Calculate Relative Humidity

Using Dry and Wet Bulb Temperatures

Relative Humidity Calculator

Enter the Dry Bulb Temperature and Wet Bulb Temperature to calculate the Relative Humidity.

Relative Humidity

— %

Dew Point Temperature: — °C

Saturation Vapor Pressure: — hPa

Actual Vapor Pressure: — hPa

Formula Used: Relative Humidity (RH) is calculated using the ratio of actual vapor pressure to saturation vapor pressure at the dry bulb temperature. The dew point is also derived from the wet bulb depression.

RH (%) = (Actual Vapor Pressure / Saturation Vapor Pressure at Dry Bulb Temp) * 100

Temperature & Humidity Data

Dry Bulb (°C)	Wet Bulb (°C)	Dew Point (°C)	Saturation Vapor Pressure (hPa)	Actual Vapor Pressure (hPa)	Relative Humidity (%)
—	—	—	—	—	—

Table dynamically updates with calculation results.

What is Relative Humidity?

Relative humidity ({primary_keyword}) is a crucial measure of atmospheric moisture. It quantifies the amount of water vapor present in the air compared to the maximum amount the air could hold at a specific temperature. Expressed as a percentage, {primary_keyword} helps us understand how ‘damp’ or ‘dry’ the air feels, directly impacting our comfort levels, health, and various industrial processes. It’s not an absolute measure of water vapor but rather a ratio, meaning its value changes even if the actual amount of water vapor remains constant, solely due to temperature fluctuations.

Who should use it? Understanding {primary_keyword} is vital for meteorologists, HVAC professionals, farmers, warehouse managers, and even homeowners concerned about mold growth or material preservation. It plays a significant role in weather forecasting, energy efficiency of buildings, the storage of sensitive goods, and personal well-being. For anyone working with climate control, agriculture, or material science, accurate {primary_keyword} calculation is indispensable.

Common Misconceptions: A frequent misunderstanding is that relative humidity tells you the total amount of water in the air. It doesn’t. Two different locations could have the same {primary_keyword} percentage but vastly different absolute amounts of moisture if their temperatures differ. Another misconception is that higher temperature always means higher humidity; while absolute humidity might increase with temperature, relative humidity can decrease if the air’s capacity to hold moisture increases more significantly.

Relative Humidity Formula and Mathematical Explanation

Calculating {primary_keyword} involves understanding vapor pressures. The process primarily relies on the dry bulb temperature (ambient air temperature) and the wet bulb temperature (temperature read by a thermometer with its bulb kept moist).

The core formula for Relative Humidity (RH) is:

RH (%) = (Actual Vapor Pressure / Saturation Vapor Pressure at Dry Bulb Temperature) * 100

To implement this, we first need to determine the actual vapor pressure and the saturation vapor pressure. Several psychrometric formulas and approximations exist. A common approach uses the Goff-Gratch equation or simpler empirical approximations for vapor pressure calculations. For practical purposes, and to keep calculations manageable without complex libraries, we can use established approximations. A widely used approximation for saturation vapor pressure (in hPa) at temperature T (in °C) is the August-Roche-Magnus formula or similar:

e_s(T) ≈ 6.1094 * exp((17.625 * T) / (T + 243.04))

Where:

• e_s(T) is the saturation vapor pressure at temperature T in hectopascals (hPa).
• T is the temperature in degrees Celsius (°C).
• exp() is the exponential function (e raised to the power of the argument).

The actual vapor pressure (e_a) can be approximated using the wet bulb temperature and the dry bulb temperature. A common psychrometric formula relates these:

e_a ≈ e_s(T_w) – (P / (L / R_v)) * (T_d – T_w)

Where:

• e_a is the actual vapor pressure.
• e_s(T_w) is the saturation vapor pressure at the wet bulb temperature (T_w).
• P is the atmospheric pressure (assumed standard at sea level, ~1013.25 hPa, though this can be a variable).
• L is the latent heat of vaporization of water (~2501 kJ/kg).
• R_v is the gas constant for water vapor (~461.5 J/(kg·K)).
• T_d is the dry bulb temperature.
• T_w is the wet bulb temperature.

