Percentage Change Calculator
Calculate the exact percentage increase or decrease between two numbers with full decimal precision and step-by-step mathematical proof.
Percentage increase or decrease
Formula for percentage change
Percentage change quantifies the relative degree of change between an initial baseline value and a final value:
Using absolute value |Old| in the denominator ensures that when initial values are negative, an increase yields a positive percentage change.
Worked examples with real numbers
Price increase ($80 to $100)
Difference: $100 − $80 = $20
Divide by initial: $20 ÷ $80 = 0.25
Stock decline (100 to 80)
Difference: 80 − 100 = −20
Divide by initial: −20 ÷ 100 = −0.20
Negative balance (−$50 to −$25)
Difference: −25 − (−50) = +25
Divide by |Initial|: 25 ÷ 50 = 0.50
Common mistakes to avoid
Dividing by new number
The denominator must always be the original baseline value (|Old|), never the new target value.
Assuming symmetry
A 20% drop followed by a 20% gain does not restore the original value ($100 − 20% = $80; $80 + 20% = $96).
Points vs. percent change
If an interest rate moves from 4% to 6%, that is a 2 percentage point increase, but a 50% relative jump.
Frequently asked questions
How do you calculate percentage change?
To calculate percentage change: subtract the old value from the new value, divide the result by the absolute value of the old value, and multiply by 100. Formula: Change (%) = ((New − Old) ÷ |Old|) × 100.
Can percentage change be negative?
Yes. If the new value is smaller than the old value, the difference (New − Old) is negative, indicating a percentage decrease. For example, changing from 100 to 80 is a −20% change (a 20% decrease).
What happens if the starting value is zero?
Percentage change from zero is mathematically undefined because division by zero is impossible. For instance, growing from $0 to $100 cannot be represented as a percentage increase.
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