Percentage increase calculator

A percent increase calculator divides the rise by the starting number and multiplies by 100. From 48 to 60 the rise is 12, and 12 / 48 = 0.25, so the increase is 25%.

Two different questions share the same words. "What is the percent increase from 48 to 60?" has a percentage for an answer. "What is 48 increased by 25%?" has a number for an answer. They are the same relationship run in opposite directions. The second one is quickest as a single multiplication: increasing by p% means multiplying by 1 + p/100, so 48 x 1.25 = 60. A 7% raise on a 52,000 salary is 52,000 x 1.07 = 55,640, with no need to work out the 7% separately and add it on.

The commonest mistake is dividing by the new number. 12 / 60 = 20%, which is a real answer to a different question: it is the decrease from 60 back down to 48. The gap is the same 12 both ways, but the base is not, so a rise and the fall that undoes it are never the same percentage.

The second mistake is reading "percent of" as "percent increase". 60 is 125% of 48, but it is 25% more than 48. The increase is the "of" figure minus 100. This is also where large increases go wrong. Doubling is a 100% increase and tripling is a 200% increase: 48 to 144 is up 200%, because 144 is three times 48. Copy that says something is "300% more" when it is three times as much has added an extra whole.

An increase from zero has no percentage. Going from 0 to 60 divides by zero, and the useful description is a rise of 60. Small starting numbers are a milder version of the same problem: 2 to 3 is a 50% increase, which is accurate and says little when the counts are that small.

Repeated increases multiply rather than add. Two 10% rises in a row are 1.1 x 1.1 = 1.21, a 21% increase overall, not 20%. Run the other way, a total increase spread over several periods is not the total divided by the number of periods. If 48 grew to 60 over three years, the average yearly increase is 1.25 to the power of one third, minus 1, which is about 7.72% a year rather than 25 / 3 = 8.33%.

If the two numbers are themselves percentages, say a rate going from 4% to 5%, the increase is 25% and also one percentage point. Both are correct, so say which one you mean.