And now, for a different perspective ....
I think we are setting ourselves up for confusion when we focus on extraneous things like the "percentage" of voltage drop, or the running amps of the appliance.
Instead ... what's your EXACT voltage at the end of the line, when the circuit is under load? I'm looking at one air conditioner right now, whose nameplate is marked "115." There's my target; I need to deliver 115 volts to the air conditioner while it is running.
If your voltage at the house is, for example, 118.2 volts, you can afford to lose about three amps.; yet, there's a joker in the deck.
The 'joker' helps you, in that the manufacturer has designed the air conditioner to tolerate slightly lower voltages; you have a 10% margin from the nameplate marking. That is, you "can" use a supply voltage as low as 106 volts.
It's best not to use this "extra" margin, as you have to allow for drops in what the power company supplies you. That will depend partly on how many of your neighbors are running their air conditioners at the time.
Now, let's look at the issue of amperage. The same unit I looked at before says it needs a 15 amp circuit and draws 4.9 amps.
Why the difference? Because the motor needs more than 4.9 amps to start up; the '4.9' figure is just to keep it running. I need my wires to be big enough to deliver 15 amps, or the air conditioner won't start.
OK, so you have a 60-amp breaker feeding the smallest possible wires to the shed. That means there's no way you can supply the shed with 60 amps of power. Your panel should have a smaller 'main' breaker, perhaps a 40-amp, or you'll be setting yourself up for lower voltages when the panel is fully loaded. Lower voltages burn out motors and give electronics nervous breakdowns.
With the panel IN the shed, you can power the air conditioner in my example with an ordinary 15-amp circuit.
You're not really allowed to simply run a 15-amp circuit from the house, for the air conditioner in my example. Since there WILL be voltage drop, especially at start-up, you'll need at least a 20-amp circuit .... and you really ought to have that on a 15-amp breaker at the shed.
Bigger wire means less voltage drop. Higher supply voltages allow for a greater drop.
Your wire is plenty large enough, for even a 30-amp panel at the shed. This would allow you to power the air conditioner, and have a lighting circuit as well as two receptacle circuits.
