Watch Now This tutorial has a related video course created by the Real Python team. Watch it together with the written tutorial to deepen your understanding: **Using NumPy's np.arange() Effectively**

**NumPy** is the fundamental Python library for numerical computing. Its most important type is an **array type** called `ndarray`

. NumPy offers a lot of array creation routines for different circumstances. `arange()`

is one such function based on **numerical ranges**. It’s often referred to as `np.arange()`

because `np`

is a widely used abbreviation for NumPy.

Creating NumPy arrays is important when you’re working with other Python libraries that rely on them, like SciPy, Pandas, Matplotlib, scikit-learn, and more. NumPy is suitable for creating and working with arrays because it offers useful routines, enables performance boosts, and allows you to write concise code.

**By the end of this article, you’ll know:**

- What
`np.arange()`

is - How to use
`np.arange()`

- How
`np.arange()`

compares to the Python built-in class`range`

- Which routines are similar to
`np.arange()`

Let’s see `np.arange()`

in action!

**Free Bonus:** Click here to get access to a free NumPy Resources Guide that points you to the best tutorials, videos, and books for improving your NumPy skills.

## Return Value and Parameters of `np.arange()`

NumPy `arange()`

is one of the array creation routines based on numerical ranges. It creates an instance of `ndarray`

with *evenly spaced values* and returns the reference to it.

You can define the interval of the values contained in an array, space between them, and their type with four parameters of `arange()`

:

```
numpy.arange([start, ]stop, [step, ], dtype=None) -> numpy.ndarray
```

The first three parameters determine the range of the values, while the fourth specifies the type of the elements:

is the number (integer or decimal) that defines the first value in the array.`start`

is the number that defines the end of the array and isn’t included in the array.`stop`

is the number that defines the spacing (difference) between each two consecutive values in the array and defaults to`step`

`1`

.is the type of the elements of the output array and defaults to`dtype`

`None`

.

`step`

can’t be zero. Otherwise, you’ll get a `ZeroDivisionError`

. You can’t move away anywhere from `start`

if the increment or decrement is `0`

.

If `dtype`

is omitted, `arange()`

will try to deduce the type of the array elements from the types of `start`

, `stop`

, and `step`

.

You can find more information on the parameters and the return value of `arange()`

in the official documentation.

## Range Arguments of `np.arange()`

The arguments of NumPy `arange()`

that define the values contained in the array correspond to the numeric parameters `start`

, `stop`

, and `step`

. You have to pass *at least one* of them.

The following examples will show you how `arange()`

behaves depending on the number of arguments and their values.

### Providing All Range Arguments

When working with NumPy routines, you have to import NumPy first:

```
>>> import numpy as np
```

Now, you have NumPy imported and you’re ready to apply `arange()`

.

Let’s see a first example of how to use NumPy `arange()`

:

```
>>> np.arange(start=1, stop=10, step=3)
array([1, 4, 7])
```

In this example, `start`

is `1`

. Therefore, the first element of the obtained array is `1`

. `step`

is `3`

, which is why your second value is 1+3, that is `4`

, while the third value in the array is 4+3, which equals `7`

.

Following this pattern, the next value would be `10`

(7+3), but counting must be ended *before* `stop`

is reached, so this one is not included.

You can pass `start`

, `stop`

, and `step`

as positional arguments as well:

```
>>> np.arange(1, 10, 3)
array([1, 4, 7])
```

This code sample is equivalent to, but more concise than the previous one.

The value of `stop`

is not included in an array. That’s why you can obtain identical results with different `stop`

values:

```
>>> np.arange(1, 8, 3)
array([1, 4, 7])
```

This code sample returns the array with the same values as the previous two. You can get the same result with any value of `stop`

strictly greater than `7`

and less than or equal to `10`

.

However, if you make `stop`

greater than `10`

, then counting is going to end after `10`

is reached:

```
>>> np.arange(1, 10.1, 3)
array([ 1., 4., 7., 10.])
```

In this case, you get the array with four elements that includes `10`

.

Notice that this example creates an array of floating-point numbers, unlike the previous one. That’s because you haven’t defined `dtype`

, and `arange()`

deduced it for you. You’ll learn more about this later in the article.

You can see the graphical representations of these three examples in the figure below:

`start`

is shown in green, `stop`

in red, while `step`

and the values contained in the arrays are blue.

As you can see from the figure above, the first two examples have three values (`1`

, `4`

, and `7`

) counted. They don’t allow `10`

to be included. In the third example, `stop`

is larger than `10`

, and it is contained in the resulting array.

