The length of the line connecting the points , , and :

The length of a circle with radius :

Circumference of a parameterized unit circle:

Length of one revolution of the helix , , expressed in cylindrical coordinates:

The length of a function curve :

Equivalently:

Compute the length of a knot:

Compute the length of Jupiter's orbit in meters:

The length can be computed using the polar representation of an ellipse:

Alternatively, use elliptic coordinates with half focal distance and constant :

Extract lines from a graphic and compute their coordinate length:

Color a Lissajous curve by distance traversed:

Color Viviani's curve on the sphere by the fraction of distance traversed:

Find mean linear charge density along a circular wire:

Compute the perimeter length of a Polygon:

ArcLength is a non-negative quantity:

ArcLength[r] is the same as RegionMeasure[r] for any one-dimensional region:

ArcLength for a parametric form is defined as an integral:

ArcLength[x,t,c] is equivalent to RegionMeasure[x,{t},c]:

For a 1D region, ArcLength is defined as the integral of 1 over that region:

The circumference of a 2D region is the ArcLength of its RegionBoundary:

The parametric form or ArcLength computes the length of possibly multiple coverings:

The region version computes the length of the image:

The length of a region of dimension other than one is Undefined: