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. 

= (p) / (Rโ‚specific) 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) = ?