astropy.stats.circvar(data, axis=None, weights=None)[source]

Computes the circular variance of an array of circular data.

There are some concepts for defining measures of dispersion for circular data. The variance implemented here is based on the definition given by [1], which is also the same used by the R package ‘CircStats’ [2].

datandarray or Quantity

Array of circular (directional) data, which is assumed to be in radians whenever data is numpy.ndarray. Dimensionless, if Quantity.

axisint, optional

Axis along which circular variances are computed. The default is to compute the variance of the flattened array.

weightsnumpy.ndarray, optional

In case of grouped data, the i-th element of weights represents a weighting factor for each group such that sum(weights, axis) equals the number of observations. See [1], remark 1.4, page 22, for detailed explanation.

circvarndarray or Quantity [:ref: ‘dimensionless’]

Circular variance.


The definition used here differs from the one in scipy.stats.circvar. Precisely, Scipy circvar uses an approximation based on the limit of small angles which approaches the linear variance.


[1] (1,2)

S. R. Jammalamadaka, A. SenGupta. “Topics in Circular Statistics”. Series on Multivariate Analysis, Vol. 5, 2001.


C. Agostinelli, U. Lund. “Circular Statistics from ‘Topics in Circular Statistics (2001)’”. 2015. <>


>>> import numpy as np
>>> from astropy.stats import circvar
>>> from astropy import units as u
>>> data = np.array([51, 67, 40, 109, 31, 358])*u.deg
>>> circvar(data) 
<Quantity 0.16356352748437508>