Calculate ideal-gas density from absolute pressure, temperature, and gas type, or reverse-solve pressure or temperature with unit conversions and volume checks.

Choose a solve target, then complete the visible required fields marked with *.

Density From Pressure Formula

The following formula is used to calculate the density of dry air from pressure using the ideal gas relationship. 

ฯ = (p) / (Rspecific T)
  • Where ฯ 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 (โ‰ˆ 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 gasโ€™s specific gas constant, or use ฯ = pM/(RuT) with molar mass M and the universal gas constant Ru.

Atmospheres (atm) to Dry-Air Density (kg/mยณ) Conversion Table (T = 298.15 K, Rspecific = 287.05)
Pressure (atm) Density (kg/mยณ)
0.250.296
0.500.592
0.750.888
11.184
1.251.480
1.501.776
22.368
33.552
44.736
55.920
7.58.879
1011.839
1517.759
2023.679
2529.598
3035.518
4047.357
5059.196
7588.794
100118.393
*Assumes constant temperature T = 298.15 K (25ยฐC) and ideal-gas dry air with Rspecific = 287.05 J/(kgยทK). 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:

  1. First, determine the pressure (Pa).
    1. The pressure (Pa) is given as 600.
  2. Next, determine the temperature (K).
    1. The temperature (K) is provided as 100.
  3. 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/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. 

ฯ = p / (Rspecific*T) = ?