### Providing Two Range Arguments

You can omit `step`

. In this case, `arange()`

uses its default value of `1`

. The following two statements are equivalent:

```
>>> np.arange(start=1, stop=10, step=1)
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.arange(start=1, stop=10)
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
```

The second statement is shorter. `step`

, which defaults to `1`

, is what’s usually intuitively expected.

Using `arange()`

with the increment `1`

is a very common case in practice. Again, you can write the previous example more concisely with the positional arguments `start`

and `stop`

:

```
>>> np.arange(1, 10)
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
```

This is an intuitive and concise way to invoke `arange()`

. Using the keyword arguments in this example doesn’t really improve readability.

**Note:** If you provide two positional arguments, then the first one is `start`

and the second is `stop`

.

### Providing One Range Argument

You have to provide *at least one argument* to `arange()`

. To be more precise, you have to provide `start`

.

But what happens if you omit `stop`

? How does `arange()`

knows when to stop counting? In this case, the array starts at `0`

and ends before the value of `start`

is reached! Again, the default value of `step`

is `1`

.

In other words, `arange()`

assumes that you’ve provided `stop`

(instead of `start`

) and that `start`

is `0`

and `step`

is `1`

.

Let’s see an example where you want to start an array with `0`

, increasing the values by `1`

, and stop before `10`

:

```
>>> np.arange(start=0, stop=10, step=1)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.arange(0, 10, 1)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.arange(start=0, stop=10)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.arange(0, 10)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
```

These code samples are okay. They work as shown in the previous examples. There’s an even shorter and cleaner, but still intuitive, way to do the same thing. You can just provide a single positional argument:

```
>>> np.arange(10) # Stop is 10, start is 0, and step is 1!
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
```

This is the most usual way to create a NumPy array that starts at zero and has an increment of one.

**Note:** The single argument defines where the counting stops. The output array starts at `0`

and has an increment of `1`

.

If you try to explicitly provide `stop`

without `start`

, then you’ll get a `TypeError`

:

```
>>> np.arange(stop=10)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: arange() missing required argument 'start' (pos 1)
```

You got the error because `arange()`

doesn’t allow you to *explicitly* avoid the first argument that corresponds to `start`

. If you provide a single argument, then it has to be `start`

, but `arange()`

will use it to define where the counting stops.

### Providing Negative Arguments

If you provide negative values for `start`

or both `start`

and `stop`

, and have a positive `step`

, then `arange()`

will work the same way as with all positive arguments:

```
>>> np.arange(-5, -1)
array([-5, -4, -3, -2])
>>> np.arange(-8, -2, 2)
array([-8, -6, -4])
>>> np.arange(-5, 6, 4)
array([-5, -1, 3])
```

This behavior is fully consistent with the previous examples. The counting begins with the value of `start`

, incrementing repeatedly by `step`

, and ending before `stop`

is reached.

### Counting Backwards

Sometimes you’ll want an array with the values decrementing from left to right. In such cases, you can use `arange()`

with a negative value for `step`

, and with a `start`

greater than `stop`

:

```
>>> np.arange(5, 1, -1)
array([5, 4, 3, 2])
>>> np.arange(7, 0, -3)
array([7, 4, 1])
```

In this example, notice the following pattern: the obtained array starts with the value of the first argument and decrements for `step`

towards the value of the second argument.

In the last statement, `start`

is `7`

, and the resulting array begins with this value. `step`

is `-3`

so the second value is 7+(−3), that is `4`

. The third value is 4+(−3), or `1`

. Counting stops here since `stop`

(`0`

) is reached before the next value (`-2`

).

You can see the graphical representations of this example in the figure below:

Again, `start`

is shown in green, `stop`

in red, while `step`

and the values contained in the array are blue.

This time, the arrows show the direction from right to left. That’s because `start`

is greater than `stop`

, `step`

is negative, and you’re basically counting backwards.

The previous example produces the same result as the following:

```
>>> np.arange(1, 8, 3)[::-1]
array([7, 4, 1])
>>> np.flip(np.arange(1, 8, 3))
array([7, 4, 1])
```

However, the variant with the negative value of `step`

is more elegant and concise.

### Getting Empty Arrays

There are several edge cases where you can obtain empty NumPy arrays with `arange()`

. These are regular instances of `numpy.ndarray`

without any elements.

