Percentage Increase / Decrease / Difference Calculator

Why the same two numbers give different percentages depending on direction

Going from A (80) to B (100) registers as both a 25% increase and a -25% decrease from this same calculator -- the increase and decrease fields are mirror images of each other by construction, since both divide by the same starting value A. The negative sign on 'decrease' simply confirms the value went up, not down.

Increase = (B - A) / A x 100 = (100 - 80) / 80 x 100 = 20/80 x 100 = 25%. Decrease = (A - B) / A x 100 = (80 - 100) / 80 x 100 = -25%. Both formulas share the identical denominator (A), which is exactly why they always come out as exact opposites of one another for any two values.

The symmetric (or 'relative') difference of 22.22% uses a genuinely different formula: |B - A| / ((A+B)/2) x 100 = 20 / 90 x 100 = 22.22% -- dividing by the average of the two values instead of just A, which produces a result that doesn't depend on which value you call 'A' and which you call 'B,' unlike the increase/decrease fields.

A separate, real trap this tool's fields don't cover

Increase = (B-A)/A. Decrease = (A-B)/A. Difference = |B-A| / ((A+B)/2). Distinct from the basic percentage calculator. Don't confuse this calculator's 'decrease' field with a different, commonly needed question: what percentage would you need to cut B by to get back down to A? That reverse question uses B, not A, as the base -- for 100 down to 80, it's (100-80)/100 = 20%, not the -25% this tool's decrease field reports (which is simply -1 times the increase, since both use A as the denominator).

This same base-switching trap is exactly why stock market commentary about 'up 50% then down 50%' being back to even is mathematically wrong -- a 50% gain takes a value from X to 1.5X, but a 50% loss calculated on that new, larger 1.5X base only returns it to 0.75X, which is 75% of the original amount, not 100%.

The symmetric difference formula exists specifically to sidestep this base-dependence problem when you need one consistent percentage-difference figure regardless of which value came first or second -- useful for comparing two values without implying a directional 'change,' like comparing two competitors' prices rather than tracking one price's change over time.

Choosing the right percentage calculation for your context

For a straightforward percentage-of calculation (like finding what 15% of 200 is) rather than comparing two values' relative change, note the footer's mention that this is distinct from a basic percentage calculator -- that's a genuinely different, simpler calculation this tool doesn't perform.

For percentage changes specifically in a financial or business metrics context (like revenue growth), the same increase formula used here applies directly -- this general-purpose calculator works for any two numbers, not just a specific domain.

Frequently Asked Questions (FAQ)