It’s been a while since I took electrical and magnetic physics, and it never was my strong point, so any help here is much appreciated.

I’m currently working on a project where I have to know the collective flux density of two permanent magnets when they are stuck together. If, for example, I have two 1-T magnets, will I have 2 Tesla after putting them together? Or is there an equation that I need to employ in order to get what I am looking for?

Imagine you are in space somewhere and the only thing around is a candle burning with 1 candlepower of illumination. That is how much total light you have.

Now imagine the light emanating equally in all directions and it strikes a sphere some distance away. If I remember right the area of a sphere is 4 pi R squared. 1 candlepower divided by all that area is the illumination density.
Going the other way, illumination density times total area get you back to the 1 candlepower A big sphere had more area than a little sphere. A big sphere will have less light per area than a little sphere. density times area gets you the total lightpower.

Electrical Fields
ditto as for the simple example above. E fields emanate the same way as described as the light example above. All you need to create an E field is a positively charged region and an negatively charged region. In the spherical example above, you could have bundle of electrons with the field emanating uniformly to an infinite ‘sink’.

Magnetic Fields
its a little messier but the flux times area concept remains. If you take a bar magnet the M field emanates off one end ( and the field strength is a finite number ) and spreads out and loops back into the other end of the magnet. The field has to close to itself, a loop. So if the bar end is 1 square inch with 10 units of field strength ( or 10 per area since the area is 1) , and it emanates out uniformly then at the time it occupies 2 square inches of area the field strength is only 5 units per area.

That is the basic concept without getting into Lorentz transformations and calculus and relativity and such.

So I think what you have here it the principle of superposition.
magnet A has a flux of 1T, that travel in a loop in one pole and out the other.
ditto for magnet B

So lets pretend the 2 magnets are half circles. You could stick them together. Magnet A is pushing 1T of flux around. magnet B is pushing around 1T of flux. So the total flux is 2T.

That is my vote. But it’s been decades since I’ve even thought about it.

You don’t give any specifics about the magnets: material, shape, coated or non-coated (coated = plated), direction of measurement, distance from measuring device, and what the magnetizing parameters are.

In my (short) experience which is measuring, not calculating the theoretical values, the biggest influences on the flux density are the coating (if any), the shape, and the distance from the measuring device.

The coating and the distance from the measuring device go together. Coating magnets (esp. small ones) leave them with rounded edges thereby raising the magnet away from the measuring device. Coating may also leave the magnet at an angle within the coating depending on the method of coating. The thickness of the coating may not be the same from magnet to magnet.

As for the shape, any chips or breaks will affect how the flux density travels around the magnet, thus changing it’s measurement due to what the curves look like that are hitting the measuring device.

When magnets are measured on a point and then rotated,there isn’t much variation within themselves depending on what your application is. When a magnet is moved horizontally across the measuring device and then graphed, the results are a (proper term is escaping me right now) cone with a rounded top. The flatness of the top gets larger the farther away from the measuring device you are.

That may not help a lot, but it’s a little more food for thought.