Calculator Inputs
Use atmospheric, planetary, or gas data. Choose molar or molecular mass input mode for more flexible physical analysis.
Formula Used
The isothermal scale height formula is:
H = RT / (Mg)
Where H is scale height, R is the universal gas constant, T is absolute temperature in kelvin, M is molar mass, and g is gravitational acceleration.
If particle mass is used, the equivalent relation becomes:
H = kT / (mg)
Pressure and density decay with altitude in an isothermal atmosphere as:
P(z) = P₀e-z/H and ρ(z) = ρ₀e-z/H
These formulas assume constant temperature and nearly constant gravity over the chosen altitude range. They work well for quick comparisons and educational estimates.
How to Use This Calculator
- Choose a preset atmosphere or keep the form custom.
- Enter temperature and gravity in your preferred units.
- Select molar mass mode or molecular mass mode.
- Provide the altitude where pressure and density should be evaluated.
- Enter a reference pressure and reference density.
- Set a target remaining ratio to find the matching altitude.
- Adjust graph range and sample points for smoother plots.
- Press the calculate button to view results, graph, and export options.
Example Data Table
Sample scale heights for several planetary or atmospheric cases.
| Case | Temperature (K) | Gravity (m/s²) | Molar Mass (g/mol) | Scale Height (m) | Scale Height (km) |
|---|---|---|---|---|---|
| Earth Standard Air | 288.15 | 9.80665 | 28.9644 | 8,434.66 | 8.4347 |
| Mars Carbon Dioxide | 210.00 | 3.72000 | 44.0100 | 10,664.96 | 10.6650 |
| Venus Carbon Dioxide | 737.00 | 8.87000 | 44.0100 | 15,697.36 | 15.6974 |
| Titan Nitrogen Rich Air | 94.00 | 1.35200 | 28.0000 | 20,645.59 | 20.6456 |
Frequently Asked Questions
1. What is scale height in physics?
Scale height is the vertical distance over which pressure or density falls by a factor of e in an isothermal atmosphere.
2. Why does higher temperature increase scale height?
Warmer gases have greater average molecular energy, so the atmosphere spreads upward more easily against gravity, producing a larger scale height.
3. Why does stronger gravity reduce scale height?
Greater gravity pulls particles downward more strongly, so pressure and density decrease faster with altitude. That makes the scale height smaller.
4. What happens when molar mass increases?
Heavier gases have smaller scale heights because more mass must be supported against the same gravitational field at the same temperature.
5. Is this calculator valid for real atmospheres?
It is best for isothermal estimates and teaching. Real atmospheres have temperature gradients, changing composition, and sometimes changing gravity with altitude.
6. Why are pressure ratio and density ratio equal here?
Under the isothermal ideal-gas model, both pressure and density follow the same exponential decay law with altitude, so their ratios match.
7. Should I use molar mass or molecular mass mode?
Use molar mass when your data is in g/mol or kg/mol. Use molecular mass when you know particle mass or atomic mass units.
8. What is the altitude for half pressure?
Half-pressure altitude is the height where pressure becomes 50 percent of the reference value. In this model, it equals H × ln(2).