., −10 vs 10) makes the ratio explode
- Rounding early can distort results—round only at display
Micro‑examples
- (100, 120) → |20| ÷ 110 × 100 = 18.18%
- (5, 8) → |3| ÷ 6.5 × 100 ≈ 46.15%
- (−10, 10) → mean = 0 → undefined/not meaningful
Mini‑FAQ
- Difference vs change? Difference is symmetric; change uses a baseline and can be ±
- Can it exceed 100%? Yes (e.g., 0 vs x → 200%)
- Negative numbers? Allowed, but watch for mean ≈ 0
Action tip
If direction matters (increase/decrease), use the Percentage Change calculator; if fairness matters, use Percentage Difference.