Absolute Difference Calculator, |a - b| and Percent

About the Absolute Difference Calculator

The Absolute Difference Calculator takes two numbers and tells you how far apart they are. Type a and b and you get the absolute difference |a - b|, the signed difference a - b, which number is larger, and the gap expressed as a percentage of a, of b and of their mean. The working is written out line by line, so you can copy it into homework, a report or a spreadsheet note.

Negative numbers, decimals, thousands separators such as 1,250.5 and scientific notation such as 1.5e3 are all accepted, and the results update as you type.

How to find the absolute difference

The formulas

The absolute difference ignores the order of the numbers and is never negative:

$$|a - b| = \lvert a - b \rvert$$

The three percentages divide that distance by a different reference value. The first two use the size (magnitude) of the number, so a percentage is never negative:

$$\frac{|a - b|}{|a|} \times 100 \qquad \frac{|a - b|}{|b|} \times 100$$

The third divides by the mean of the two numbers. It is usually called the percent difference and gives the same answer whichever number you call a:

$$\frac{|a - b|}{\left| \frac{a + b}{2} \right|} \times 100$$

Worked examples

Absolute difference, percent difference and percent change

These three terms are often mixed up.

• Absolute difference is the plain distance |a - b|, in the same units as the numbers. Use it when the size of the gap matters, such as the gap between two temperatures, two prices or two test scores.
• Percent difference divides the gap by the mean of the two values. Use it when neither value is the starting point, for example comparing two measurements of the same thing or two similar products.
• Percent change divides by the old value and keeps the sign, so an increase and a decrease differ. Use it when one number came first, such as last year to this year. The Percentage Calculator handles percent change, increases and decreases.

When a percentage is undefined

A percentage divides by a reference value, and you cannot divide by zero. If a is 0, the "of a" tile shows "undefined (division by zero)". If a and b are opposite numbers such as -4 and 4, the mean is 0 and the percent difference is undefined. This is not an error with your input, so the other tiles still show their values.

Rounding and very large numbers

Computers store most decimals approximately, so 0.3 - 0.1 is really 0.19999999999999998 inside the machine. Results are rounded to 12 significant digits, so you see the 0.2 you expect. If the difference of two numbers is too large to represent, such as 1e308 and -1e308, the page says so instead of printing a meaningless value.

Privacy

Nothing is uploaded; every calculation runs in your browser and never leaves your device.

Related tools

To work with a whole set of values, such as their range, mean and median, use the Number List Calculator. For percent change, discounts and finding a percentage of a number, use the Percentage Calculator.

Frequently asked questions