Well there are tables.

There is also a hydrostatic equation

dp/dz = -dens(g)

dens is average density of air at sea level. (it happens to be about 1.3 kg/m3 at normal temp)

g is gravitational acceleration (9.8 m/sec^2)

The way I see it,

dens can be calculated from n/V = P/RT

where P is about 1 atm at sea level and T = 273K (0 C). (Although temp really isn't on average zero C at the surface, setting it at 0C now makes it unnecessary to readjust P for 0 C at altitude.)

n/V is related to density through a costant (weighted average MW of air).

The equation can be integrated to solve for P at a delta z.

Of course, you have to be careful with the units.