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
Percentage change is (new value − old value) ÷ |old value| × 100. Going from 80 to 100 is a 25% increase, while going from 100 to 80 is a 20% decrease, because the starting value is always the base. Enter an original and a new value above to get the change, or switch tabs for percentage difference or a new value after a change.
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.
Undo and Recovery Table
Because the base changes, the percentage that reverses a move is never the same size as the move itself. Left: the decrease that cancels an increase. Right: the gain needed to recover from a loss.
| Increase | Decrease that undoes it | Loss | Gain needed to recover |
|---|---|---|---|
| +10% | 9.09% | −10% | 11.11% |
| +20% | 16.67% | −20% | 25% |
| +25% | 20% | −25% | 33.33% |
| +50% | 33.33% | −50% | 100% |
| +100% | 50% | −75% | 300% |
| +200% | 66.67% | −90% | 900% |
The rule behind the table: after an increase of p%, you need a decrease of p ÷ (100 + p) to get back. After a loss of p%, you need a gain of p ÷ (100 − p).
Four Worked Examples
A price increase
Gas goes from $3.19 to $3.49 a gallon. The change is $0.30, and 0.30 ÷ 3.19 × 100 = 9.40% increase.
A decrease
Website visitors fall from 1,250 to 980. The change is −270, and −270 ÷ 1,250 × 100 = −21.6%, a 21.6% decrease.
Percentage difference
One store charges $42 for an item and another charges $48. Neither price is the "before", so use the % Difference tab: |42 − 48| ÷ ((42 + 48) ÷ 2) × 100 = 6 ÷ 45 × 100 = 13.33%.
A negative starting value
A small business goes from a $20,000 loss (−20,000) to a $5,000 profit. The change is +25,000, and dividing by the absolute value of the start gives 25,000 ÷ 20,000 × 100 = +125%. Without the absolute value you would get −125%, which wrongly suggests things got worse.
Edge Cases: Zero, Negatives and Small Bases
- Starting at 0: percentage change is undefined, because the formula divides by the old value. Report the absolute change instead ("up 25 from zero"). The calculator says so rather than showing a number.
- 0 to 0: nothing changed, so the calculator shows 0%.
- Negative start: the calculator divides by the absolute value of the start, as spreadsheet users do with =(B1−A1)/ABS(A1). Results across zero are still hard to read, so quote the raw numbers alongside the percent.
- Tiny bases give huge percents: going from 1 to 5 is a 400% increase. When the starting number is small, the absolute change is often the more honest figure.
- Percentage difference with negatives: the calculator averages the absolute values, |A| and |B|, so 5 and −5 give a 200% difference instead of a division by zero.
To find a percent of a number or what percent one number is of another, use the percentage calculator. For growth that repeats every year, the compound interest calculator shows how it builds up.
Method and sources. Percentage change = (new − old) ÷ |old| × 100. Percentage difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100. New value = original × (1 + percent ÷ 100). Compound annual growth rate = (end ÷ start)1/years − 1. Every figure in the table and examples was computed with these formulas.
Frequently Asked Questions
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.
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.
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.
Because each percentage is taken from a different base. Start at $100: a 100% increase adds $100 and gives $200. A 50% decrease on $200 removes $100 and brings you back to $100. Equal percentages do not cancel: +100% then −100% takes $100 to $200 and then to $0, and +10% then −10% leaves $99. This is why a 50% loss on an investment needs a 100% gain just to break even.
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.
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.
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.
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.
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.
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 works forward only, from an original value to a new one, so use the division above to go backward.
No. Percentage change divides by the starting value, and dividing by zero has no answer. Going from 0 to 40 is not a 100% or an infinite increase; it is an increase of 40. Report the absolute change, or describe the item as new. Going from 0 to 0 is simply no change.
Divide the change by the absolute value of the starting number. From −20 to 10, the change is +30, and 30 ÷ 20 × 100 = +150%. Using −20 as the divisor would give −150%, which points the wrong way. In Excel or Google Sheets, use =(B1−A1)/ABS(A1).
Use the compound annual growth rate, not the simple average: (end ÷ start)1/years − 1. A value that grows from 50,000 to 65,000 over 4 years changed 30% in total, but its average yearly change is 1.30.25 − 1 = 6.78%, not 7.5%. Dividing the total by the number of years ignores compounding.