What is Atmospheric Pressure?
Atmospheric pressure is the force per unit area exerted against a surface by the weight of the air above that surface in Earth's atmosphere. As elevation increases, atmospheric pressure decreases because there is less overlying atmospheric mass.
How to Use This Calculator
This calculator determines atmospheric pressure at a given height using the barometric formula. Enter the base pressure (typically sea level pressure of 101,325 Pa), the temperature in Kelvin, and the height in meters above the base level.
The Barometric Formula
The atmospheric pressure at a given height is calculated using:
$$P = P_0 \cdot e^{\frac{-g \cdot M \cdot H}{R \cdot T}}$$
Where:
- P = Atmospheric pressure at height H (Pa)
- P₀ = Base pressure at reference level (Pa)
- g = Gravitational acceleration (9.8 m/s²)
- M = Molar mass of air (0.028969 kg/mol)
- H = Height above reference level (m)
- R = Universal gas constant (8.3144626 J/(mol·K))
- T = Temperature (K)
Example Calculation
Given:
- Base Pressure (P₀) = 101,325 Pa
- Height (H) = 2,000 m
- Temperature (T) = 288 K
Solution:
$$P = 101325 \cdot e^{\frac{-9.8 \times 0.028969 \times 2000}{8.3144626 \times 288}}$$
$$P = 101325 \cdot e^{\frac{-567.71}{2394.57}}$$
$$P = 101325 \cdot e^{-0.237}$$
$$P = 101325 \times 0.789$$
$$P \approx 79,920 \text{ Pa}$$
Result: At 2,000 meters above sea level with a temperature of 288 K, the atmospheric pressure is approximately 79,920 Pa (or about 79.9 kPa).
Practical Applications
Aviation
Pilots use atmospheric pressure calculations to determine altitude and adjust instruments for accurate readings at different elevations.
Meteorology
Weather forecasters analyze pressure variations to predict weather patterns and storm systems.
Engineering
Engineers account for atmospheric pressure changes when designing pressurized systems, HVAC equipment, and structures at various altitudes.
Mountain Climbing
Mountaineers use pressure calculations to understand oxygen availability and prepare for altitude-related challenges.
Understanding the Variables
Base Pressure (P₀)
Standard atmospheric pressure at sea level is 101,325 Pa (1 atmosphere). This serves as the reference point for calculations.
Temperature (T)
Temperature significantly affects atmospheric pressure. The standard temperature at sea level is 288.15 K (15°C). Temperature decreases with altitude in the troposphere.
Height (H)
The vertical distance above the reference level (typically sea level). Pressure decreases exponentially with increasing height.
Factors Affecting Atmospheric Pressure
Altitude
The primary factor - pressure decreases exponentially as you go higher due to less atmospheric mass above.
Temperature
Warmer air is less dense, resulting in lower pressure. Temperature variations affect the rate of pressure decrease with altitude.
Weather Systems
High and low-pressure systems cause local variations in atmospheric pressure independent of altitude.
Humidity
Water vapor is less dense than dry air, so humid air at the same temperature and pressure is slightly less dense.
Pressure Units Conversion
- 1 atmosphere (atm) = 101,325 Pa
- 1 bar = 100,000 Pa
- 1 millibar (mb) = 100 Pa
- 1 mmHg (torr) = 133.322 Pa
- 1 psi = 6,894.76 Pa
Limitations of the Formula
This barometric formula assumes:
- Constant temperature with altitude (isothermal atmosphere)
- Uniform gravitational field
- Ideal gas behavior
For more accurate results over large altitude ranges, use the International Standard Atmosphere (ISA) model which accounts for temperature variation with altitude.