How to correctly calibrate / adjust "pressure" and "altitude" values

Measured values from climate module are (very) different as values measured by other way.

For example

BC Climate kit:
pressure 968hPa
altitude 382m

Weather station Davis Vanage Vue:
pressure 1 019hPa

altitude (which I know from other devices or fro maps) is 442m

I am looking for some calculation how to get similar pressure as it is shown on weather station using real altitude (which I know). I checked some websites, but I didn’t find anything useful.

Does someone have this calculation?

Public weather stations and meteorology institutions usually don’t show absolute atmospheric pressure but value adjusted to sea level (0 meeters). This is the way how you can compare pressure in different altitudes.
Value from Climate Module is absolute pressure. To compare with public data you need to calculate it to the sea level.
For example your value 968 hPa in 442 m matches to 1018.92 hPa @ 20°C. You can use some online calculator:
Maybe it coud be good point to upgrade BC firmware. Allow specific altitude and calculates correction to sea level value.

Thank you! It helped me. As you mentioned to add this correction - it can be useful, because lot of people is more familiar with pressure in sea level.

Here is formula which I used:

h … altitude (real)
P … absolute pressure (from sensor)
T … temperature

P0 = P*(1−((0,0065h)/(T+0,0065h+273,15)))^−5,257

At this moment I need to postprocess some data to calculate it, because the temperature value is received at different moment as pressure value. I need to store last temperature value and recalculate pressure using this value.