The term (L / R_v) is approximately 5450 K. So, the formula simplifies to:

e_a ≈ e_s(T_w) – (P / 5450) * (T_d – T_w)

For simplicity in this calculator, we will use a more direct approximation often found in meteorological tables or derived from psychrometric charts, which bypasses explicit calculation of atmospheric pressure by implicitly using standard conditions or specific empirical fits. A common approximation for actual vapor pressure derived from wet bulb depression is:

e_a ≈ e_s(T_w) – 0.666 * (T_d – T_w) (This simplification implicitly assumes standard atmospheric pressure and uses an empirical coefficient, though more precise methods exist).

A more widely accepted approximation for actual vapor pressure (e_a) based on dry bulb (T_d) and wet bulb (T_w) temperatures, assuming standard atmospheric pressure (~1013.25 hPa):

e_a = e_s(T_w) – (0.001016 * P) * (T_d – T_w) (where P is in hPa). A common simplification factor is used, which essentially derives from the psychrometric constant. A widely used approximation for the actual vapor pressure `ea` is: `ea = es(Tw) – A * (Td – Tw)`, where `A` is the psychrometric constant, approximately 0.666 hPa/°C for ventilated psychrometers over water.

Let’s use the following robust approximation for the actual vapor pressure `ea` and saturation vapor pressure `es`:

1. Calculate saturation vapor pressure at the wet bulb temperature: e_s(T_w) ≈ 6.1094 * exp((17.625 * T_w) / (T_w + 243.04))

2. Calculate actual vapor pressure: e_a ≈ e_s(T_w) – 0.001016 * (25 + T_w) * (T_d – T_w) — This form is less common and might be specific. A more standard form related to pressure P: e_a = e_s(T_w) – (P/1000) * (0.666 * (T_d – T_w)). For our calculator, we will use a commonly cited formula that approximates the psychrometric constant’s effect:

Simplified Calculation Steps:

a) Calculate saturation vapor pressure at the wet bulb temperature (e_s(T_w)) using the formula above.

b) Calculate the actual vapor pressure (e_a) using the formula: e_a = e_s(T_w) – (0.00066 * (T_d – T_w)). This is a very simplified approximation. A more accurate one commonly used: e_a = e_s(T_w) – 0.001016 * P * (T_d – T_w). Assuming P = 1013.25 hPa, then 0.001016 * P ≈ 1.03.

Let’s refine the actual vapor pressure calculation using a standard approximation:
e_a = e_s(T_w) – (P / R_v * L) * (T_d – T_w)
A common approximation for (P / R_v * L) at standard pressure is ~0.00066 hPa/°C. So, e_a ≈ e_s(T_w) – 0.00066 * (T_d – T_w). (Note: this can vary slightly based on the specific constant used and pressure).
For this calculator, we’ll use a widely accepted approximation:

Actual Vapor Pressure (e_a): e_a = e_s(T_w) – 0.000662 * (T_d – T_w) * (1013.25) / 1000 (this form is often seen but the multiplication by P/1000 is tricky). A cleaner form is often directly derived empirically.

Let’s use the internationally recognized approach based on saturation vapor pressure at wet bulb and the wet bulb depression:

1. Calculate e_s(T_d): Saturation vapor pressure at Dry Bulb Temperature.
2. Calculate e_s(T_w): Saturation vapor pressure at Wet Bulb Temperature.
3. Calculate e_a: Actual vapor pressure. A common empirical formula is: e_a = e_s(T_w) – 0.00066 * P * (T_d – T_w). Assuming P = 1013.25 hPa, this simplifies to e_a = e_s(T_w) – 0.678 * (T_d – T_w). The coefficient 0.678 depends on the psychrometric constant and pressure. A frequently used approximation is indeed around 0.66.

4. Calculate RH: RH = (e_a / e_s(T_d)) * 100.

We will use these formulas within the JavaScript for calculation. The dew point temperature is also calculated based on the actual vapor pressure.

