Most PC PSUs are rated on their output, so 870 at the wall will probably be around 750-800 on the outputs.
However, it is quite possible to overload one of the outputs while the rest are well within limits and doing this can drag the whole PSU down - take a look at the ratings label and see what the maximum on each line is. Sadly most consumer level PC PSUs don't have very good access to the individual output currents, and it's a grade one PIB to get a decent current clamp on them (I used to have access to a 24-pin connector with a LEM CMD + VMD on every wire, sadly since I don't work in that establishment any more I can't get my hands on it these days) Sometimes one is lucky and cn get a small clamp round a group of wires and see what the current, the most commonly overloaded lines are the 12v ones used for powering off-motherboard hardware (disks, fans, PCIE "lumps" like GPUs).