C_L_max can also be calculated from power-off stall speed.
Since C_L is defined by L = 0.5 * rho * v^2 * S * C_L, where L = lift, rho = air density, v = airspeed, S = wing area; since L = W at stall; and since C_L = C_L_max at stall,
C_L_max = 2 * W / (rho * v_stall^2 * S)
It's a handy way to calculate C_L_max based on things that are easier to find in literature (stall speed, weight, and wing area).