How do you calculate how much an arm with gears can lift

There’s more to it than just how much torque can lift. The force is exerted over a distance, and how much that distance varies depends on the specific build.

Think of it like an arm. If your arm is shorter, it can lift more weight more easily than if it was a lot longer.

If this is referring to finding the correct gear ratio for your application, we can guess, but trial and error is the best method.

you need to know the stall torque of your motors, the gear ratio, the length of your arm, and how much load is on the end.

We were just doing this in POE for bridges and trusses I can’t imagine how hard it could be for an arm as well as it probably will be statically indeterminate.

While VEX parts do make rapid prototyping easy, I would highly encourage doing some math before utilizing trial and error.

Do the math, see approximately what kind of loads you are working with, build a prototype based on the math, and tune it from there. One resource the OP can utilize is the VEX EDR Curriculum. The following pages can get them started:

https://curriculum.vexrobotics.com/curriculum/mechanical-power-transmission/gear-ratios.html

https://curriculum.vexrobotics.com/curriculum/lifting-mechanisms/rotating-joints.html