**The built-in JavaScript Math object includes a number of useful functions for performing a variety of mathematical operations. Let’s dive in and take a look at how they work and what you might use them for.**

## Math.max and Math.min

These functions pretty much do what you’d expect: they return the maximum or minimum of the list of arguments supplied:

```
Math.max(1,2,3,4,5)
<< 5 Math.min(4,71,-7,2,1,0)
<< -7
```

The arguments *all* have to be of the `Number`

data type. Otherwise, `NaN`

will be returned:

```
Math.max('a','b','c')
<< NaN Math.min(5,"hello",6)
<< NaN
```

Watch out, though. JavaScript will attempt to *coerce* values into a number:

```
Math.min(5,true,6)
<< 1
```

In this example, the Boolean value `true`

is coerced into the number `1`

, which is why this is returned as the minimum value. If you’re not familiar with type coercion, it happens when the operands of an operator are of different types. In this case, JavaScript will attempt to convert one operand to an equivalent value of the other operand’s type. You can read more about type coercion in *JavaScript: Novice to Ninja, 2nd Edition*, in Chapter 2.

A list of numbers needs to be supplied as the argument, not an array, but you can use the spread operator (`...`

) to unpack an array of numbers:

```
Math.max(...[8,4,2,1])
<< 8
```

The `Math.max`

function is useful for finding the high score from a list of scores saved in an array:

```
const scores = [23,12,52,6,25,38,19,37,76,54,24]
const highScore = Math.max(...scores)
<< 76
```

The `Math.min`

function is useful for finding the best price on a price-comparison website:

```
const prices = [19.99, 20.25, 18.57, 19,75, 25, 22.50]
const bestPrice = Math.min(...prices)
<< 18.57
```

## Absolute Values

An **absolute value** is simply the size of the number, no matter what its size. This means that positive numbers stay the same and negative numbers lose their minus sign. The `Math.abs`

function will calculate the absolute value of its argument:

```
Math.abs(5)
<< 5 Math.abs(-42)
<< 42 Math.abs(-3.14159)
<< 3.14159
```

Why would you want to do this? Well, sometimes you want to calculate the *difference* between two values, which you work out by subtracting the smallest from the largest, but often you won’t know which is the smallest of the two values in advance. To get around, this you can just subtract the numbers in any order and take the absolute value:

```
const x = 5
const y = 8 const difference = Math.abs(x - y)
<< 3
```

A practical example might be on a money-saving website, where you want to know how much you could save by calculating the difference between two deals, since you’d be dealing with live price data and wouldn’t know in advance which deal was the cheapest:

```
const dealA = 150
const dealB = 167 const saving = Math.abs(dealA - dealB)
<< 17
```

## Math.pow

`Math.pow`

performs power calculations, like these:

```
3⁴ = 81
```

In the example above, 3 is known as the **base** number and 4 is the **exponent**. We would read it as “3 to the power of 4 is 81”.

The function accepts two values — the base and the exponent — and returns the result of raising the base to the power of the exponent:

```
Math.pow(2,3)
<< 8 Math.pow(8,0)
<< 1 Math.pow(-1,-1)
<< -1
```

`Math.pow`

has pretty much been replaced by the infix exponentiation operator (`**`

) — introduced in ES2016 — which does exactly the same operation:

```
2 ** 3
<< 8 8 ** 0
<< 1 (-1) ** (-1)
<< -1
```

## Calculating Roots

Roots are the inverse operation to powers. For example, since 3 squared is 9, the square root of 9 is 3.

`Math.sqrt`

can be used to return the square root of the number provided as an argument:

```
Math.sqrt(4)
<< 2 Math.sqrt(100)
<< 10 Math.sqrt(2)
<< 1.4142135623730951
```

This function will return `NaN`

if a negative number or non-numerical value is provided as an argument:

```
Math.sqrt(-1)
<< NaN Math.sqrt("four")
<< NaN
```

But watch out, because JavaScript will attempt to coerce the type:

```
Math.sqrt('4') << 2 Math.sqrt(true)
<< 1
```

`Math.cbrt`

returns the cube root of a number. This accepts all numbers — including negative numbers. It will also attempt to coerce the type if a value that’s not a number is used. If it can’t coerce the value to a number, it will return `NaN`

:

```
Math.cbrt(1000)
<< 10 Math.cbrt(-1000)
<< -10 Math.cbrt("10")
<< 2.154434690031884 Math.cbrt(false)
<< 0
```

