My house has 200 amp service. I am running power to my new shed 250 feet from the house and need no more than 60 amps. What size wire (direct bury) do I need and should I be looking at copper or aluminum?

Also, is there a formula to calculate the wire size based on amps, distance, voltage drop, etc. that a layman can use? Thanks.

No calculations are necessary. The cable sizes are specified by the NEC Code.

I've read that #6 is rated at 55 to 60 Amps (copper). I suspect that you would need to go to #4 for alum. However, I am not an expert on code and I am not a professional electrician.

If it were me doing the work and cost was not an object I would opt to use the #6 UDS cable. UDS (Underground Distribution System) cable is direct bury. I'm not sure that UF (Underground Feeder) cable is direct bury,

One more word of caution, if you go with direct bury cable, plan on trenching 26 inches deep and adding 2" of sand, then the cable, then the back-fill.

In fact for longer lengths you do need to do voltage drop calculations and perhaps use heavier wire. I try to leave questions like this to tkrussell and feel you can trust his answers.

You will need to use #4/0 aluminum to keep the max recommended voltage drop at or below 2%.

The cable charts in the NEC do not take long runs into consideration. Any over 100 foot and/or loaded 100% require voltage drop calcs be done.

I use:

2 x length of circuit x max amps x ohms per 1000 ft of chosen wire, see tables in NEC for resistance of various wires and power sources.

Divide result by 1000 will arrive at the actual volts dropped.

2 x 250 x 48 (80% of 60) x .33 Ohms for #4/0 Al,PVC conduit,AC / 1000= 7.9

2% of 240 is 7.2.

This is a excessive length for 120/240 volts.

Copper would be excessive cost.

You may want to consider using step up and down transformers to run at a higher voltage but allow for smaller wire.

Transformers are costly also, close to $1000.00 for the two you need.