SME
Meteorology · Problem type
Pressure at an altitude
Use this for “Sea-level pressure is 1,013.25 hPa and the scale height is 8 km. What is the pressure 1.6 km up?”
Diagram
p
=
p₀
e
−z ÷ H
=
1,013.25
×
e
−1.6 ÷ 8
p = 829.6 hPa
Each
H
up,
the
pressure
falls
to
1
e
of
what
it
was.
This is an example. Type your own values to start a new problem.
p₀
Sea-level pressure
example · hPa
z
Altitude
example
H
Scale height
example · km
p
Pressure
calculated · hPa
Formulas
p
=
p₀
×
e
−
z
÷
H
829.5789
=
1,013.25
×
e
−1.6 ÷ 8
Assumptions
•
The column is at one temperature, so its scale height H stays the same all the way up.
•
H = Rd T ÷ g, with Rd = 287 J/(kg·K) and g = 9.81 m/s², is 8 km for air near 273 K.
•
Real air cools with height, so the answer drifts from a measured one high up.
Step-by-step
WE KNOW
p₀ = 1,013.25 hPa, z = 1.6 km, H = 8 km
FIND
pressure (p)
Step 1 · Find pressure (p)
Use p = p₀ × e−z ÷ H
Each scale height climbed divides the pressure by e.
p
=
1,013.25
×
e
−1.6 ÷ 8
p
=
1,013.25
×
e
−0.2
p
=
1,013.25
×
0.8187
p
=
829.5789
hPa
Check
Put the numbers back in. Both sides should match.
829.5789
=
1,013.25
×
e
−1.6 ÷ 8
✓
Topic check
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