I don't think there are any simple equations to turn hp or torque into acceleration. We know that distance=initial velocity times time plus one half times the acceleration times the time squared. We also know that force equals mass times acceleration. The problem is with the force part of the f=ma equation. We can rearrange it to a=f/m but where do we get force? At any instant, I think it is the torque of the motor times the gearing minus any losses. But it constantly changes as the rpm changes and the gears change. So you'd have to do a lot of work to try and calculate this.
Maybe that difficulty is why the on-line calculators are empherical. They use published (or test) information to develop a relationship.