What is the difference between percentage change and percentage difference?

Change is measured against where you started, so 50 to 100 is a 100 percent rise while 100 to 50 is a 50 percent fall, even though both moves are the same 50. Difference is measured against the average of the two and is symmetric. This calculates change, which is what people almost always mean.

Why does up 10 percent then down 10 percent not return to the start?

Because the second percentage is taken from a larger number. 100 up 10 percent is 110, and 110 down 10 percent is 99. This is the most common percentage mistake there is, and it is why discounts and markups do not cancel out.

Why does it refuse a change from zero?

Because any rise from nothing is infinite, so there is no answer to give. Reporting a large number instead would be inventing one.

Percentage Calculator

Five percentage questions, with the working shown.

Calculation

First number

Second number

Five percentage questions, with the working shown.

How to use it

Pick the calculation. Five of them, phrased as the question rather than as a formula.
Enter the two numbers. Thousands separators are fine, so you can paste from a spreadsheet.
Check the working. The expression is shown with your numbers in it, under the answer.

When you would use this

Percentages are arithmetic anyone can do and get wrong, which is why every version of this calculation exists as its own page across the web. Rather than five pages this is one, with the question phrased in words instead of as a formula. The part worth reading is the working. Every answer comes with the expression that produced it and your numbers substituted in, because the risk with a percentage calculator is not that the arithmetic is wrong, it is that you asked it the wrong question. Seeing the expression is what catches that. Two things trip people up regularly. Percentage change is measured against where you started, so a rise from 50 to 100 is 100 percent while a fall from 100 to 50 is 50 percent, and those are the same absolute move in opposite directions. And percentages do not reverse: adding 10 percent and then taking 10 percent away leaves you at 99, not 100, because the second percentage is of a larger number. Numbers with thousands separators are read as written, so you can paste straight out of a spreadsheet.

Questions

What is the difference between percentage change and percentage difference?: Change is measured against where you started, so 50 to 100 is a 100 percent rise while 100 to 50 is a 50 percent fall, even though both moves are the same 50. Difference is measured against the average of the two and is symmetric. This calculates change, which is what people almost always mean.
Why does up 10 percent then down 10 percent not return to the start?: Because the second percentage is taken from a larger number. 100 up 10 percent is 110, and 110 down 10 percent is 99. This is the most common percentage mistake there is, and it is why discounts and markups do not cancel out.
Why does it refuse a change from zero?: Because any rise from nothing is infinite, so there is no answer to give. Reporting a large number instead would be inventing one.