Permanent Rod Magnet (magnetic field vs dimensions)

How is the strength of magnetic field of a permanent rod magnet related to its dimensions? What would make it stronger: the increase in its length or its diameter?

Strength in which relation? When placed in a suitable magnetic circuit, the volume matters. Application specific magnetic circuits require the magnet shape optimized to it.

I'm interested in the magnetic field strength as a function of the distance to the face of the magnet. The strength of the magnetic field decreases as you move farther from the face of a permanent rod magnet. I'd like to understand how the length and diameter of a magnet affect the strength of that magnetic field. (A formula if there is one) I understand that a bigger magnet will create a stronger magnetic field but my question is what would you rather increase the length or diameter in order to get a stronger magnetic field.

You are talking about magnet field in air?

The far field will depend in a first order on the magnet's volume, as said. It follows a 1/d3 field strength rule.

The permeability of space is not important as long as it stays constant. Let's say you have a permanent rod magnet that is 10mm long and has a diameter of 4mm. You placed an analog hall effect sensor 3mm away from the face of the magnet and you are reading 2V. What would you rather do - make your magnet longer or wider to make the magnetic field stronger 3mm away (have your hall effect sensor give you a higher reading than 2V) Assuming everything else is constant and you are just changing the dimension of your magnet.

Your example isn't far field of course. In this case, the exact magnet shape needs to be considered. I would preferably use a 2.5D or 3D magnetostatic simulator like Quickfield.

I guess however, that a magnet with roughly L = D gives the best results among different types of same volume/mass.

Try out some online calculator, e.g.

http://www.dextermag.com/magnetic-field-calculators

That would answer your question much more quickly than any formula.

Eddy_C thank you for the link. That's exactly what I was looking for. Would you know by any chance what formula they used to do their field calculations.

danst83,
for a rod magnet the magnetic field on the axis,
see for example following link:

http://www.ibsmagnet.com/fluxdensity/index.php

If the magentic field at off-axis location is of interest (and is no longer resticted to on-axis),
then formula are getting very complex (depending also on geometry of the magnet).

In general, one has to attribute for every elementary magnetic dipole
the magnet constists of, that is, one has to integrate over the
total magnetic volume the field contribution each magnetic dipole generates
at the point of interst (e.g. the location of your hall sensor).

That gives then a lot of mathematics - but thanks to
those ready-to-use online calculators, several most common
magnetic configurations can be investigated easily.