# compute gyration command

## Syntax

``` LAMMPS
compute ID group-ID gyration
```

-   ID, group-ID are documented in [compute](compute) command
-   gyration = style name of this compute command

## Examples

``` LAMMPS
compute 1 molecule gyration
```

## Description

Define a computation that calculates the radius of gyration $R_g$ of the
group of atoms, including all effects due to atoms passing through
periodic boundaries.

$R_g$ is a measure of the size of the group of atoms, and is computed as
the square root of the $R_g^2$ value in this formula

$$R_g^2 = \frac{1}{M} \sum_i m_i (r_i - r_{\text{cm}})^2$$

where $M$ is the total mass of the group, $r_{\text{cm}}$ is the
center-of-mass position of the group, and the sum is over all atoms in
the group.

A $R_g^2$ tensor, stored as a 6-element vector, is also calculated by
this compute. The formula for the components of the tensor is the same
as the above formula, except that $(r_i - r_{\text{cm}})^2$ is replaced
by $(r_{i,x} - r_{\text{cm},x}) \cdot (r_{i,y} - r_{\text{cm},y})$ for
the $xy$ component, and so on. The six components of the vector are
ordered $xx$, $yy$, $zz$, $xy$, $xz$, $yz$. Note that unlike the scalar
$R_g$, each of the six values of the tensor is effectively a \"squared\"
value, since the cross-terms may be negative and taking a square root
would be invalid.

:::: note
::: title
Note
:::

The coordinates of an atom contribute to $R_g$ in \"unwrapped\" form, by
using the image flags associated with each atom. See the [dump
custom](dump) command for a discussion of \"unwrapped\" coordinates. See
the Atoms section of the [read_data](read_data) command for a discussion
of image flags and how they are set for each atom. You can reset the
image flags (e.g., to 0) before invoking this compute by using the [set
image](set) command.
::::

## Output info

This compute calculates a global scalar ($R_g$) and a global vector of
length 6 ($R_g^2$ tensor), which can be accessed by indices 1\--6. These
values can be used by any command that uses a global scalar value or
vector values from a compute as input. See the [Howto
output](Howto_output) page for an overview of LAMMPS output options.

The scalar and vector values calculated by this compute are
\"intensive\". The scalar and vector values will be in distance and
distance$^2$ [units](units), respectively.

## Restrictions

> none

## Related commands

[compute gyration/chunk](compute_gyration_chunk), [compute
gyration/shape](compute_gyration_shape)

## Default

none