If the splines are the same diametral pitch then the diameter corresponds to number of splines linearly.

If, however, the diametral pitch is changed then you have things like the larger diameter shaft with fewer splines. A prime example of this is on GM and Ford input shafts. A common style is 10 splines. The Ford is 1 1/16" diameter, the GM is 1 1/8", and there are trucks with 10 splines with input shaft 1 3/8". Each example is using a different diametral pitch when they design the splines.

We're luckier when it comes to axles, because MOST of the popular axles use the same diametral pitch. So in general, we know that a 29 spline axle is stronger than a 27 spline and weaker than a 30. This is disregarding the strength of the axle material, of course. However the strength of the axle in torsion increases by the cube of the increase in diameter, so you can see that increasing from a 27 spline to a 31 spline increases strength by 51%.

Had enough?

R.