The rule
difference % = |a − b| ÷ ((a + b) ÷ 2) × 100
Why it works
Percentage difference divides by the mean of the two values rather than by one of them. That makes it symmetric: swapping the values gives the same answer, which is what you want when neither is a 'before'.
How to do it by hand
- Take the absolute difference between the two values
- Work out their mean by adding and halving
- Divide the difference by the mean
- Multiply by 100
What is worth knowing
Percentage difference and percentage change answer different questions and get confused constantly. Change has a direction — from a starting value to a final one — and is asymmetric. Difference has no direction and is symmetric. Between 40 and 60 the difference is 40 % of their mean, while the change from 40 to 60 is +50 % and from 60 to 40 is −33 %. Three different numbers, all correct, all answering different questions. Use difference when comparing two measurements of equal standing, and change when one clearly came first.