Percent Change Calculator

This page is the percentage calculator set up for one job: comparing a starting number with a finishing one. The Calculate menu offers only Percentage change from X to Y, so there is nothing to choose before you type.

1. Type the starting number in Old value (X). It begins at 80.
2. Type the finishing number in New value (Y). It begins at 100.
3. Read the large result. It says Increase of or Decrease of, followed by the percent to two decimal places. For 80 and 100 it reads Increase of 25.00%.
4. Check the small table underneath: Difference is Y minus X, which is 20 here, and Multiplier is Y divided by X, which is 1.25x.
5. Look at the formula line, which repeats your own numbers so you can copy the working into a report or a homework answer.

Order matters. The old value always goes first, and swapping the two boxes gives a different answer, for reasons explained further down.

Percent change measures a movement against where you started: (new - old) / |old| x 100. A positive answer is an increase and a negative one is a decrease. The bars around the old value mean the calculator divides by its size, ignoring any minus sign.

These rows can all be reproduced in the tool:

The multiplier is the quickest way to read a result. Anything above 1 is growth, anything below 1 is shrinkage, and 0.875x means the new value is 87.5 percent of the old one. The same arithmetic suits prices, pay, traffic, grades and populations.

Read the Difference line alongside the percent, because a big percent on a tiny base can mislead. A town that grows from 12,000 to 13,800 people has risen by 15.00 percent, a gain of 1,800. A shop that sells 2 items one week and 3 the next has risen by 50.00 percent, but the difference is only one sale. Quote both numbers when you report a change, so that readers can judge its size for themselves.

Going from 80 to 100 is a 25 percent increase. Going back from 100 to 80 is a 20 percent decrease. The gap is 20 both times, but the base is different: the first change is measured against 80 and the second against 100. Since the base is always the old value, the same two numbers produce two answers depending on direction.

The same effect explains why gains and losses do not cancel. Raise 100 by 10 percent and you reach 110. Cut that by 10 percent and you reach 99, a net fall of 1 percent. To undo a fall of 20 percent you need a rise of 25 percent, and to undo a fall of 50 percent you need a rise of 100 percent.

Do not confuse a percent change with percentage points. If an interest rate moves from 4 percent to 5 percent, it rose by 1 percentage point, but the percent change is 25.00 percent. Type 4 and 5 to see it. News reports often blur the two, so check which one a headline means.

If the old value is 0, the calculator shows a warning that the starting value cannot be zero, because a percent of zero has no meaning. Report the plain difference in that case. Negative starting values are also awkward. The sign of the percent still follows the direction of the movement, but the multiplier line is plain Y divided by X and can come out negative, so rely on the Difference line instead.

When neither number is clearly the starting point, such as two quotes from two suppliers, use the percentage difference calculator. To apply a known rate to a number, use the percentage increase calculator or the percentage decrease calculator. The full set of modes lives on the percentage calculator.

Results show two decimals and are rounded for display. If you compare share prices or investments, treat the figures as information only, not financial advice. The numbers stay in your browser.