I saw some people with basic equations, but it is more complicated than that. You need to either use actuator disk theory(easy) or blade element theory.
actuator disk theory, is a rough estimate and does not take into account the rotor dik properties, Assumes there is a complete disk with a pressure difference. Based on conservation of energy, mass, and momentum.
Vsubh=sqrt( weight/(rho(air density*disk area)) to get velocity of air to hover.
Power to hover= Weight*V subh
Power to climp(max)/power to hover = (V-climb/V subh)+sqrt(1+(V-climb/V subh)^2)
and solve for V-climb.
Blade element analysis involves the atual rotor design, which I am learning about now. It would give a much better estimate.