If you provide equal values for `start`

and `stop`

, then you’ll get an empty array:

```
>>> np.arange(2, 2)
array([], dtype=int64)
```

This is because counting ends before the value of `stop`

is reached. Since the value of `start`

is equal to `stop`

, it can’t be reached and included in the resulting array as well.

One of the unusual cases is when `start`

is greater than `stop`

and `step`

is positive, or when `start`

is less than `stop`

and `step`

is negative:

```
>>> np.arange(8, 2, 1)
array([], dtype=int64)
>>> np.arange(2, 8, -1)
array([], dtype=int64)
```

As you can see, these examples result with empty arrays, *not* with errors.

## Data Types of `np.arange()`

The types of the elements in NumPy arrays are an important aspect of using them. When working with `arange()`

, you can specify the type of elements with the parameter `dtype`

.

**Note:** Here are a few important points about the types of the elements contained in NumPy arrays:

- All elements in a NumPy array are of the same type called
**dtype**(short for**data type**). - NumPy dtypes allow for more granularity than Python’s built-in numeric types.
- In some cases, NumPy dtypes have aliases that correspond to the names of Python built-in types.
- Usually, NumPy routines can accept Python numeric types and vice versa.
- Some NumPy dtypes have platform-dependent definitions.

If you want to learn more about the dtypes of NumPy arrays, then please read the official documentation.

You are free to omit `dtype`

. In this case, `arange()`

will try to deduce the dtype of the resulting array. It depends on the types of `start`

, `stop`

, and `step`

, as you can see in the following example:

```
>>> x = np.arange(5)
>>> x
array([0, 1, 2, 3, 4])
>>> x.dtype
dtype('int64')
>>> x.itemsize # In bytes
8
```

Here, there is one argument (`5`

) that defines the range of values. Its type is `int`

. That’s why the dtype of the array `x`

will be one of the integer types provided by NumPy. In this case, NumPy chooses the `int64`

dtype by default. This is a 64-bit (8-bytes) integer type.

The array in the previous example is equivalent to this one:

```
>>> x = np.arange(5, dtype=int)
>>> x
array([0, 1, 2, 3, 4])
>>> x.dtype
dtype('int64')
```

The argument `dtype=int`

*doesn’t* refer to Python `int`

. It translates to NumPy `int64`

or simply `np.int`

.

NumPy offers you several integer fixed-sized dtypes that differ in memory and limits:

8-bit signed integer (from`np.int8`

:`-128`

to`127`

)8-bit unsigned integer (from`np.uint8`

:`0`

to`255`

)16-bit signed integer (from`np.int16`

:`-32768`

to`32767`

)16-bit unsigned integer (from`np.uint16`

:`0`

to`65535`

)32-bit signed integer (from`np.int32`

:`-2**31`

to`2**31-1`

)32-bit unsigned integer (from`np.uint32`

:`0`

to`2**32-1`

)64-bit signed integer (from`np.int64`

:`-2**63`

to`2**63-1`

)64-bit unsigned integer (from`np.uint64`

:`0`

to`2**64-1`

)

If you want other integer types for the elements of your array, then just specify `dtype`

:

```
>>> x = np.arange(5, dtype=np.int32)
>>> x
array([0, 1, 2, 3, 4], dtype=int32)
>>> x.dtype
dtype('int32')
>>> x.itemsize # In bytes
4
```

Now the resulting array has the same values as in the previous case, but the types and sizes of the elements differ. The argument `dtype=np.int32`

(or `dtype='int32'`

) forces the size of each element of `x`

to be 32 bits (4 bytes).

When your argument is a decimal number instead of integer, the dtype will be some NumPy floating-point type, in this case `float64`

:

```
>>> y = np.arange(5.0)
>>> y
array([0., 1., 2., 3., 4.])
>>> y.dtype
dtype('float64')
```

The values of the elements are the same in the last four examples, but the dtypes differ.

Generally, when you provide at least one floating-point argument to `arange()`

, the resulting array will have floating-point elements, even when other arguments are integers:

```
>>> np.arange(1, 5.1)
array([1., 2., 3., 4., 5.])
>>> np.arange(1, 5.1).dtype
dtype('float64')
>>> np.arange(0, 9, 1.5)
array([0. , 1.5, 3. , 4.5, 6. , 7.5])
>>> np.arange(0, 9, 1.5).dtype
dtype('float64')
```

In the examples above, `start`

is an integer, but the dtype is `np.float64`

because `stop`

or `step`

are floating-point numbers.

