One way to theoretically derive the capillary length, is to imagine a liquid droplet at the point where surface tension balances gravity.
Let there be a spherical droplet with radius ,
The characteristic Laplace pressure , due to surface tension, is equal to
where  is the surface tension. The pressure due to gravity (hydrostatic pressure)  of a column of liquid is given by
where  is the droplet density,  the gravitational acceleration, and  is the height of the droplet.
At the point where the Laplace pressure balances out the pressure due to gravity ,