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.

- Scientific calculator
- Thermometer

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.

#### Things You'll Need

References

- "Physics for Scientists & Engineers with Modern Physics"; Douglas C. Giancoli; 2008
- Texas A&M University: Hypsometric Equation
- University of Maryland, Baltimore County; Chapter 9: Air Pressure and Winds

About the Author

John Woloch writes professionally for various websites. He has published in the Dutch journal "Crux" and writes frequently on oil painting, classical languages and topics involving math and biochemistry. Woloch holds a Master of Arts in English from the University of Chicago, a Master of Arts in classics from Ohio State University and a postbaccalaureate pre-medical degree from Georgetown University.

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