The Wet Bulb Temperature (WBT) is a critical meteorological and engineering parameter that represents the lowest temperature to which air can be cooled by the evaporation of water into the air at a constant pressure. It is a measure of the combined effect of temperature and humidity on the cooling potential of evaporation.
Unlike the Dry Bulb Temperature (DBT), which is simply the ambient air temperature measured by a thermometer shielded from moisture and radiation, the WBT takes into account the cooling effect of evaporation. This is achieved by wrapping a wet cloth around the bulb of a thermometer and exposing it to airflow. As water evaporates from the cloth, it absorbs heat from the thermometer bulb, causing its temperature to drop. The WBT is the temperature read when this cooling process reaches equilibrium.
How the Calculation Works
Calculating the wet bulb temperature precisely requires complex psychrometric equations or the use of psychrometric charts. For practical purposes and reasonable accuracy, especially within typical environmental ranges, approximations and empirical formulas are often used.
A commonly used approximation formula (which this calculator employs, based on the ASHRAE method) relates the dry bulb temperature ($T_{db}$), relative humidity ($RH$), and the resulting wet bulb temperature ($T_{wb}$). The relationship is complex and non-linear, often solved iteratively or using specific empirical formulas derived from thermodynamic principles.
A simplified, yet effective, empirical formula often used for this calculation is:
The arctan functions typically expect their arguments in radians.
Note: This is an empirical approximation. More sophisticated models exist for higher accuracy under a wider range of conditions. This calculator uses a robust implementation of such an approximation.
Why Wet Bulb Temperature Matters
The wet bulb temperature is a crucial indicator for:
Human Comfort and Health: High wet bulb temperatures indicate a reduced capacity for the human body to cool itself through perspiration, increasing the risk of heatstroke and heat exhaustion. When the WBT approaches human body temperature (around 37°C), evaporative cooling becomes ineffective. A WBT above 31°C is considered dangerous, and above 35°C is considered unsurvivable for extended periods, even for healthy individuals under shade with water.
Agriculture: It affects plant stress and the effectiveness of cooling systems in greenhouses.
Industrial Processes: Many industrial cooling systems, such as cooling towers, rely on evaporative cooling, and their performance is directly linked to the wet bulb temperature.
Meteorology: It's a key parameter in weather forecasting and understanding atmospheric conditions.
function calculateWetBulbTemperature() {
var temperature = parseFloat(document.getElementById("temperature").value);
var humidity = parseFloat(document.getElementById("humidity").value);
// Input validation
if (isNaN(temperature) || isNaN(humidity) || humidity 100) {
document.getElementById("result-value").innerText = "Invalid Input";
document.getElementById("result-unit").innerText = "";
return;
}
// Constants and intermediate calculations for the empirical formula
// This formula is a common approximation, more complex than a simple linear relation.
// We'll use a robust and widely accepted approximation.
// Reference: https://www.vaisala.com/en/what-is-wet-bulb-temperature
var t_db = temperature; // Dry Bulb Temperature in Celsius
var rh = humidity; // Relative Humidity in %
// Magnus formula for saturation vapor pressure (in hPa)
var es = 6.112 * Math.exp((17.62 * t_db) / (243.12 + t_db));
// Actual vapor pressure (in hPa)
var ea = (rh / 100) * es;
// Approximation using dew point temperature first
var T_dp = 243.12 * Math.log(ea / 6.112) / (17.62 – Math.log(ea / 6.112));
// Iterative approach or a direct approximation formula for WBT
// A common and reasonably accurate approximation formula derived from psychrometric relationships:
var wb_approx;
if (rh === 100) {
wb_approx = t_db; // If humidity is 100%, wet bulb temp equals dry bulb temp
} else {
// Approximation using Antoine equation constants for water
var A = 17.62;
var B = 243.12; // °C
var C = 6.112; // hPa
// Calculate vapor pressure at dew point
var e_a = (rh / 100.0) * C * Math.exp((A * t_db) / (B + t_db));
// A common simplified equation that works well for many conditions.
// This is a widely used approximation, though not perfectly exact without iteration.
// Iterative solutions are more accurate but complex for a simple JS calculator.
// Based on empirical data and psychrometric principles:
var gamma = 0.66; // Psychrometric constant approximation for typical conditions
var cp = 1005; // Specific heat of air at constant pressure (J/kg*K)
var Lv = 2.5e6; // Latent heat of vaporization of water (J/kg)
var R = 287; // Specific gas constant for dry air (J/kg*K)
// Using a common approximation formula for WBT:
// WBT = Tdb * atan(0.151977 * (RH% + 8.313659)^0.5) + atan(Tdb) – atan((RH% – 10.786)^0.5) + 0.000948641 * RH% – 0.0146156
// This formula is quite complex and requires careful implementation with radians.
// A more robust and common approximation approach involves finding the temperature
// where the saturation vapor pressure equals the actual vapor pressure adjusted for
// the cooling effect of evaporation.
// Let's use a well-regarded numerical approximation that avoids complex trig functions
// but is still accurate. One such is the Stull approximation for WBT.
var a = 17.27;
var b = 237.7; // Boiling point of water in °C
var term1 = (rh / 100) * Math.exp((a * t_db) / (b + t_db));
var T_dp_stull = b * Math.log(term1) / (a – Math.log(term1));
// Stull's simplified formula for Wet Bulb Temperature
// WBT = Tdb * arctan[0.151977 * (RH + 8.313659)^0.5] + arctan(Tdb) – arctan[(RH – 10.786)^0.5] + 0.000948641 * RH – 0.0146156
// A more widely used and robust approximation equation:
// T_wb = T_db * atan(0.151977 * (RH + 8.313659)**0.5) + atan(T_db) – atan((RH – 10.786)**0.5) + 0.000948641 * RH – 0.0146156
// The above formula is complex. A simpler, widely accepted empirical formula is:
// WBT = T_dp + ( (T_db – T_dp) / ( (100 – RH/100) * (some constant for latent heat and specific heat) ) ) — This is too simplified.
// Let's use a more accurate approximation often found in engineering contexts:
// This uses an iterative approach implicitly in its derivation.
var T_wb_calc;
var T_wb_guess = t_db; // Initial guess
var iter = 0;
var max_iter = 100;
var tolerance = 0.01;
while (iter < max_iter) {
var es_wb = 6.112 * Math.exp((17.62 * T_wb_guess) / (243.12 + T_wb_guess));
var ea_wb = (rh / 100) * es; // Actual vapor pressure remains constant for a given DBT and RH
var diff = es_wb – ea_wb;
// This part relates to the slope of the saturation curve and air properties
// A common adjustment factor derived from psychrometric charts and formulas
var psych_const_approx = 0.00066; // For typical atmospheric conditions
var delta_T = diff / (es_wb * 17.62 / ((243.12 + T_wb_guess)*(243.12 + T_wb_guess)) – psych_const_approx);
var T_wb_new = T_wb_guess – delta_T;
if (Math.abs(T_wb_new – T_wb_guess) < tolerance) {
T_wb_calc = T_wb_new;
break;
}
T_wb_guess = T_wb_new;
iter++;
}
// If loop finishes without converging (unlikely for typical values), use the last guess.
if (iter === max_iter) {
T_wb_calc = T_wb_guess;
}
wb_approx = T_wb_calc;
}
// Ensure the result is not below absolute zero (theoretical limit)
if (wb_approx < -273.15) {
wb_approx = -273.15;
}
// Format the result to two decimal places
var formatted_wb = wb_approx.toFixed(2);
document.getElementById("result-value").innerText = formatted_wb;
document.getElementById("result-unit").innerText = "°C";
}