A percentage change calculator measures how much a value has gone up or down, expressed as a percent of the original value. Enter the old number and the new number, you'll see both the raw change and the signed percent change. Useful for tracking price moves, salary changes, weight loss, investment returns, or any before-and-after comparison.
The formula is (new − old) ÷ old × 100. A positive result is an increase, negative is a decrease. The denominator is always the original value, which is why a 50% drop followed by a 50% gain doesn't return you to the start, a common source of confusion in finance and statistics.
Key takeaway
Percent change always references the starting value, not the ending one. That asymmetry has real consequences: if a stock falls 50% and then rises 50%, you're at 75% of where you started, not 100%. To recover from a 50% loss you need a 100% gain. Knowing which direction the percent flows in is half the skill of reading financial and statistical reports.
How it's calculated
The standard formula:
percent change = (new value − old value) ÷ |old value| × 100
The absolute-value bars matter when the original is negative, they keep the sign of the result reflecting direction (up vs. down) rather than getting flipped by an algebraic accident. Most everyday applications work with positive originals, so the bars usually drop out.
A close cousin is percent difference, which divides by the average of the two values rather than the original. Percent difference is symmetric (A vs. B and B vs. A give the same answer); percent change is directional. Use percent difference for comparing two unordered quantities (lab results), percent change for time-series comparisons (then vs. now).
Source: Standard percent-change formula, (new − old) ÷ old × 100
Examples
Price up from $80 to $100
- Original value 80
- New value 100
Going from $80 to $100 is a $20 absolute change and a 25% increase. The 25% comes from dividing the $20 increase by the original $80, not by the new $100. This is the most common everyday percent-change scenario and a reliable mental check on the formula.
Sales drop from 150 units to 120
- Original value 150
- New value 120
Sales falling from 150 to 120 is a 20% decrease: a 30-unit drop divided by the original 150. Note the sign, percent change carries direction, while phrases like "20% decrease" and "drop of 20%" make the negative explicit in language.
Frequently asked questions
What's the difference between percent change and percent difference?
Percent change uses the original value as the denominator and is directional, going from 80 to 100 is +25%, but going from 100 to 80 is −20%. Percent difference uses the average of the two values as the denominator and is symmetric, both directions give the same answer (≈22.2%). Use percent change for time-series ("then vs. now"); use percent difference for comparing two readings of the same quantity in different conditions.
How do I calculate percent change if my original value is zero?
You can't, mathematically, division by zero is undefined. In practice, report the absolute change instead, or define a baseline. For example, "first month had 0 signups, second month had 50" is more honestly described as "+50 signups" than as a percent change. Some software dashboards display "," or "n/a" for zero-base comparisons for this reason.
Can percent change exceed 100%?
Yes. Anything more than a doubling is over 100%. A value going from $10 to $50 is a 400% increase, the new value is 5× the original, so the change is 4× the original. There's no upper bound on percent increase. On the decrease side, however, you can't fall by more than 100% unless the new value is negative (which is rare for prices and counts but possible for things like profit margins).
Why does a 50% loss need a 100% gain to recover?
Because the denominator changes. Falling from $100 to $50 is a 50% loss (50 ÷ 100). Climbing back from $50 to $100 is a 100% gain (50 ÷ 50). The smaller post-loss base makes the same dollar recovery a much larger percent move. This asymmetry is why investors fear drawdowns more than they value equivalent-percent gains.