How this calculator works
Subtract the starting value from the ending value and divide by the starting value. The result is signed. Negative starting values are accepted, and the sign follows that calculation. To find an ending value, multiply the start by one plus the percentage change expressed as a fraction.
Formula
Change (%) = (new - old) / old × 100. Final value = old × (1 + r/100), where r is the entered percentage.
Worked example
From 80 to 100, the gain is 20 compared with a start of 80, so the change is 25%. From 100 to 80, the change is -20%. Applying 25% to 80 gives 100.
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Frequently asked questions
Why does reversing the values give a different percentage?
Reversing them changes the denominator. A gain of 20 on 80 is 25%, while a loss of 20 on 100 is 20%.
Can the starting value be zero?
It cannot be zero when calculating change because that requires division by the start. Applying a known percentage change to zero gives zero.
Can the ending value be negative?
Yes. The change is signed, so a move from 100 to -50 gives -150%. The formula does not restrict the ending value.