If you specify `dtype`

, then `arange()`

will try to produce an array with the elements of the provided data type:

```
>>> y = np.arange(5, dtype=float)
>>> y
array([0., 1., 2., 3., 4.])
>>> y.dtype
dtype('float64')
```

The argument `dtype=float`

here translates to NumPy `float64`

, that is `np.float`

. It *doesn’t* refer to Python `float`

. Fixed-size aliases for `float64`

are `np.float64`

and `np.float_`

.

When you need a floating-point dtype with lower precision and size (in bytes), you can explicitly specify that:

```
>>> z = np.arange(5, dtype=np.float32)
>>> z
array([0., 1., 2., 3., 4.], dtype=float32)
>>> z.dtype
dtype('float32')
```

Using `dtype=np.float32`

(or `dtype='float32'`

) makes each element of the array `z`

32 bits (4 bytes) large. The size of each element of `y`

is 64 bits (8 bytes):

```
>>> y.itemsize # In bytes
8
>>> z.itemsize # In bytes
4
```

The difference between the elements of `y`

and `z`

, and generally between `np.float64`

and `np.float32`

, is the memory used and the precision: the first is larger and more precise than the latter.

In many cases, you won’t notice this difference. However, sometimes it’s important. For example, TensorFlow uses `float32`

and `int32`

. Similarly, when you’re working with images, even smaller types like `uint8`

are used.

When `step`

is not an integer, the results might be inconsistent due to the limitations of floating-point arithmetic.

## Beyond Simple Ranges With `np.arange()`

You can conveniently combine `arange()`

with operators (like `+`

, `-`

, `*`

, `/`

, `**`

, and so on) and other NumPy routines (such as `abs()`

or `sin()`

) to produce the ranges of output values:

```
>>> x = np.arange(5)
>>> x
array([0, 1, 2, 3, 4])
>>> 2**x
array([ 1, 2, 4, 8, 16])
>>> y = np.arange(-1, 1.1, 0.5)
>>> y
array([-1. , -0.5, 0. , 0.5, 1. ])
>>> np.abs(y)
array([1. , 0.5, 0. , 0.5, 1. ])
>>> z = np.arange(10)
>>> np.sin(z)
array([ 0. , 0.84147098, 0.90929743, 0.14112001, -0.7568025 ,
-0.95892427, -0.2794155 , 0.6569866 , 0.98935825, 0.41211849])
```

This is particularly suitable when you want to create a plot in Matplotlib.

If you need a multidimensional array, then you can combine `arange()`

with `.reshape()`

or similar functions and methods:

```
>>> a = np.arange(6).reshape((2, 3))
>>> a
array([[0, 1, 2],
[3, 4, 5]])
>>> a.shape
(2, 3)
>>> a.ndim
2
```

That’s how you can obtain the `ndarray`

instance with the elements `[0, 1, 2, 3, 4, 5]`

and reshape it to a two-dimensional array.

## Comparison of `range`

and `np.arange()`

Python has a built-in class `range`

, similar to NumPy `arange()`

to some extent. `range`

and `np.arange()`

have important distinctions related to application and performance. You’ll see their differences and similarities.

The main difference between the two is that `range`

is a built-in Python class, while `arange()`

is a function that belongs to a third-party library (NumPy).

In addition, their purposes are different! Generally, `range`

is more suitable when you need to **iterate** using the Python `for`

loop. If you want to create a NumPy array, and apply fast loops under the hood, then `arange()`

is a much better solution.

### Parameters and Outputs

Both `range`

and `arange()`

have the same parameters that define the ranges of the obtained numbers:

`start`

`stop`

`step`

You apply these parameters similarly, even in the cases when `start`

and `stop`

are equal.

However, when working with `range`

:

- You have to provide integer arguments. Otherwise, you’ll get a
`TypeError`

. - You can’t specify the type of the yielded numbers. It’s always
`int`

.

`range`

and `arange()`

also differ in their return types:

creates an instance of this class that has the same features as other sequences (like`range`

`list`

and`tuple`

), such as membership, concatenation, repetition, slicing, comparison, length check, and more.returns an instance of NumPy`arange()`

`ndarray`

.

### Creating Sequences

You can apply `range`

to create an instance of `list`

or `tuple`

with evenly spaced numbers within a predefined range. You might find comprehensions particularly suitable for this purpose.

However, creating and manipulating NumPy arrays is often faster and more elegant than working with lists or tuples.