Variable Table:

Variable	Meaning	Unit	Typical Range
Td	Dry Bulb Temperature	°C	-50 to 50
Tw	Wet Bulb Temperature	°C	-50 to 50 (Tw ≤ Td)
RH	Relative Humidity	%	0 to 100
es(T)	Saturation Vapor Pressure	hPa	~0.1 to ~118 (at 50°C)
ea	Actual Vapor Pressure	hPa	0 to ~118 (depends on RH and Td)
Tdp	Dew Point Temperature	°C	-50 to 50 (Tdp ≤ Td)

Practical Examples (Real-World Use Cases)

Understanding how to interpret relative humidity calculations is key. Here are a couple of examples:

Example 1: Comfortable Indoor Environment

Scenario: An office building’s HVAC system maintains an indoor temperature of 24°C (Dry Bulb) and aims for a comfortable humidity level. A sensor reads 19°C (Wet Bulb).

Inputs:

• Dry Bulb Temperature: 24°C
• Wet Bulb Temperature: 19°C

Calculation:

• Saturation Vapor Pressure at 24°C (e_s(24)) ≈ 29.84 hPa
• Saturation Vapor Pressure at 19°C (e_s(19)) ≈ 21.93 hPa
• Actual Vapor Pressure (e_a) ≈ e_s(19) – 0.000662 * (24 – 19) * 1013.25 ≈ 21.93 – 0.000662 * 5 * 1013.25 ≈ 21.93 – 3.35 ≈ 18.58 hPa
• Relative Humidity = (18.58 / 29.84) * 100 ≈ 62.27%
• Dew Point Temperature ≈ 14.8 °C

Interpretation: At 62.27% relative humidity, the air might feel slightly humid but is generally acceptable for many indoor environments. Temperatures around 20-24°C with RH between 40-60% are considered optimal for human comfort and minimizing the risk of mold and dust mites. This result indicates the system is working but perhaps slightly above the ideal upper limit for maximum comfort.

Example 2: Greenhouse Conditions

Scenario: A farmer is monitoring conditions in a greenhouse for sensitive plants. The current temperature is 30°C (Dry Bulb), and the wet bulb thermometer reads 26°C.

Inputs:

• Dry Bulb Temperature: 30°C
• Wet Bulb Temperature: 26°C

Calculation:

• Saturation Vapor Pressure at 30°C (e_s(30)) ≈ 42.45 hPa
• Saturation Vapor Pressure at 26°C (e_s(26)) ≈ 33.71 hPa
• Actual Vapor Pressure (e_a) ≈ e_s(26) – 0.000662 * (30 – 26) * 1013.25 ≈ 33.71 – 0.000662 * 4 * 1013.25 ≈ 33.71 – 2.67 ≈ 31.04 hPa
• Relative Humidity = (31.04 / 42.45) * 100 ≈ 73.12%
• Dew Point Temperature ≈ 23.5 °C

Interpretation: A relative humidity of 73.12% in a greenhouse can be problematic for many plants, increasing the risk of fungal diseases and impacting transpiration rates. The farmer might need to activate ventilation or dehumidification systems to lower the humidity, especially if the target range for the specific crops is lower (e.g., 50-60%).

How to Use This Relative Humidity Calculator

Our calculator is designed for simplicity and accuracy. Follow these steps:

1. Input Dry Bulb Temperature: Enter the current ambient air temperature in degrees Celsius (°C) into the “Dry Bulb Temperature” field.
2. Input Wet Bulb Temperature: Enter the temperature measured by a wet-bulb thermometer (a thermometer covered in wet cloth and exposed to airflow) in degrees Celsius (°C) into the “Wet Bulb Temperature” field. Ensure the wet bulb temperature is less than or equal to the dry bulb temperature.
3. Calculate: Click the “Calculate” button.
4. Read Results: The calculator will display:
   • Relative Humidity (%): The primary result, shown prominently.
   • Dew Point Temperature (°C): The temperature at which air becomes saturated.
   • Saturation Vapor Pressure (hPa): The maximum vapor pressure the air can hold at the dry bulb temperature.
   • Actual Vapor Pressure (hPa): The current amount of water vapor present in the air.
5. Interpret: Use the results to understand the air’s moisture content. For example, high RH may require ventilation, while low RH might necessitate humidification.
6. Reset: Click “Reset” to clear the fields and revert to default values.
7. Copy: Click “Copy Results” to copy all calculated values and key assumptions to your clipboard for use elsewhere.

Decision-Making Guidance: Use these results to adjust environmental controls (like HVAC systems, humidifiers, dehumidifiers, or ventilation) to achieve desired humidity levels for comfort, health, or specific applications like agriculture or storage.

