Percentage Change Calculator

Percentage change formula

Percentage change expresses the difference between two values as a share of the starting value. Subtract the original from the new value, divide by the original, and multiply by 100:

percentage change = ((new − original) ÷ |original|) × 100
absolute difference = new − original

A positive result is an increase and a negative result is a decrease. The calculator divides by the absolute value of the original so that the sign of the answer always matches the direction of movement, even when the starting value is negative (for example, a loss of −200 improving to −50 is shown as a +75% change, i.e. an improvement).

Worked examples

Example 1: a price rise from 50 to 65

Difference: 65 − 50 = 15. Divide by the original: 15 ÷ 50 = 0.3. Multiply by 100: +30%. The price rose by 30%, an absolute increase of 15.

Example 2: website visits fall from 1,200 to 900

Difference: 900 − 1,200 = −300. Divide: −300 ÷ 1,200 = −0.25. Result: −25%, a 25% decrease of 300 visits.

Example 3: a temperature from −10 to 5

Difference: 5 − (−10) = 15. Divide by |−10| = 10: 1.5, so the change is +150%. Note that percentage change on scales with an arbitrary zero, like Celsius, is mathematically valid but rarely meaningful — the absolute difference of 15 degrees is usually the more useful figure.

How to read the result

The headline figure carries a plus or minus sign, and the sentence beneath translates it into words ("a 30% increase"). The two bars compare the original (blue) and the new value (amber) at the same scale, so you can see the size of the shift at a glance. The formula line shows exactly which numbers were used.

Report both numbers when you can. "Sales rose 200%" sounds impressive, but if that is from 1 unit to 3 units, the absolute difference of 2 tells the real story. Conversely, a small percentage of a large base — 2% of a $5 million budget — can be a big absolute amount.

Percentage change vs. percentage difference vs. percentage points

These three ideas are often confused:

• Percentage change has a direction: it measures from an old value to a new one, and the old value is the base.
• Percentage difference compares two values with no "before" and "after", usually dividing by their average. It is symmetric and always positive.
• Percentage points describe the gap between two percentages. An interest rate moving from 4% to 5% is a rise of 1 percentage point, but a 25% percentage change.

This tool calculates percentage change. If you already know the starting value and the rate and want the end result, use the percentage increase calculator or the percentage decrease calculator instead.

Limits of the formula

Percentage change is undefined when the original value is zero, because you cannot divide by zero — going from 0 to 10 is an infinite relative increase. In that case the calculator shows a friendly error and you should report the absolute difference instead.

Percentage changes are also not symmetric. A rise from 50 to 100 is +100%, but the fall from 100 back to 50 is only −50%. That is why a 50% loss needs a 100% gain to recover. For the same reason, you cannot add successive percentage changes: +10% followed by −10% gives a net change of −1%, not zero. To combine several periods, multiply the growth factors (1.10 × 0.90 = 0.99) and convert back.

Finally, when the original value is very small or close to zero, tiny absolute moves produce huge percentages that can mislead. Treat results over a few hundred percent with care and always look at the underlying values.

Common uses

Percentage change is the standard way to compare figures over time. Businesses report revenue growth quarter over quarter, investors track how a share price moved since purchase, and households compare this year's energy bill with last year's. Teachers use it to show improvement between a pre-test and a post-test, and analysts use it to compare categories of very different sizes on an equal footing: a store that grew from 40 to 50 sales (+25%) improved faster than one that grew from 1,000 to 1,100 (+10%), even though the second added more sales.

When you present a percentage change, always state the period and the base. "Up 12% year over year, from 2,500 to 2,800" is far more informative than "up 12%".