Find Minimum And Maximum

What this calculator does

You have got a set of numbers and you want the two ends of it: the smallest and the largest. Picking them out by eye is easy for five numbers and a real chore for five hundred. This does it in one go.

Paste your numbers in and it returns the minimum and the maximum. It runs right here in the browser, on the built-in maths, nothing to install.

Using the calculator

1. Enter your numbers, separated by commas, spaces, or line breaks: 1.618, 2, 3.14, -8.5.
2. Press Calculate.

It gives you the maximum and the minimum of the set. Reset clears the box.

Minimum, maximum, and the range between them

The minimum is simply the smallest number in your set, and the maximum is the largest. Nothing subtle there. Negative numbers sort the way you would expect: -8.5 is smaller than -1, which is smaller than 0.

The reason you often want both together is what sits between them. The gap from the smallest to the largest is called the range, and it is the plainest measure there is of how spread out your numbers are:

range = maximum − minimum

A small range means your numbers are bunched tightly together. A big one means they are scattered. So the moment you have the two extremes, you also have a quick feel for the spread of the whole set.

A worked example

Take the set 1.618, 2, 3.14 and -8.5.

• The minimum is -8.5, the only negative and the smallest.
• The maximum is 3.14, the largest.
• The range is 3.14 − (-8.5) = 11.64. Subtracting a negative adds it on, which is why the spread is wider than either number alone might suggest.

Why the extremes are worth a look first

The minimum and maximum are usually the first thing to check in any set of numbers, and for good reason. They tell you the bounds, the floor and ceiling everything else sits within. They are the fastest way to spot an outlier, a value that sits far from the rest, since an odd one out almost always shows up as a surprising minimum or maximum. And they are often a quick sanity check: if a column of ages throws up a maximum of 200 or a minimum of -4, you have found a data-entry slip before it causes any trouble. Once you know the extremes, the average tells you where the middle of the set sits.

Questions people ask

How do you find the minimum and maximum?

Scan the whole set for the smallest value and the largest value. This tool does that for you and returns both at once.

What is the range?

The maximum minus the minimum. It is the simplest measure of how spread out a set of numbers is. For -8.5 up to 3.14, the range is 11.64.

How are negative numbers handled?

The same as any others. A more negative number is smaller, so -8.5 counts as less than -1, and can be the minimum.

Can this help me spot an outlier?

Often, yes. An outlier usually shows up as a minimum or maximum that sits surprisingly far from the rest of your numbers, which makes the extremes a fast first check.

How do I separate the numbers?

Commas, spaces or line breaks all work.

References

A note on where this comes from. The minimum and maximum are the simplest order statistics of a data set, and their difference, the range, is a basic measure of spread in descriptive statistics, as set out in references such as the NIST/SEMATECH e-Handbook of Statistical Methods. For further reading, see Sample maximum and minimum.

1. NIST/SEMATECH, e-Handbook of Statistical Methods, on the range and measures of spread. https://www.itl.nist.gov/div898/handbook/