# Air Density Calculator

*“Modelling of the Variation of Air Density with Altitude through Pressure, Humidity and Temperature“*EMD International A/S (2005)

Welcome to our online **air density calculator**, a tool that will help you calculate the density of air in kg/m^{3} and many other units.

The air density at sea level and zero humidity is 1.225 kg/m³, but depending on altitude, it could go even down to 0.122 kg/m³. Therefore, it's important to **consider atmospheric conditions when calculating air density**. For that reason, we created this online air density calculator.

Other tools can be helpful in conjunction with this calculator:

- Air pressure at altitude calculator: To calculate the barometric pressure (air pressure) depending on the location altitude.
- Dew point calculator: To calculate the dew point and learn more about it.
- Relative humidity calculator: We can use the relative humidity instead of the dew point to calculate the moist air density. Use this tool to calculate it and learn more about it.

## The air density calculator - Dry air density formula

At zero humidity, we can use the widely known ideal gas law to know what is the density of air formula:

**ρ _{air} = P/(R_{air}T)**

where:

— density of air, in**ρ**_{air}**kg/m**;^{3}— Air pressure, in**P****Pa**;— Specific gas constant of dry air (**R**_{air}**287.05 J/(kg K)**); and— Air temperature, in**T****K**.

## What is the density of air considering humidity?

To calculate the density of moist air, this calculator uses a model based on **Dalton's law for partial pressures**, which says:

*"The pressure of a gas mixture is equal to the sum of the partial pressures of each gas."*

With partial pressures, we refer to the pressures each gas would exert if it existed alone at the mixture temperature and volume.

We can extend Dalton's law to the density of gas mixtures, such as the mixture of air and vapor (moist air):

**ρ _{air} = P_{d}/(R_{d}T) + P_{v}/(R_{v}T)**

where:

— Air density, in**ρ**_{air}**kg/m**;^{3}— Partial pressure of dry air, in**P**_{d}**Pa**;— Partial water vapor pressure, in**P**_{v}**Pa**;— Specific gas constant of dry air (**R**_{d}**287.05 J/(kg K)**); and— Specific gas constant of water vapor (**R**_{v}**461.495 J/(kg K)**);

This calculator uses the previous equation to calculate the density of moist air.

### Calculating water vapor partial pressure

There are two ways of calculating * P_{v}*, depending on whether we know the dew point (

*) or the relative humidity (*

**T**_{dew}*):*

**RH****P**_{v}= E_{s}(T_{dew})**P**_{v}= RH × E_{s}(T)

In either case, we use the following polynomial (suggested by * E_{s}*:

**E _{s}(T) = 6.1078/[p(T)]^{8}**

**p(T) = c**_{0}+ T(c_{1}+ T(c_{2}+ T(c_{3}+ T(c_{4}+ T(c_{5}+ T(c_{6}+ T(c_{7}+ T(c_{8}+ Tc_{9}))))))))where:

**c**_{0}**= 0.99999683****c**_{1}**= -0.90826951 × 10**^{-2}**c**_{2}**= 0.78736169 × 10**^{-4}**c**_{3}**= -0.61117958 × 10**^{-6}**c**_{4}**= 0.43884187E-8 × 10**^{-8}**c**_{5}**= -0.29883885 × 10**^{-10}**c**_{6}**= 0.21874425 × 10**^{-12}**c**_{7}**= -0.17892321 × 10**^{-14}**c**_{8}**= 0.11112018 × 10**^{-16}**c**_{9}**= -0.30994571 × 10**^{-19}

If we know the dew point, we use the * P_{v} = E_{s}(T_{dew})* equation, evaluating

*at the dew point*

**E**_{s}*. If we know the relative humidity instead of*

**(T**_{dew})*, we use*

**T**_{dew}*, evaluating*

**P**_{v}= RH × E_{s}(T)*at the air temperature (*

**E**_{s}*).*

**T**### Calculating partial pressure of dry air

According to Dalton's law, the **partial pressure** of dry air is simply the total pressure minus the partial water vapor pressure:

**P _{d} = P - P_{v}**

### What is the dew point?

The **dew point** is the temperature at which the water vapor contained in the air reaches its saturation state. The water vapor will condense and form liquid water — dew — when we cool the air down to the dew point.

There are several ways to approximate the dew point. Our online air density calculator uses the following formula:

**DP = 243.12α/(17.62 - α)****α = ln(RH/100) + 17.62T/(243.12 + T)**

And that's it! Hopefully, now you're able to know what is the density of air at sea level or any other altitude.