BL = 150 ÷ (T ÷ D²)
T = [150 ÷ (BL ÷ D)] x D
T = Rate of Twist BL = Bullet Length D = Diameter (Bullet) in Thousandths
Gyroscopic force from spin tends to keep the bullet pointed in the same direction. Atmospheric resistance produces forces which tend to tip the bullet sideways. As long as the spin produces more stabilizing force than the atmospheric resistance produces upsetting force, the bullet will fly straight, i.e.,stabilize.
For practical purposes, as long as we spin a bullet fast enough to be stable, a little exra spin doesn't seem to hurt. However, if you want the gun to shoot well at long ranges, you don't want the bullet 'over-stabilized' very much. As the trajectory arches over and starts down you want the bullet axis to follow the trajectory line. A bullet that does this is said to 'trail'. If the bullet is spinning too fast, it will continue to keep its spin axis pointed along the bore line and end up flying through the air partly sideways. That's not good.
The Greenhill Formula is an excellent formula and was developed from trial-and-error shooting tests. The factor of 150 in the formula isn't dependant upon bullet shape or specific initial velocity - this was established by experience in the shooting tests.