Percentage calculator

What percent is X of Y. Divide the part by the whole, then multiply by 100. This is the one behind test scores, discounts and any question phrased as "out of".

What is X percent of Y. Turn the percentage into a decimal by dividing by 100, then multiply. This is the one behind tax, tips and interest.

Percent increase or decrease. Subtract the old value from the new one, divide by the old value, and multiply by 100. The starting value is always the denominator, which is why swapping the two numbers does not just flip the sign.

The absolute value on the denominator is there so a move from -50 to -25 reads as a 50% increase, which is the direction it actually went, rather than a decrease.

A rise and a fall of the same percentage do not cancel. Take 100 up by 20% and you have 120. Take 120 down by 20% and you lose 24, landing on 96, not 100. Each percentage is measured against a different base. If you want the net effect, put your real start and end values into the third mode rather than adding the percentages up.

Percent and percentage points are different things. A rate moving from 20% to 25% has risen by 5 percentage points, and also by 25% of itself. Both are correct and they are not interchangeable. Use percentage points whenever the thing you are comparing is already a percentage.

You cannot have a percentage increase from zero. Growth from 0 to 40 is real, but the formula divides by the starting value, and dividing by zero has no answer. This page says so instead of printing infinity or a made up number. Report the absolute change instead.

Order matters in the third mode. 80 to 100 is a 25% increase. 100 to 80 is a 20% decrease. Same two numbers, same gap of 20, different denominators.

45 out of 60. 45 divided by 60 is 0.75, so 75%.

18% of 250. 0.18 multiplied by 250 is 45, leaving 205 as the other 82%.

80 up to 100. The difference is 20, divided by the starting 80 is 0.25, so a 25% increase. Reverse it and 100 down to 80 is 20 divided by 100, a 20% decrease.

How do I work out what percent one number is of another?

Divide the part by the whole and multiply by 100. 45 out of 60 is 45 divided by 60, which is 0.75, so 75%. The first mode on this page does exactly that as you type.

How do I find a percentage of a number?

Divide the percentage by 100 and multiply by the number. 18% of 250 is 0.18 multiplied by 250, which is 45. The second mode also shows what is left over after taking that share away.

How do I calculate percentage increase or decrease?

Subtract the old value from the new one, divide by the old value, and multiply by 100. Going from 80 to 100 is 20 divided by 80, which is 25%, an increase. Going from 100 to 80 is minus 20 divided by 100, which is a 20% decrease. The two are not the same size, which is why the order of the numbers matters.

Why can I not calculate a percentage increase from zero?

Because the formula divides by the starting number, and dividing by zero has no answer. A rise from 0 to 40 is an increase of 40 in absolute terms, but there is no percentage that describes it. The calculator says so and shows you the absolute change instead of printing infinity.

Does a 20% rise followed by a 20% fall get me back to where I started?

No. 100 rises by 20% to 120, then falls by 20% of 120, which is 24, landing on 96. Each percentage is taken from a different base, so they do not cancel. Use the third mode with your actual start and end values rather than adding the percentages up.

What is the difference between percent and percentage points?

If a rate moves from 20% to 25%, that is a rise of 5 percentage points, and also a 25% increase in the rate itself. Both statements are true and they describe different things. Use percentage points when the quantity you are comparing is already a percentage.