We nominally use a simpler SPICE model for hand calculations to get a first cut draft. These values get us in the ball park and then we fine tune the design In a simulator. SPICE models (higher level) have a lot of parameters which are taken into account by the simulators for calculation and that can be the reason for not getting the same exact values as hand calculations.
Its is way too off ( numbers/off by orders) then you should check the biasing conditions, sizing, values used for hand calculation and sims.
This is non-physical formula which is far away from transistor behavior (it uses non-physical parameters, too - like infamous threshold voltage). So, you can't expect accurate value calculated by this.
If you want an accurate estimation of mosfet parameters, look for any charge compact model (like EKV or ACM) and apply their formulas.