Enter the pressure and the temperature into the Density From Pressure Calculator to estimate the density of dry air using the ideal gas relationship. The calculator will evaluate and display the density.
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Density From Pressure Formula
The following formula is used to calculate the density of dry air from pressure using the ideal gas relationship.
\rho = \frac{p}{R_{\text{specific}}\,T}- Where ρ is the (mass) density of dry air (kg/m^3)
- p is the (absolute) pressure (Pa)
- T is the (absolute) temperature (K)
- Rspecific is the specific gas constant for dry air (≈ 287.05 J/(kg·K))
To calculate density from pressure (for dry air, ideal-gas approximation), divide the pressure by the product of the absolute temperature and the specific gas constant. For other gases, use that gas’s specific gas constant, or use ρ = pM/(RuT) with molar mass M and the universal gas constant Ru.
| Pressure (atm) | Density (kg/m³) |
|---|---|
| 0.25 | 0.296 |
| 0.50 | 0.592 |
| 0.75 | 0.888 |
| 1 | 1.184 |
| 1.25 | 1.480 |
| 1.50 | 1.776 |
| 2 | 2.368 |
| 3 | 3.552 |
| 4 | 4.736 |
| 5 | 5.920 |
| 7.5 | 8.879 |
| 10 | 11.839 |
| 15 | 17.759 |
| 20 | 23.679 |
| 25 | 29.598 |
| 30 | 35.518 |
| 40 | 47.357 |
| 50 | 59.196 |
| 75 | 88.794 |
| 100 | 118.393 |
| *Assumes constant temperature T = 298.15 K (25°C) and ideal-gas dry air with Rspecific = 287.05 J/(kg·K). Calculator formula: ρ (kg/m³) = p (Pa) ÷ (Rspecific × T). Pressure converted with 1 atm = 101325 Pa. | |
How to Calculate Density From Pressure?
The following example problems outline how to calculate density from pressure (dry air, ideal-gas approximation).
Example Problem #1:
- First, determine the pressure (Pa).
- The pressure (Pa) is given as: 600.
- Next, determine the temperature (K).
- The temperature (K) is provided as: 100.
- Finally, calculate the Density From Pressure using the equation above:
ρ = p / (Rspecific*T)
The values given above are inserted into the equation below:
ρ = 600 / (287.05*100) = 0.0209 (kg/m^3)
Example Problem #2:
For this problem, the variables needed are provided below:
pressure (Pa) = 159
temperature (K) = 134
This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer.
ρ = p / (Rspecific*T) = ?
