Percentage Change Calculator

Percentage change vs. percentage difference

Percentage change — direction matterschange % = (new − old) ÷ |old| × 100 Percentage difference — symmetric, no directiondifference % = |a − b| ÷ ((a + b) ÷ 2) × 100

These answer different questions and are often confused. Change has a reference point — you went from one value to another, so 100 → 150 is a 50% increase while 150 → 100 is a 33.3% decrease. Same two numbers, different answers, and both are correct.

Difference has no reference point. It compares two measurements of equal standing — two lab results, two products, two candidates — by dividing by their average. It gives the same answer whichever order you put them in, which is exactly the property you want when neither is "the original".

Compound growth over multiple periods

Compound annual growth rateCAGR = (end ÷ start)^1/n − 1

If revenue grew from $2m to $5m over four years, the total change is 150% — but the annual rate is not 150 ÷ 4 = 37.5%. Growth compounds, so the correct figure is (5/2)^(1/4) − 1 ≈ 25.7% per year. Enter the number of periods above to get this automatically.

CAGR smooths away all the volatility in between. A company that grew 200% then fell 40% has the same CAGR as one that grew steadily to the same endpoint, and the two are not equally healthy businesses.

Reading percentage claims critically

Percentage change is the most frequently manipulated statistic in public life, and almost always through the choice of baseline rather than through wrong arithmetic.

Relative versus absolute risk. “Cuts your risk by 50%” means little without the starting figure. Halving a 2-in-10,000 risk saves one person in ten thousand; halving a 2-in-10 risk saves one in ten.
Cherry-picked start dates. Any trend can be reversed by choosing the right starting point. Always ask why that year.
Small bases. Going from 2 to 3 is a 50% increase and usually means nothing.
Percent of a percent. A tax rate falling from 20% to 15% is a 5 percentage-point cut and a 25% reduction. Both are true; one sounds far more generous.

The recovery gap

An investment falls 40% then rises 40%. It is not back to even — $100 becomes $60, then $84. Recovering a 40% fall needs a 67% rise, and a 50% fall needs 100%. This asymmetry is why avoiding large losses matters more than capturing large gains.

Traps to watch for

Negative starting values make percentage change ambiguous. A move from −50 to 25 is not sensibly described as a percentage.
Zero starting values make it undefined — you cannot express any change as a percentage of nothing.
Asymmetry. A 50% drop needs a 100% rise to recover. A 90% drop needs a 900% rise. This is why crash recoveries take so much longer than the crash did.
Small bases inflate everything. Going from 2 customers to 3 is a 50% increase and means almost nothing.

Frequently asked questions

How do I calculate percentage increase?

Subtract the old value from the new one, divide by the old value, and multiply by 100. From 120 to 150: (150 − 120) ÷ 120 × 100 = 25%.

Why isn't a 50% decrease reversed by a 50% increase?

Because the base changes. 100 minus 50% is 50; 50 plus 50% is 75, not 100. Recovering from a 50% fall requires a 100% rise off the smaller base.

What is the difference between percentage change and percentage difference?

Percentage change is directional and divides by the original value. Percentage difference is symmetric and divides by the average of the two values, which makes it the right choice when neither number is a starting point.

How do I calculate average annual growth?

Use CAGR: divide the ending value by the starting value, raise to the power of one over the number of periods, then subtract one. Enter the number of periods above and it is computed for you.