Key Factors That Affect Relative Humidity Results

Several factors influence the measured and calculated {primary_keyword}:

1. Temperature (Dry Bulb): As temperature increases, the air’s capacity to hold moisture increases. If the absolute amount of water vapor stays the same, the {primary_keyword} will decrease. Conversely, a drop in temperature, with constant absolute moisture, leads to higher {primary_keyword}.
2. Temperature (Wet Bulb): The wet bulb temperature is critical for determining actual vapor pressure. Evaporative cooling causes the wet bulb to read lower than the dry bulb. The greater the difference (wet bulb depression), the drier the air and the lower the actual vapor pressure.
3. Atmospheric Pressure: While standard atmospheric pressure (1013.25 hPa) is often assumed, actual pressure variations (e.g., due to altitude or weather systems) can slightly affect the calculated actual vapor pressure and thus the RH. Higher pressure slightly increases saturation vapor pressure.
4. Altitude: Higher altitudes typically have lower atmospheric pressure. This affects the psychrometric constant and the relationship between wet bulb depression and actual vapor pressure. Lower pressure means less water vapor is needed to reach saturation.
5. Air Movement (Ventilation): Adequate airflow around the thermometers is essential for accurate wet bulb readings. Stagnant air can lead to higher wet bulb temperatures than actual conditions warrant, artificially lowering the calculated RH.
6. Water Purity: The accuracy of the wet bulb reading depends on the water used to moisten the cloth. Impurities can affect the evaporation rate and thus the measured temperature.
7. Measurement Accuracy: The precision of the dry bulb and wet bulb thermometers themselves directly impacts the accuracy of the calculated {primary_keyword}.

Frequently Asked Questions (FAQ)

What is the ideal relative humidity?

The ideal range for human comfort and health is generally considered to be between 40% and 60% {primary_keyword}. Below 40%, air can feel dry, leading to dry skin, irritated sinuses, and static electricity. Above 60%, it can promote mold growth, dust mites, and a feeling of clamminess.

Can relative humidity be over 100%?

Technically, no. 100% {primary_keyword} means the air is saturated – it cannot hold any more water vapor at that temperature. When air reaches saturation, water vapor begins to condense into liquid (dew, fog, or clouds). Supersaturation can occur briefly under specific conditions but is generally unstable.

What is the difference between relative humidity and absolute humidity?

Absolute humidity measures the actual mass of water vapor in a given volume of air (e.g., grams per cubic meter). Relative humidity is a percentage, comparing the current absolute humidity to the maximum possible at that temperature. The same absolute humidity can result in different {primary_keyword} levels depending on temperature.

Why is the wet bulb temperature always lower than the dry bulb temperature?

The wet bulb thermometer is cooled by the evaporation of water from its covering. This evaporative cooling effect reduces the temperature reading. The rate of evaporation, and thus the cooling effect, depends on how dry the surrounding air is. Drier air allows for more evaporation and a larger difference between dry and wet bulb temperatures (wet bulb depression).

Does the calculator account for altitude or atmospheric pressure changes?

This calculator primarily uses standard atmospheric pressure (1013.25 hPa) for its calculations. While atmospheric pressure variations exist, this calculator provides a very accurate estimate for most common scenarios. For highly precise scientific or industrial applications at significantly different altitudes, specialized psychrometric calculators that accept barometric pressure as an input might be necessary.

How does temperature affect the wet bulb depression?

The wet bulb depression (the difference between dry bulb and wet bulb temperatures) is a key indicator of air dryness. A small depression means the air is close to saturation (high RH), while a large depression indicates dry air (low RH). Temperature influences the *potential* for evaporation and the saturation vapor pressure, affecting this relationship.

Can this calculator be used for Fahrenheit temperatures?

No, this specific calculator is designed for Celsius (°C) inputs. You would need to convert Fahrenheit temperatures to Celsius before using this tool (Fahrenheit to Celsius: C = (F – 32) * 5/9).

What are the limitations of using dry and wet bulb temperatures?

The accuracy of readings depends heavily on proper psychrometer design and use (adequate ventilation, accurate thermometers, sufficient water). Extreme temperatures or very high humidity can sometimes make accurate wet bulb readings challenging. Moreover, the formulas used are approximations, albeit very good ones for most practical purposes.