Relative Humidity Calculator

An essential tool to calculate relative humidity from wet and dry bulb temperature readings.

What is Relative Humidity?

Relative Humidity (RH) is a crucial meteorological and HVAC parameter that measures the amount of water vapor present in the air, expressed as a percentage of the maximum amount the air could hold at that specific temperature. It’s a ratio, not an absolute measurement. For instance, an RH of 50% means the air currently holds half the water vapor it is capable of holding at its temperature. Understanding how to calculate relative humidity using dry and wet bulb temperatures is fundamental for professionals in meteorology, agriculture, and air conditioning design.

This measurement is distinct from absolute humidity, which gives the actual mass of water vapor in a unit volume of air. Relative humidity is what we “feel” – high RH on a hot day makes it feel more oppressive because sweat evaporates less effectively. This calculator is specifically designed for anyone needing to determine RH from psychrometric readings (dry and wet bulb temperatures).

The Formula to Calculate Relative Humidity

The calculation is based on the psychrometric principle, which relates the temperatures from a dry thermometer and a wetted-bulb thermometer to the air’s moisture content. The process involves several steps, primarily using approximations like the Magnus-Tetens formula to find vapor pressures.

1. Calculate Saturation Vapor Pressure (SVP): First, we determine the saturation vapor pressure at the dry bulb temperature (T) and the wet bulb temperature (Tw). This is the pressure at which water vapor is in equilibrium with its liquid state. A common formula is:
   SVP(T) = 6.112 * exp((17.67 * T) / (T + 243.5))
2. Calculate Actual Vapor Pressure (AVP): The actual vapor pressure (E) is then estimated using the wet bulb temperature and the Sprung/Psychrometric formula, which accounts for the cooling effect of evaporation:
   AVP = SVP(Tw) – P_atm * A * (T – Tw)
3. Calculate Relative Humidity: Finally, the relative humidity is the ratio of the actual vapor pressure to the saturation vapor pressure at the dry bulb temperature, multiplied by 100.
   RH (%) = (AVP / SVP(T)) * 100

For more about related calculations, you might be interested in a Dew Point Calculator.

Key Variables in the Calculation

Variable	Meaning	Unit (Auto-Inferred)	Typical Range
T	Dry Bulb Temperature (ambient air temperature)	°C or °F	-20 to 50 °C
Tw	Wet Bulb Temperature (evaporative cooling temperature)	°C or °F	-20 to 50 °C (must be ≤ T)
P_atm	Atmospheric Pressure (assumed standard 1013.25)	hPa (or mbar)	~980 to 1050 hPa
AVP / E	Actual Vapor Pressure	hPa	0 to 120 hPa
SVP	Saturation Vapor Pressure	hPa	0 to 125 hPa
RH	Relative Humidity	%	0 to 100%

Practical Examples

Example 1: A Warm, Moderately Humid Day

• Inputs:
  • Dry Bulb Temperature: 25 °C
  • Wet Bulb Temperature: 20 °C
  • Units: Celsius
• Results:
  • Relative Humidity: ~60%
  • This indicates a comfortable but noticeably humid condition.

Example 2: A Hot, Dry Day

• Inputs:
  • Dry Bulb Temperature: 95 °F (35 °C)
  • Wet Bulb Temperature: 77 °F (25 °C)
  • Units: Fahrenheit
• Results:
  • Relative Humidity: ~40%
  • Despite the high temperature, the large difference between wet and dry bulb readings reveals the air is relatively dry, allowing for effective evaporative cooling. A better understanding of this can be found with an Enthalpy Calculator.

