At standard temperature and pressure, air weighs approximately 1.229 kilograms per cubic meter. Now imagine a column of air extending 20 miles straight up from the surface of the earth. The weight of the air in this column creates atmospheric pressure. That is why atmospheric pressure decreases as you climb a mountain: the higher you go, the less air you have above you. The hypsometric equation expresses this relationship between air pressure and altitude. Use hectopascals (hPa) in the equation.

Read the temperature in Fahrenheit degrees on your thermometer. For example, the temperature is 37 F.

Multiply the atmospheric pressure in hectopascals times 100 using a scientific calculator. For example, the pressure is 1037 hPa: 1037 x 100 = 103700.

Divide your answer by 101325 using a scientific calculator. For example, 103700/101325 = 1.2034.

Take the natural log of your answer using a scientific calculator. For example, ln (1.2034) = 0.02316.

Multiply your answer times 287.053 using a scientific calculator. For example, 0.02316 x 287.053 = 6.6507.

Multiply your answer times the product of the temperature plus 459.67 and 5/9 using a scientific calculator. For example, 6.6507 x [(37 + 459.67) x 5/9] = 1835.116.

Divide your answer by -9.8 using a scientific calculator. For example, 1835.116/-9.8 = -187.25. Your altitude is -187.25 meters, or 187.25 meters below sea level.

#### References

- Portland State Aerospace Society: A Quick Derivation Relating Altitude to Air Pressure
- "Physics for Scientists & Engineers with Modern Physics"; Douglas C. Giancoli; 2008
- Texas A&M University: Hypsometric Equation
- Metropolitan State College of Denver: Thermodynamic Equation of State
- University of Maryland, Baltimore County; Chapter 9: Air Pressure and Winds

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