Is there an algorithm for solar eclipse duration?

[StephenG1CMZ]

On this website https://hemel.waarnemen.com/Computing/eclipse.html (using different symbols than Meeus*) I see:
"The magnitude of a partial eclipse is equal to the fraction of the solar diameter that is covered by the Moon and given by:

mag = (rs + rm - Δ) / (2 rs)

For an annular eclipse (and I suppose this could also apply to a total solar eclipse), the magnitude is simply:

mag = rm / rs"
implying that an annular eclipse is not categorised as a partial eclipse, and has a different equation.

(*Update: Actually, a different formula)