How to Calculate the Evaporation Rate of Water

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How to Calculate the Evaporation Rate of Water

Understanding how quickly water evaporates from a surface is crucial for various applications, from managing swimming pool water levels and estimating reservoir losses to designing industrial cooling systems. The evaporation rate is not constant; it is a dynamic process driven by the energy balance and atmospheric conditions surrounding the water body.

While precise evaporation calculations often require complex meteorological data including solar radiation and net energy flux (like the Penman equation), we can estimate the rate effectively using empirical formulas based on the mass transfer method. This approach focuses on the primary drivers: vapor pressure deficit and wind speed.

The Key Factors Driving Evaporation

The rate at which liquid water turns into vapor depends primarily on four interacting factors:

  1. Water Temperature: Warm water has higher kinetic energy, allowing molecules to escape the surface more easily. Crucially, higher water temperature increases the saturation vapor pressure at the surface.
  2. Air Temperature and Relative Humidity: These determine how much water vapor the air already holds versus how much it can hold. The difference between the saturation vapor pressure at the water's surface and the actual vapor pressure in the surrounding air is called the Vapor Pressure Deficit (VPD). A higher VPD means a faster evaporation rate. For example, on a hot day (35°C) with low humidity (20%), evaporation will be much faster than on a cool, foggy day.
  3. Wind Speed: As water evaporates, the air immediately above the surface becomes saturated. Wind blows this saturated air away, replacing it with drier air, thereby maintaining a high vapor pressure deficit and sustaining the evaporation process. A stagnant layer of air slows evaporation significantly.
  4. Surface Area: Evaporation occurs only at the interface between water and air. The larger the surface area, the more total volume of water will be lost over time, although the rate per square meter might remain the same.

The Calculation Formula

The calculator below uses a simplified empirical mass transfer formula, often adapted for engineering estimations for open water tanks or pools. It approximates the rate based on the vapor pressure difference and a wind function coefficient.

The underlying logic approximates: Rate = (Mass Transfer Coefficient varying with Wind) × (Saturation Vapor Pressure of Water – Actual Vapor Pressure of Air) × Surface Area.

Use the calculator below to estimate daily water loss based on your specific conditions.

Water Evaporation Rate Calculator

Estimate daily water volume loss from an open surface.

Note: 1 m/s = 3.6 km/h
// Function to calculate saturation vapor pressure using the Magnus formula approximation (returns hPa) function getSaturationVaporPressure(tempC) { if (tempC 100) return 0; // Safety bounds // Formula: 6.112 * exp((17.67 * T) / (T + 243.5)) var vaporPressure = 6.112 * Math.exp((17.67 * tempC) / (tempC + 243.5)); return vaporPressure; } function calculateEvaporation() { // Get input values var area = parseFloat(document.getElementById('surfaceArea').value); var waterT = parseFloat(document.getElementById('waterTemp').value); var airT = parseFloat(document.getElementById('airTemp').value); var humidity = parseFloat(document.getElementById('relHumidity').value); var wind = parseFloat(document.getElementById('windSpeed').value); var resultBox = document.getElementById('evapResult'); // Reset result box styling resultBox.style.display = 'block'; resultBox.style.backgroundColor = '#fff'; resultBox.style.border = '1px solid #ddd'; // Input validation if (isNaN(area) || isNaN(waterT) || isNaN(airT) || isNaN(humidity) || isNaN(wind)) { resultBox.innerHTML = 'Error: Please enter numerical values for all fields.'; resultBox.style.backgroundColor = '#f8d7da'; resultBox.style.borderColor = '#f5c6cb'; return; } if (area <= 0 || humidity 100 || wind < 0) { resultBox.innerHTML = 'Error: Please ensure Surface Area is positive, Humidity is between 0-100%, and Wind Speed is non-negative.'; resultBox.style.backgroundColor = '#f8d7da'; resultBox.style.borderColor = '#f5c6cb'; return; } // 1. Calculate Vapor Pressures in hPa var Es_water = getSaturationVaporPressure(waterT); // Saturation VP at water temp surface var Es_air_sat = getSaturationVaporPressure(airT); // Saturation VP if air was saturated at its temp var Ea_air_actual = Es_air_sat * (humidity / 100); // Actual VP in the air based on RH // Calculate Vapor Pressure Deficit (difference between water surface saturated VP and air actual VP) var vaporPressureDeficit_hPa = Es_water – Ea_air_actual; // If deficit is negative (air is warmer and wetter than the water surface), condensation might occur. // For this calculator, we assume evaporation is 0 if conditions favor condensation. if (vaporPressureDeficit_hPa < 0) { vaporPressureDeficit_hPa = 0; } // 2. Apply Empirical Formula // We use a simplified engineering formula often cited for open tanks: E_rate = (C1 + C2*V) * (Psat_w – Pactual_a) // A common approximation yields rate in kg/m²/h (roughly mm depth per hour) when Pressure is in kPa and Wind in m/s. // Coefficients often used: C1=0.089, C2=0.0782 (assuming specific standard conditions, good for estimation). var vpDeficit_kPa = vaporPressureDeficit_hPa / 10; // Convert hPa to kPa // Evaporation flux in kg per m² per hour (equivalent to mm of depth per hour) var evaporationFlux_mm_h = (0.089 + 0.0782 * wind) * vpDeficit_kPa; if (evaporationFlux_mm_h < 0) evaporationFlux_mm_h = 0; // Final safety check // 3. Calculate Totals based on Surface Area // Total Liters per hour (Since 1 kg water approx 1 Liter, and flux is per m²) var totalLitersPerHour = evaporationFlux_mm_h * area; var totalLitersPerDay = totalLitersPerHour * 24; // Depth loss in mm per day var depthLoss_mm_day = evaporationFlux_mm_h * 24; // 4. Display Results var resultHTML = '

Calculation Results:

'; resultHTML += 'Total Daily Evaporation: ' + totalLitersPerDay.toFixed(1) + ' Liters/Day'; resultHTML += 'Hourly Rate: ' + totalLitersPerHour.toFixed(2) + ' Liters/Hour'; resultHTML += '
'; resultHTML += 'Equivalent Water Level Drop: approximately ' + depthLoss_mm_day.toFixed(2) + ' mm over 24 hours.'; resultHTML += '*This estimation uses a simplified mass transfer formula assuming constant conditions. Actual rates may vary due to solar radiation, barometric pressure changes, and water turbulence.'; resultBox.innerHTML = resultHTML; }

Interpreting the Results

The calculator provides an estimate of the total volume of water lost per day (in Liters) and the corresponding drop in water level (in millimeters). For example, if you have a 30 m² pool and the calculator indicates a loss of 150 Liters per day, this roughly corresponds to a 5mm drop in water level across the entire surface over 24 hours.

Keep in mind that this is an estimation for "quiet" water. Factors like swimmers agitating a pool, fountains, or waterfalls increase the surface area exposed to air and will significantly increase the actual evaporation rate beyond this baseline calculation.

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