Focal length for a fisheye is defined the same basic way as for other lenses: it is the distance from the lens’s rear nodal/principal point to the image plane when focused at infinity. In other words, rays from a single point at infinity are brought to focus at the focal plane a focal-length distance behind the lens.

What changes with a fisheye is not the definition of focal length, but the projection used to map scene angle onto the sensor. Unlike a rectilinear lens, fisheyes may be equidistant or use other mappings, so two fisheyes with the same focal length can render angle and distortion differently.

For example, an equidistant fisheye uses:

R = f × θ

where θ is the angle from the optical axis (in radians) and R is the image height. For a 180° field of view, θ runs to ±90° = ±π/2, so an 8mm equidistant fisheye gives:

R = 8 × π/2 ≈ 12.6mm

That produces about a 25mm image circle. So focal length still has its normal optical meaning; field of view and image coverage then depend on the fisheye’s projection design and sensor size.