Two numbers, two different answers
How much bigger one number is than another and how much smaller the other is than the first — two different answers — plus the ratio and the symmetric difference.
"How much bigger is A than B" and "how much smaller is B than A" sound like mirror images, but the answers differ because the base differs. 120 is 20 percent above 100, while 100 is 16.7 percent below 120.
So both are shown at once. It is the cleanest defence against a base swap — the same gap can be presented as 20 percent growth or a 16.7 percent shortfall depending on which number someone divides by.
What this calculator shows
- How far the first exceeds the second and how far the second falls short of the first
- The absolute gap and the ratio between them
- The symmetric difference against the mean, for when neither number is the natural base
What to keep in mind
- Neither number may be zero — percent difference from zero is undefined.
- Negative inputs still compute, but the interpretation gets slippery; check that the question still makes sense.
FAQs
Why aren't the two percentages the same?
Because the divisors differ. A gap of twenty is 20 percent of 100 but only 16.7 percent of 120. Always establish what the percentage is of.
What is a percentage point?
The gap between two percentages. A rate moving from 10 to 12 percent has risen by two percentage points — a 20 percent increase. Conflating the two is a common reporting error.
When should I use the symmetric difference?
When neither value is the reference — comparing two measurements of the same quantity, say. Dividing by the mean makes the answer independent of the order.
How is this different from percentage change?
Change implies a before and an after. Here the two numbers are peers, which is why three ways of comparing them are shown.
Worked example
A metric rising from 100 to 120
Input: 120 and 100
Output: 20% higher, 16.67% lower
Note: The ratio is 1.2. The symmetric difference against the mean of 110 is 18.18 percent, used when both figures are equally valid measurements.