Convert pressure to density for air or another ideal gas from absolute pressure and temperature, or solve density to pressure; common gas presets included.
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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.
- Where ฯ is the (mass) density of dry air (kg/m3)
- p is the (absolute) pressure (Pa)
- T is the (absolute) temperature (K)
- Rspecific is the specific gas constant for dry air (โ 287.05 J/(kgยทK))
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 gasโs specific gas constant, or use ฯ = pM/(RuT) with molar mass M and the universal gas constant Ru.
| Absolute pressure (atm) | Density (kg/mยณ) |
|---|---|
| 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 |
| *Theoretical ideal-gas values at T = 298.15 K (25ยฐC), using absolute pressure and the rounded dry-air Rspecific = 287.05 J/(kgยทK). High-pressure rows are not validated real-air densities; use a suitable equation of state or compressibility factor Z for real gas: ฯ = pM/(ZRT). Calculator formula: ฯ (kg/mยณ) = p (Pa) รท (Rspecific ร 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:
ฯ = p / (Rspecific*T)
The values given above are inserted into the equation below:
ฯ = 600 / (287.05*100) = 0.0209 (kg/m3)
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.
ฯ = p / (Rspecific*T) = ?
