Range Calculator

What the range calculator does

The range is the distance from the smallest value in your data to the largest. It is the simplest way there is to measure how spread out a set of numbers is. This calculator finds it, and shows you the minimum and maximum it used to get there.

It is quick, it is easy to picture, and it is a fast way to spot an outlier lurking at one end. Below is how it works and where its simplicity starts to cost you.

How to use it

1. Enter your numbers in the box, separated by commas, spaces, or new lines.
2. Press Calculate for the range along with the smallest and largest values, or Reset to clear it.

How the range is worked out

There is nothing to it. Find the largest number, find the smallest, and take the difference:

Range = largest value minus smallest value

That single number tells you how wide a span your data covers from end to end. The calculator shows the minimum and maximum next to it, so you can see exactly which two values the span is built from.

Its strength, and its blind spot

The strength of the range is that anyone can understand it. A range of 40 says the data spans 40 units, and that is that. But the same simplicity is its blind spot: the range is built from only two numbers and ignores everything in between. It cannot tell you whether the rest of your data is bunched tightly in the middle or spread evenly across the gap, because it never looks.

That also makes the range sensitive to a single outlier, since one freak value at either end sets the whole span. And the range tends to grow as you collect more data, simply because a bigger set has more chances to turn up an extreme value. So the range is a fine first glance, but for a fuller measure of spread, the standard deviation or the interquartile range look at all of the data, not just its edges.

A worked example: eight numbers

Take the eight numbers 2, 4, 4, 4, 5, 5, 7, 9. The smallest is 2 and the largest is 9, so the range is 9 minus 2 = 7.

Notice what the range does not see. Six of these eight numbers sit between 4 and 5, packed tightly together, yet the range of 7 says nothing about that clustering. It reports only the width of the span, which is why it is best read alongside a measure that uses the whole set.

Entering your data, and the rounding

You can separate your numbers with commas, spaces, or new lines, in any mix, and the order does not matter, since the calculator only needs to find the smallest and largest. The range is shown exactly as the subtraction gives it.

Questions people ask

What is the range in statistics?

The difference between the largest and smallest values in a data set. It is the simplest measure of how spread out the data is.

How do you find the range?

Subtract the smallest value from the largest. The calculator does this and also shows you both values so you can check them.

Why is the range affected by outliers?

Because it uses only the two most extreme values. A single unusually high or low number becomes one end of the span and sets the whole range on its own.

Range or standard deviation?

The range is quicker and easier to picture, but it looks at only two numbers. The standard deviation uses every value, so it gives a fuller measure of spread. They work well read together.

References

A quick note on where the methods here come from. The range and the other measures of spread are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers the range and how outliers affect it.

1. NIST/SEMATECH e-Handbook of Statistical Methods (measures of spread). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (measures of the spread of the data). https://openstax.org/details/books/introductory-statistics-2e