About the percentage change calculation
Percentage change measures movement relative to the starting value, which is why it is not reversible. Going from 100 to 150 is a 50% rise, but coming back from 150 to 100 is only a 33.3% fall. The direction you measure from changes the answer, and that asymmetry causes real confusion in reporting and in investing.
Formula
Change = ((New − Old) ÷ |Old|) × 100
A positive result is an increase, negative is a decrease.
The absolute value on the denominator keeps the sign meaningful for negative bases.Worked example
From 100 to 150: ((150 − 100) ÷ 100) × 100 = +50%. From 150 back to 100: ((100 − 150) ÷ 150) × 100 = −33.33%.
Frequently asked questions
Why is a 50% gain not cancelled by a 50% loss?
Because each percentage is measured against a different base. A 50% loss after a 50% gain leaves you at 75% of where you started. To recover from a 50% loss you need a 100% gain — which is why large drawdowns are so damaging.
What if the starting value is zero?
Percentage change is undefined, because you cannot divide by zero. Any move from zero is an infinite percentage increase. This calculator returns zero rather than infinity, but the honest answer is that the measure does not apply.
Percentage change or percentage difference?
Change is directional and uses the original value as the base. Percentage difference is symmetric and divides by the average of the two values, so it gives the same answer whichever order you supply them in. Use change when there is a clear before and after.
Sources
- Standard relative change formula