How to Use This Relative Humidity Calculator

1. Select Your Units: Begin by choosing between Celsius (°C) and Fahrenheit (°F) from the dropdown menu. The calculator will adapt all calculations accordingly.
2. Enter Dry Bulb Temperature: Input the ambient air temperature measured by a standard thermometer into the “Dry Bulb Temperature” field.
3. Enter Wet Bulb Temperature: Input the temperature measured by a psychrometer’s wet bulb thermometer into the “Wet Bulb Temperature” field. Note that this value must be less than or equal to the dry bulb temperature.
4. Read the Results: The calculator instantly updates to show the primary result (Relative Humidity in %) and key intermediate values like Actual Vapor Pressure, Saturation Vapor Pressure, and the calculated Dew Point. The accompanying chart also updates visually.

Interpreting the results is key. A small difference between the wet and dry bulb temperatures signifies high relative humidity, while a large difference indicates dry air. Check out our Air Density Calculator for related atmospheric metrics.

Key Factors That Affect Relative Humidity

• Air Temperature: This is the most significant factor. As air temperature increases, its capacity to hold water vapor increases. Therefore, if the absolute amount of moisture stays the same, RH will decrease as the air warms up.
• Water Vapor Content: The actual amount of moisture in the air. Adding water vapor (e.g., from evaporation) at a constant temperature will increase relative humidity.
• Atmospheric Pressure: While this calculator uses a standard pressure for simplicity, changes in atmospheric pressure (like those from altitude changes) do affect humidity calculations slightly. Higher altitude (lower pressure) can influence evaporation rates.
• Proximity to Water Bodies: Areas near oceans, lakes, and rivers naturally have more moisture available for evaporation, leading to higher average relative humidity.
• Wind and Air Movement: Wind can transport moist or dry air from one region to another, rapidly changing local humidity.
• Vegetation: Plants release water vapor through a process called transpiration, which can significantly increase local humidity, especially in densely forested areas.

Frequently Asked Questions (FAQ)

1. Why can’t the wet bulb temperature be higher than the dry bulb temperature?

The wet bulb temperature is cooled by evaporation. This process can only cool the thermometer to, at most, the current air (dry bulb) temperature. If they are equal, it means no evaporation is occurring, which signifies 100% relative humidity.

2. What does 100% relative humidity mean?

It means the air is fully saturated with water vapor and cannot hold any more at its current temperature. At this point, water will condense into liquid, forming dew, fog, or clouds.

3. How accurate is this calculator?

This calculator uses well-established and widely accepted formulas for psychrometric calculations. It assumes standard atmospheric pressure (1013.25 hPa). For most practical purposes, it is highly accurate. For scientific applications requiring extreme precision, pressure adjustments may be needed. You can find more specific engineering tools like a Pipe Flow Calculator for different needs.

4. Does this calculation work below freezing?

The formulas change slightly for temperatures below freezing (0 °C or 32 °F) as the water on the wet bulb becomes ice (a “frost bulb”). This calculator is optimized for temperatures above freezing.

5. What is a “psychrometer”?

A psychrometer (or hygrometer) is the instrument used to measure wet and dry bulb temperatures. A sling psychrometer is a common type, which is spun in the air to ensure adequate airflow over the wet bulb for accurate readings.

6. How does changing from Celsius to Fahrenheit affect the result?

It doesn’t. The calculator converts all inputs to a standard internal unit (Celsius) before performing calculations, so the final relative humidity percentage is correct regardless of your chosen input unit.

7. What is Dew Point?

The dew point is the temperature to which air must be cooled to become saturated with water vapor (i.e., reach 100% RH). Our calculator provides this as an intermediate value, as it is a direct result of the psychrometric calculation.

8. Can I use this for HVAC design?

Yes, this is a fundamental calculation in HVAC for determining the moisture content of air to design heating, cooling, and dehumidification systems. For advanced work, professionals often use a full Psychrometric Chart.

Related Tools and Internal Resources

Explore other calculators that delve into the properties of air, energy, and thermodynamics:

• Dew Point Calculator: Find the temperature at which condensation begins.
• Air Density Calculator: Calculate the density of air based on temperature, pressure, and humidity.
• Online Psychrometric Chart: An interactive chart for advanced HVAC and engineering analysis.
• Enthalpy Calculator: Understand the total heat content of the air.