Percentage Change Calculator
Increase · Decrease · Difference · New Value
% Change
% Difference
New Value
Percentage difference compares two values without a "before" and "after" — uses their average as the reference.
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Use positive for increase, negative for decrease (e.g. -15 for 15% decrease)
Enter two values to calculate the percentage change, difference, or new value.
Percentage Change
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Step-by-step calculation
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Percentage Change Formulas
There are three related but distinct percentage calculations. Choosing the right one depends on what you're trying to measure.
% Change (Increase or Decrease):
((New Value - Old Value) / |Old Value|) × 100
% Difference (no before/after):
(|A - B| / ((A + B) / 2)) × 100
New Value after % Change:
New Value = Original × (1 + Percentage / 100)
((New Value - Old Value) / |Old Value|) × 100
% Difference (no before/after):
(|A - B| / ((A + B) / 2)) × 100
New Value after % Change:
New Value = Original × (1 + Percentage / 100)
Percentage Change vs Difference
Percentage change requires a direction (before and after). Percentage difference treats both values equally — it uses the average as the denominator. Use "change" for time-series data (last year vs this year). Use "difference" when comparing two values with no inherent order (city A vs city B).
Common Errors to Avoid
Always divide by the original (old) value, not the new one. A price going from $50 to $100 is a 100% increase, not 50%. Going from $100 to $50 is a 50% decrease. These are not symmetric — a 100% increase followed by a 50% decrease returns to the original, not a net 50% change.
Percentage Point vs Percent Change
A tax rate going from 20% to 25% is a 5 percentage point increase, but a 25% relative increase (5/20 × 100). These measure different things. "Percentage points" describes an absolute change in a percentage figure. "Percent change" describes the relative change. Confusing the two is one of the most common errors in reporting statistics.
Real-World Applications
Percentage change is used everywhere: stock price movements, inflation rates, sales growth, grade changes, population growth, salary increases. Any time you want to express how much something has changed relative to where it started, percentage change is the right tool.
Frequently Asked Questions
How do you calculate percentage change?+
Percentage change formula: ((New Value - Old Value) / |Old Value|) × 100. Example: price increases from $80 to $100. Change = (100 - 80) / 80 × 100 = 25% increase. If price drops from $100 to $80: (80 - 100) / 100 × 100 = -20% (a 20% decrease). Always divide by the original value, not the new one. A positive result means an increase; negative means a decrease.
What is the difference between percentage change and percentage difference?+
Percentage change has a clear direction — it measures change from an original value to a new value. The original is the denominator. Percentage difference compares two values with no inherent "before" or "after" — it uses their average as the denominator. Example: comparing the population of two cities. Neither is the "original," so you use percentage difference. Formula: |A - B| / ((A + B) / 2) × 100.
How do I calculate a 20% increase?+
To apply a percentage increase: New Value = Original × (1 + Percentage/100). For a 20% increase on $500: 500 × 1.20 = $600. Or equivalently: $500 × 0.20 = $100 increase, then $500 + $100 = $600. For quick mental math: 10% = move decimal one place ($50), so 20% = $100. This calculator's "New Value" mode handles this automatically for any percentage and original value.
Why is a 50% decrease not the reverse of a 100% increase?+
Because percentage change is calculated relative to different bases. Starting at $100: a 100% increase → $200. Then a 50% decrease on $200 → $100. So they cancel out. But if you say "first +100%, then -100%": $100 → $200 → $0. The math isn't symmetric because the denominator changes. This is why investment returns don't simply add/subtract — a 50% loss requires a 100% gain just to break even.
How do I calculate percentage change in Excel?+
In Excel: if old value is in A1 and new value in B1, the formula is =(B1-A1)/ABS(A1), then format the cell as Percentage. Or use =(B1-A1)/ABS(A1)*100 if you want a number without percentage formatting. For multiple rows, drag the formula down. ABS() handles cases where the original value is negative, ensuring the correct sign for the percentage change.
What does a negative percentage change mean?+
A negative percentage change means the new value is less than the original value — a decrease. A -15% change means the new value is 15% lower than the original. Example: a stock dropping from $200 to $170 is a -15% change: (170-200)/200 × 100 = -15%. In context, this might be described as "a 15% decrease" or "a 15% decline." The sign indicates direction; the magnitude indicates size of the change.
How is percentage change used in finance?+
Finance uses percentage change constantly: stock returns (price today vs price yesterday); year-over-year revenue growth (this quarter vs same quarter last year); inflation (CPI this month vs same month last year); portfolio performance (portfolio value change since inception). In finance, percentage change is often called "return" or "rate of change." For multi-period returns, analysts use compound growth rates (CAGR) rather than simple percentage change, to account for compounding.
What is a percentage point?+
A percentage point is an absolute difference between two percentages. If unemployment rises from 4% to 6%, that's a 2 percentage point increase. But the relative percentage change is (6-4)/4 × 100 = 50%. Both statements are correct but mean different things. Politicians and media often conflate these, sometimes deliberately. "Taxes increased 2 percentage points" (absolute) vs "taxes increased 50%" (relative) describe the same event but have very different implications. Always check which is being used.
How do I find what percentage one number is of another?+
To find what percentage X is of Y: (X / Y) × 100. Example: what percentage is 30 of 120? (30/120) × 100 = 25%. This is different from percentage change (which measures change from an original). "What percent of" directly gives the ratio as a percentage. Use the standard Percentage Calculator for this — or the calculation above. Quick check: if the result is over 100%, X is larger than Y.
How do I calculate the original value before a percentage change?+
To reverse-calculate the original: Original = New Value / (1 + Percentage/100). Example: a price is now $120 after a 20% increase. What was the original? 120 / 1.20 = $100. A common mistake: subtracting 20% from $120 gives $96 — wrong! You need to divide by the multiplier, not subtract the percentage of the new value. The "New Value" mode in this calculator can solve for either direction by using a negative percentage.