It’s possible to calculate other roots using the exponentiation operator and a fractional power. For example, the fourth root of a number can be found by raising it to the power one-quarter (or 0.25). So the following code will return the fourth root of 625:

```
625 ** 0.25
<< 5
```

To find the fifth root of a number, you would raise it to the power of one fifth (or 0.2):

```
32 ** 0.2
<< 2
```

In general, to find the nth root of a number you would raise it to the power of `1/n`

, so to find the sixth root of a million, you would raise it to the power of 1/6:

```
1000000 ** (1/6)
<< 9.999999999999998
```

Notice that there’s a rounding error here, as the answer should be exactly 10. This will often happen with fractional powers that can’t be expressed exactly in binary. (You can read more about this rounding issue in “A Guide to Rounding Numbers in JavaScript“.)

Also note that you can’t find the roots of negative numbers if the root is even. This will return `NaN`

. So you can’t attempt to find the 10th root of -7, for example (because 10 is even):

```
(-7) ** 0.1 << NaN
```

One reason you might want to calculate roots is to work out growth rates. For example, say you want to 10x your profits by the end of the year. How much do your profits need to grow each month? To find this out, you’d need to calculate the 12th root of 10, or 10 to the power of a twelfth:

```
10 ** (1/12)
<< 1.2115276586285884
```

This result tells us that the monthly growth factor has to be around 1.21 in order to 10x profits by the end of the year. Or to put it another way, you’d need to increase your profits by 21% every month in order to achieve your goal.

## Logs and Exponentials

**Logarithms** — or logs for short — can be used to find the exponent of a calculation. For example, imagine you wanted to solve the following equation:

```
2ˣ = 100
```

In the equation above, `x`

certainly isn’t an integer, because 100 isn’t a power of 2. This can be solved by using base 2 logarithms:

```
x = log²(100) = 6.64 (rounded to 2 d.p.)
```

The `Math`

object has a `log2`

method that will perform this calculation:

```
Math.log2(100)
<< 6.643856189774724
```

It also has a `log10`

method that performs the same calculations, but uses 10 as the base number:

```
Math.log10(100)
<< 2
```

This result is telling us that, to get 100, you need to raise 10 to the power of 2.

There’s one other log method, which is just `Math.log`

. This calculates the natural logarithm, which uses Euler’s number — `e`

(approximately 2.7) — as the base. This might seem to be a strange value to use, but it actually occurs often in nature when exponential growth happens — hence the name “natural logarithms”:

```
Math.log(10)
<< 4.605170185988092 Math.log(Math.E)
<< 1
```

The last calculation shows that Euler’s number (`e`

) — which is stored as the constant `Math.E`

— needs to be raised to the power of 1 to obtain itself. This makes sense, because any number to the power of 1 is in fact itself. The same results can be obtained if 2 and 10 are provided as arguments to `Math.log2`

and `Math.log10`

:

```
Math.log2(2)
<< 1 Math.log10(10)
<< 1
```

Why would you use logarithms? It’s common when dealing with data that grows exponentially to use a logarithmic scale so that the growth rate is easier to see. Logarithmic scales were often used to measure the number of daily COVID-19 cases during the pandemic as they were rising so quickly.

If you’re lucky enough to have a website that’s growing rapidly in popularity (say, doubling every day) then you might want to consider using a logarithmic scale before displaying a graph to show how your popularity is growing.

## Hypotenuse

You might remember studying Pythagoras’ theorem at school. This states that the length of the longest side of a right-angled triangle (the **hypotenuse**) can be found using the following formula:

```
h² = x² + y²
```

Here, x and y are the lengths of the other two sides.

The `Math`

object has a `hypot`

method that will calculate the length of the hypotenuse when provided with the other two lengths as arguments. For example, if one side is length 3 and the other is length 4, we can work out the hypotenuse using the following code:

```
Math.hypot(3,4)
<< 5
```

But why would this ever be useful? Well, the hypotenuse is a measure of the shortest distance between two points. This means that, if you know the x and y coordinates of two elements on the page, you could use this function to calculate how far apart they are:

```
const ship = {x: 220, y: 100}
const boat = {x: 340, y: 50} const distance = Math.hypot(ship.x - boat.x,ship.y - boat.y)
```

I hope that this short roundup has been useful and helps you utilize the full power of the JavaScript Math object in your projects.

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