Free · Physics models
Isothermal Pressure with Height
Estimate pressure above a reference level in an isothermal ideal-air column.
- Formula & worked example
- Private in your browser
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
pressure = 89996.674 Pascal.
p = p₀ exp(kh/T), with the fixed captured k near −0.03416 K/m.
Worked example
Enter these known values and leave the other values blank.
- Pressure at sea level (P==0==)
- 101325 Pa
- Altitude (h)
- 1000 m
- Temperature (T)
- 15 °C
- Pressure (P)
- 89996.7 Pa
Assumptions and limitations
- Estimate pressure above a reference level in an isothermal ideal-air column.
- Temperature is constant with height. The model does not use the tropospheric temperature lapse rate and is not the full standard atmosphere.
- Positive absolute pressure and temperature above absolute zero are required for physical use. Height is measured from the level assigned p₀.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
Common questions
Is this the standard atmosphere?
It assumes constant temperature, so it differs from the usual atmosphere with a temperature lapse rate.
Can the reference be above sea level?
Yes. Set the reference pressure and measure height relative to that level.
References
Enforce the explicitly stated physical domain: Absolute temperature must be positive. Absolute pressure must be positive. Reference absolute pressure must be positive.