Percent Change Calculator
Calculate the percentage increase or decrease between two values
By Waqar Mushtaq · Last updated:
Percent change measures how much a value has grown or shrunk relative to where it started, expressed as a percentage of the original value. It's the single most common way to describe price moves, growth rates, test score changes, and year-over-year comparisons -- "up 12%," "down 30%" -- because a raw difference alone doesn't say whether that gap is big or small relative to the starting point. This calculator takes an original value and a new value and returns the signed percent change, the plain difference between them, and a couple of worked examples that show why increasing and then decreasing by the same percentage doesn't bring you back to where you started.
How Percent Change Is Calculated
O(1) calculationV_old = original value · V_new = new value
Subtract the original value from the new value to get the raw change, divide that by the absolute value of the original number, then multiply by 100. Using the absolute value in the denominator keeps the sign of the answer meaningful even when the original value itself is negative (for example, a temperature moving from -10 to -5 is correctly reported as a 50% increase, not a -50% one).
Example -- price increase: a product goes from $50 to $65. (65 - 50) / |50| × 100 = 15 / 50 × 100 = +30%
Example -- price decrease: a product goes from $80 to $60. (60 - 80) / |80| × 100 = -20 / 80 × 100 = -25%
A positive result is a percent increase; a negative result is a percent decrease. Percent change is undefined when the original value is 0, since there's no base amount to measure the change against.
Use Cases
Tracking Price Changes
Retailers advertise discounts and markups as percentages ("20% off," "price up 8% this quarter") because a percentage communicates the scale of a change independent of the item's absolute price -- a $10 increase means something very different on a $20 item than a $2,000 one.
Analyzing Growth Rates
Year-over-year revenue growth, population change, and website traffic trends are almost always reported as percent change rather than raw numbers, since it lets you compare growth across businesses, cities, or time periods of very different sizes.
Grading and Test Score Comparisons
Comparing a student's score across two tests, or a metric before and after an intervention, is clearer as a percent change than as a raw point difference, especially when the two tests have different maximum scores.
Spotting Asymmetric Swings
A value that drops 50% and then rises 50% does not return to its starting point -- the comparison table below this calculator's result shows exactly why, using your own numbers, which is a common source of confusion in financial and statistical reporting.
Frequently Asked Questions
What is the difference between percent change and percentage points?
Percent change is a relative measure -- it expresses the change as a fraction of the original value (e.g. an interest rate moving from 4% to 5% is a 25% percent change, since 1 is 25% of 4). A percentage-point change is the plain difference between two percentages (e.g. that same move is "1 percentage point"). The two numbers describe the same event very differently, so it matters which one is being reported.
Why is the result undefined when the original value is 0?
Percent change divides by the original value, and division by zero has no defined result. If something went from 0 to any nonzero amount, it technically grew by an infinite percentage, which isn't a meaningful number to report -- most sources instead describe that case in absolute terms (e.g. "went from 0 to 50 units").
Why does a 50% increase followed by a 50% decrease not return to the original value?
Because each percentage is calculated against a different base. Increasing 100 by 50% gives 150; decreasing that 150 by 50% gives 75, not 100 -- the second percentage is taken from the larger, already-increased number. This asymmetry is why percent changes don't simply cancel out, even when the percentages look equal.
Can percent change be negative, and what does that mean?
Yes -- a negative result means the new value is lower than the original, i.e. a percent decrease. A positive result means a percent increase. The sign is determined by comparing the new value to the original, not by either value individually being positive or negative.
Methodology
The formula above is implemented as a standalone module covered by unit tests, so its worked examples are re-checked on every change to the site. It is verified against the authoritative sources listed below.
Maintained by Waqar Mushtaq. Spotted a result that looks wrong? Report it and it becomes a failing test.