Percentage Change Calculator
Calculate the percentage increase or decrease between any two values. Handles negative numbers, shows direction and absolute change with the full formula.
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How It Works
Subtract the old value from the new to get the absolute change. Divide by the absolute value of the old number. Multiply by 100. A positive result is an increase; negative is a decrease.
((V2 − V1) / |V1|) × 100(250 − 200) / |200| × 100 = +25%When the original value is negative, the absolute value in the denominator prevents the sign from flipping incorrectly. Going from −25 to 25 is a 200% increase, not −200%.
(V2 − V1) / |V1| × 100(25 − (−25)) / |−25| × 100 = +200%When the new value is smaller than the old, the result is negative. The magnitude tells you how much the value dropped as a share of the original.
((V2 − V1) / |V1|) × 100 → negative(80 − 100) / 100 × 100 = −20%Use old period as V1 and new period as V2. Percentage change is the standard metric for growth rates and lets you compare performance across different-sized bases.
((New − Old) / Old) × 100($1.2M − $1M) / $1M × 100 = +20%Two sequential percentage changes do not simply add. A 20% increase then a 20% decrease is a net −4% because each operates on a different base.
Net = (1 + r1) × (1 + r2) − 1(1.20 × 0.80) − 1 = −4%Electricity bill went from $148 to $186. Enter V1 = 148, V2 = 186. Result: +25.68% — now you know the exact size of the increase to budget next month.
(186 − 148) / |148| × 10038 / 148 × 100 = +25.68%Quick Reference
Common percentage changes — verify instantly above.
Increase
200 → 250
+25%
Decrease
100 → 80
−20%
Increase
50 → 75
+50%
Decrease
200 → 150
−25%
Negative V1
−25 → 25
+200%
Negative V1
−25 → −50
−100%
Big increase
10 → 40
+300%
No change
100 → 100
0%
Tips & Shortcuts
A 20% increase followed by a 20% decrease does NOT return to the original — net result is −4% because each change uses a different base.
To reverse a percentage change: if something increased 25%, it needs a 20% decrease to return. Reverse percentages are never equal.
For multiple periods, compound the changes: (1 + r1) × (1 + r2) × ... − 1. Never add the percentages together.
When comparing growth across different-sized bases, percentage change is more meaningful than the absolute change alone.
A −100% change means the value reached zero. Percentage decrease cannot exceed −100% with the standard formula.
The order matters: 3.50 → 2.625 is −25%. But 2.625 → 3.50 is +33.33%. Different bases produce different percentages.
Common Mistakes
Adding percentage changes: 10% + 10% = 20%
Sequential changes compound: (1.10 × 1.10) − 1 = 21%, not 20%.
Using the new value as the denominator instead of the old
Always divide by the original (old) value, not the new result.
Forgetting |V1| when the old value is negative
Divide by the absolute value of V1 to get the correct direction of change.
Thinking 100% increase then 100% decrease returns to start
100 → +100% → 200 → −100% → 0. You end up at zero, not the original.
Confusing percentage change with percentage difference
Percentage change is directional (old → new). Percentage difference is symmetric.
Reporting change without stating the base period
Always say "25% increase from Q1 to Q2", not just "25% increase".
Frequently Asked Questions
Percentage change = ((V2 − V1) / |V1|) × 100. Subtract old from new, divide by the absolute value of old, multiply by 100.
When V1 is negative, |V1| ensures the direction of change (increase or decrease) is mathematically correct.
Percentage change is directional — it goes from old to new. Percentage difference has no direction and compares two numbers symmetrically.
Yes. Going from 5 to 20 is a 300% increase. There is no ceiling on percentage increase, though percentage decrease is capped at −100%.
A negative percentage change means the new value is smaller than the old — a decrease. −25% means the value dropped by one quarter.
No. 100 → +50% → 150 → −50% → 75. Percentage changes multiply, not add, so they are not symmetric.
Because each percentage applies to a different base. If a price rises 20% then falls 20%: start at $100 → +20% → $120 → −20% of $120 → $96. Net: −4%, not 0. To compound changes: multiply the factors. +20% then −20% = 1.20 × 0.80 = 0.96 (−4%). To return exactly to $100 from $120, you need a 16.67% decrease, not 20% — because 20% of $120 is $24, which overshoots.
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