numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0)[source]

Return evenly spaced numbers over a specified interval.

Returns num evenly spaced samples, calculated over the interval [start, stop].

The endpoint of the interval can optionally be excluded.

Changed in version 1.16.0: Non-scalar start and stop are now supported.

Changed in version 1.20.0: Values are rounded towards -inf instead of 0 when an integer dtype is specified. The old behavior can still be obtained with np.linspace(start, stop, num).astype(int)


The starting value of the sequence.


The end value of the sequence, unless endpoint is set to False. In that case, the sequence consists of all but the last of num + 1 evenly spaced samples, so that stop is excluded. Note that the step size changes when endpoint is False.

numint, optional

Number of samples to generate. Default is 50. Must be non-negative.

endpointbool, optional

If True, stop is the last sample. Otherwise, it is not included. Default is True.

retstepbool, optional

If True, return (samples, step), where step is the spacing between samples.

dtypedtype, optional

The type of the output array. If dtype is not given, the data type is inferred from start and stop. The inferred dtype will never be an integer; float is chosen even if the arguments would produce an array of integers.

New in version 1.9.0.

axisint, optional

The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end.

New in version 1.16.0.


There are num equally spaced samples in the closed interval [start, stop] or the half-open interval [start, stop) (depending on whether endpoint is True or False).

stepfloat, optional

Only returned if retstep is True

Size of spacing between samples.

See also


Similar to linspace, but uses a step size (instead of the number of samples).


Similar to linspace, but with numbers spaced evenly on a log scale (a geometric progression).


Similar to geomspace, but with the end points specified as logarithms.


>>> np.linspace(2.0, 3.0, num=5)
array([2.  , 2.25, 2.5 , 2.75, 3.  ])
>>> np.linspace(2.0, 3.0, num=5, endpoint=False)
array([2. ,  2.2,  2.4,  2.6,  2.8])
>>> np.linspace(2.0, 3.0, num=5, retstep=True)
(array([2.  ,  2.25,  2.5 ,  2.75,  3.  ]), 0.25)

Graphical illustration:

>>> import matplotlib.pyplot as plt
>>> N = 8
>>> y = np.zeros(N)
>>> x1 = np.linspace(0, 10, N, endpoint=True)
>>> x2 = np.linspace(0, 10, N, endpoint=False)
>>> plt.plot(x1, y, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.plot(x2, y + 0.5, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.ylim([-0.5, 1])
(-0.5, 1)