Percentage Change Calculator
Calculate the percentage increase or decrease between an old value and a new value. The standard way to express growth, discounts, and rates of change.
Last updated: May 2026
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About this calculator
Percentage change expresses how much a value has grown or shrunk relative to its starting point, as a percentage. The formula is percentage change = ((new value − old value) / |old value|) × 100, where the difference between the new and old values is divided by the absolute value of the original, then multiplied by 100. A positive result indicates an increase, and a negative result indicates a decrease. Using the original value as the denominator is what makes it a meaningful relative measure: a $10 rise on a $20 item (50%) is far more significant than a $10 rise on a $1,000 item (1%). The absolute value in the denominator handles cases where the original is negative, keeping the sign of the change determined by the numerator. This metric is everywhere: price changes, investment returns, population growth, salary raises, and statistical reporting all rely on it. Edge cases require care: if the old value is zero, the percentage change is undefined (you cannot divide by zero), because there is no baseline to grow from. Also note that percentage changes are not symmetric — a 50% increase followed by a 50% decrease does not return you to the start, because each percentage is taken from a different base. And a 100% decrease means the value fell to zero, while there is no upper limit on a percentage increase.
How to use
Example 1 — a value rising from 50 to 75. Enter Old Value = 50, New Value = 75. Percentage change = ((75 − 50) / 50) × 100 = (25 / 50) × 100 = 50%. Verify: the value increased by 25, which is half of the original 50, hence a 50% increase. Example 2 — a value falling from 200 to 150. Enter Old Value = 200, New Value = 150. Percentage change = ((150 − 200) / 200) × 100 = (−50 / 200) × 100 = −25%. Verify: the value dropped by 50 out of 200, a quarter of the original, so a 25% decrease, shown as negative.
Frequently asked questions
What is the difference between percentage change and percentage points?
Percentage change measures the relative change between two values, while a percentage-point change measures the simple arithmetic difference between two percentages. For example, if an interest rate rises from 4% to 5%, that is a 1 percentage-point increase but a 25% percentage change (since 1 is a quarter of 4). Confusing the two is a very common and consequential error, especially in finance and news reporting. Use 'percentage points' when comparing two percentages directly, and 'percentage change' when expressing relative growth or decline. This calculator computes percentage change; for percentage points you would just subtract the two percentages.
Why isn't a 50% increase cancelled by a 50% decrease?
Because each percentage is calculated from a different base. If you start at 100 and increase by 50%, you reach 150; a subsequent 50% decrease is taken from 150, removing 75 and leaving 75, not the original 100. The increase was based on 100 but the decrease was based on the larger 150, so they do not offset. This asymmetry is a frequent source of confusion in investing, where a 50% loss requires a 100% gain to break even. Always remember that consecutive percentage changes compound on shifting bases rather than simply adding and subtracting.
What happens if the old value is zero?
Percentage change is undefined when the original value is zero, because the formula would require dividing by zero, which has no meaningful result. Intuitively, there is no baseline to measure growth against — going from 0 to any number is an 'infinite' percentage increase. In practice, this case is usually handled by reporting the change differently, such as stating the absolute increase or noting 'new' where there was nothing before. If your old value is zero, this calculator cannot produce a valid percentage. Consider whether an absolute change or a different metric better communicates what happened.
How do I reverse a percentage change to find the original value?
To find the original value from the new value and the percentage change, divide rather than multiply. If something increased by 25% to reach 150, the original was 150 ÷ 1.25 = 120, not 150 minus 25%. The common mistake is subtracting the same percentage, which gives the wrong answer because the percentage was based on the smaller original number. For a decrease of 20% to a new value of 80, the original was 80 ÷ 0.80 = 100. Always divide by (1 + change as a decimal) to recover the starting figure. This is especially important when backing out pre-tax or pre-discount prices.
When should I NOT use this calculator?
Avoid it when the original value is zero or negative in a way that makes a relative comparison meaningless, since the result will be undefined or hard to interpret. Do not use percentage change when you actually mean percentage points — comparing two rates or percentages directly calls for subtraction, not this relative formula. It is also the wrong tool for compounding multiple sequential changes, where you must multiply the growth factors rather than add the percentages. And be cautious comparing percentage changes across very different base sizes, since a large percentage on a tiny base can be misleading. For absolute differences, simply subtract the values instead.