How To Calculate Saturation Vapor Pressure From Temperature

Magnus Formula:

\[ e_s = 6.112 \times \exp\left(\frac{17.67 \times T}{T + 243.5}\right) \]

Saturation Vapor Pressure (e_s):

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1. What is the Magnus Formula?

The Magnus formula is an empirical relationship that calculates the saturation vapor pressure of water over liquid water as a function of temperature. It provides an accurate estimation of vapor pressure for meteorological and environmental applications.

2. How Does the Calculator Work?

The calculator uses the Magnus formula:

\[ e_s = 6.112 \times \exp\left(\frac{17.67 \times T}{T + 243.5}\right) \]

Where:

\( e_s \) — Saturation vapor pressure (hPa)
\( T \) — Temperature (°C)
\( \exp \) — Exponential function

Explanation: The formula approximates the relationship between temperature and the maximum amount of water vapor the air can hold before condensation occurs.

3. Importance of Saturation Vapor Pressure Calculation

Details: Accurate vapor pressure calculation is crucial for weather forecasting, humidity measurement, climate studies, and various industrial processes involving air-water vapor mixtures.

4. Using the Calculator

Tips: Enter temperature in degrees Celsius. The calculator will compute the saturation vapor pressure in hectopascals (hPa).

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for the Magnus formula?
A: The formula is valid for temperatures between -45°C to 60°C, which covers most meteorological applications.

Q2: How accurate is the Magnus formula?
A: The Magnus formula provides accuracy within 0.1% to 1% compared to more complex thermodynamic equations for most practical purposes.

Q3: What are typical values of saturation vapor pressure?
A: At 0°C: 6.11 hPa, at 20°C: 23.39 hPa, at 40°C: 73.78 hPa. The value approximately doubles for every 10-11°C temperature increase.

Q4: How does saturation vapor pressure relate to relative humidity?
A: Relative humidity = (actual vapor pressure / saturation vapor pressure) × 100%. It indicates how close the air is to being saturated.

Q5: Are there different versions of the Magnus formula?
A: Yes, there are several slightly different coefficient sets for the Magnus formula, but the version with coefficients 6.112, 17.67, and 243.5 is widely accepted for meteorological use.