Let’s compare the performance of creating a `list`

using the comprehension against an equivalent NumPy `ndarray`

with `arange()`

:

```
>>> import timeit
>>> n = 1
>>> timeit.timeit(f'x = [i**2 for i in range({n})]')
>>> timeit.timeit(f'x = np.arange({n})**2', setup='import numpy as np')
```

Repeating this code for varying values of `n`

yielded the following results on my machine:

Size: `n` |
Time Per Loop: `range` |
Time Per Loop: `arange()` |
Ratio |
---|---|---|---|

1 | 497 ns | 1.14 µs | 0.41 |

10 | 2.24 µs | 1.28 µs | 1.74 |

100 | 20.0 µs | 1.37 µs | 14.6 |

1,000 | 211 µs | 2.92 µs | 72.3 |

These results might vary, but clearly you can create a NumPy array much faster than a list, except for sequences of very small lengths. (The application often brings additional performance benefits!)

This is because NumPy performs many operations, including looping, on the C-level. In addition, NumPy is optimized for working with vectors and avoids some Python-related overhead.

### Python `for`

Loops

If you need values to iterate over in a Python `for`

loop, then `range`

is usually a better solution. According to the official Python documentation:

The advantage of the

`range`

type over a regular`list`

or`tuple`

is that a`range`

object will always take the same (small) amount of memory, no matter the size of the range it represents (as it only stores the`start`

,`stop`

and`step`

values calculating individual items and subranges as needed). (Source)

`range`

is often faster than `arange()`

when used in Python `for`

loops, especially when there’s a possibility to break out of a loop soon. This is because `range`

generates numbers in the lazy fashion, as they are required, one at a time.

In contrast, `arange()`

generates all the numbers at the beginning.

For more information about `range`

, you can check The Python range() Function (Guide) and the official documentation.

## Other Routines Based on Numerical Ranges

In addition to `arange()`

, you can apply other NumPy array creation routines based on numerical ranges:

is similar to`linspace()`

`arange()`

in that it returns evenly spaced numbers. But you can specify the number of values to generate as well as whether to include the endpoint and whether to create multiple arrays at once.are similar to`logspace()`

and`geomspace()`

`linspace()`

, except the returned numbers are spaced evenly on the logarithmic scale.return grids of points represented as arrays.`meshgrid()`

,`ogrid()`

, and`mgrid()`

All these functions have their specifics and use cases. You can choose the appropriate one according to your needs.

As you already saw, NumPy contains more routines to create instances of `ndarray`

.

## Quick Summary

To use NumPy `arange()`

, you need to import `numpy`

first:

```
>>> import numpy as np
```

Here’s a table with a few examples that summarize how to use NumPy `arange()`

. It could be helpful to memorize various uses:

Example | Result |
---|---|

`np.arange(start=1, stop=10, step=3)` |
`array([1, 4, 7])` |

`np.arange(1, 10, 3)` |
`array([1, 4, 7])` |

`np.arange(1, 10, 3, dtype=float)` |
`array([1., 4., 7.])` |

`np.arange(1.0, 10, 3)` |
`array([1., 4., 7.])` |

`np.arange(0, 1.1, 0.5)` |
`array([0. , 0.5, 1. ])` |

`np.arange(2, 6)` |
`array([2, 3, 4, 5])` |

`np.arange(5)` |
`array([0, 1, 2, 3, 4])` |

`np.arange(-8, -2, 2)` |
`array([-8, -6, -4])` |

`np.arange(7, 0, -3)` |
`array([7, 4, 1])` |

`np.arange(8, 2)` |
`array([])` |

Don’t forget that you can also influence the memory used for your arrays by specifying NumPy dtypes with the parameter `dtype`

.

## Conclusion

You now know how to use NumPy `arange()`

. The function `np.arange()`

is one of the fundamental NumPy routines often used to create instances of NumPy `ndarray`

. It has four arguments:

the first value of the array`start`

:where the array ends`stop`

:the increment or decrement`step`

:the type of the elements of the array`dtype`

:

You also learned how NumPy `arange()`

compares with the Python built-in class `range`

when you’re creating sequences and generating values to iterate over.

You saw that there are other NumPy array creation routines based on numerical ranges, such as `linspace()`

, `logspace()`

, `meshgrid()`

, and so on.

If you have questions or comments, please put them in the comment section below.

Watch Now This tutorial has a related video course created by the Real Python team. Watch it together with the written tutorial to deepen your understanding: **Using NumPy's np.arange() Effectively**