Solar Elevation Angle Calculator

Solar Elevation Angle Calculator

Enter your location, date, and time to calculate the sun's elevation and azimuth angles.

° ° hours
function calculateSolarAngles() { var latitudeDeg = parseFloat(document.getElementById('latitude').value); var longitudeDeg = parseFloat(document.getElementById('longitude').value); var dateStr = document.getElementById('calcDate').value; var timeStr = document.getElementById('calcTime').value; var timeZoneOffsetHours = parseFloat(document.getElementById('timeZoneOffset').value); if (isNaN(latitudeDeg) || isNaN(longitudeDeg) || isNaN(timeZoneOffsetHours) || !dateStr || !timeStr) { document.getElementById('result').innerHTML = 'Please enter valid numbers for all fields and select a date/time.'; return; } // Validate latitude and longitude ranges if (latitudeDeg 90) { document.getElementById('result').innerHTML = 'Latitude must be between -90 and 90 degrees.'; return; } if (longitudeDeg 180) { document.getElementById('result').innerHTML = 'Longitude must be between -180 and 180 degrees.'; return; } // 1. Convert Local Date/Time to UTC // Create a local date object var localDateTimeStr = dateStr + 'T' + timeStr + ':00'; var localDate = new Date(localDateTimeStr); // Adjust to UTC based on the provided timeZoneOffsetHours // getTime() returns milliseconds since epoch. // timeZoneOffsetHours * 60 * 60 * 1000 converts hours to milliseconds. var utcMilliseconds = localDate.getTime() – (timeZoneOffsetHours * 60 * 60 * 1000); var utcDate = new Date(utcMilliseconds); // 2. Calculate Day of Year (n) for UTC date var startOfYear = new Date(utcDate.getFullYear(), 0, 0); var diff = utcDate – startOfYear; var oneDay = 1000 * 60 * 60 * 24; var n = Math.floor(diff / oneDay); // 3. Calculate B (in radians) var B_rad = (n – 1) * 2 * Math.PI / 365.25; // 4. Calculate Solar Declination (delta_rad) var delta_rad = 0.006918 – 0.399912 * Math.cos(B_rad) + 0.070257 * Math.sin(B_rad) – 0.006758 * Math.cos(2 * B_rad) + 0.000907 * Math.sin(2 * B_rad) – 0.002697 * Math.cos(3 * B_rad) + 0.00148 * Math.sin(3 * B_rad); // 5. Calculate Equation of Time (EoT_minutes) var EoT_minutes = 229.18 * (0.000075 + 0.001868 * Math.cos(B_rad) – 0.032077 * Math.sin(B_rad) – 0.014615 * Math.cos(2 * B_rad) – 0.040849 * Math.sin(2 * B_rad)); // 6. Calculate Local Solar Time (LST_hours) var utcHours = utcDate.getUTCHours() + utcDate.getUTCMinutes() / 60 + utcDate.getUTCSeconds() / 3600; var LST_hours = utcHours + EoT_minutes / 60 + (longitudeDeg / 15); // 7. Calculate Hour Angle (omega_rad) var omega_deg = 15 * (LST_hours – 12); var omega_rad = omega_deg * Math.PI / 180; // 8. Convert Latitude to Radians var lat_rad = latitudeDeg * Math.PI / 180; // 9. Calculate Solar Zenith Angle (theta_z_rad) var cos_theta_z = Math.sin(lat_rad) * Math.sin(delta_rad) + Math.cos(lat_rad) * Math.cos(delta_rad) * Math.cos(omega_rad); // Clamp cos_theta_z to avoid NaN from Math.acos due to floating point inaccuracies cos_theta_z = Math.max(-1, Math.min(1, cos_theta_z)); var theta_z_rad = Math.acos(cos_theta_z); var theta_z_deg = theta_z_rad * 180 / Math.PI; // 10. Calculate Solar Elevation Angle (elevation_deg) var elevation_deg = 90 – theta_z_deg; // 11. Apply Atmospheric Refraction Correction var refraction_deg = 0; if (elevation_deg > -0.5 && elevation_deg <= 85) { var tan_elev = Math.tan(elevation_deg * Math.PI / 180); // Formula for refraction in arcminutes, then convert to degrees refraction_deg = (58.1 / tan_elev – 0.07 / (tan_elev * tan_elev * tan_elev) + 0.000086 / (tan_elev * tan_elev * tan_elev * tan_elev * tan_elev)) / 3600; } var elevation_corrected_deg = elevation_deg + refraction_deg; if (elevation_corrected_deg 0) { // Only calculate azimuth if sun is above horizon var Y = -Math.sin(omega_rad) * Math.cos(delta_rad); var X = Math.cos(lat_rad) * Math.sin(delta_rad) – Math.sin(lat_rad) * Math.cos(delta_rad) * Math.cos(omega_rad); var azimuth_rad = Math.atan2(Y, X); azimuth_deg = azimuth_rad * 180 / Math.PI; azimuth_deg = (azimuth_deg + 360) % 360; // Ensure 0-360 range (North=0, East=90) } else { azimuth_deg = NaN; // Azimuth is undefined when sun is below horizon } var resultsHtml = '

Calculation Results:

'; resultsHtml += 'Solar Elevation Angle: ' + elevation_corrected_deg.toFixed(2) + '°'; resultsHtml += 'Solar Zenith Angle: ' + theta_z_deg.toFixed(2) + '°'; if (!isNaN(azimuth_deg)) { resultsHtml += 'Solar Azimuth Angle: ' + azimuth_deg.toFixed(2) + '° (North = 0°, East = 90°)'; } else { resultsHtml += 'Solar Azimuth Angle: Undefined (Sun is below the horizon)'; } document.getElementById('result').innerHTML = resultsHtml; } .solar-elevation-calculator { background-color: #f9f9f9; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 600px; margin: 20px auto; font-family: Arial, sans-serif; } .solar-elevation-calculator h2 { color: #333; text-align: center; margin-bottom: 20px; } .solar-elevation-calculator p { color: #555; line-height: 1.6; } .calculator-inputs label { display: block; margin-bottom: 5px; font-weight: bold; color: #444; } .calculator-inputs input[type="number"], .calculator-inputs input[type="date"], .calculator-inputs input[type="time"] { width: calc(100% – 22px); padding: 10px; margin-bottom: 15px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; } .calculator-inputs .unit { margin-left: -30px; display: inline-block; width: 20px; text-align: right; color: #666; } .calculator-inputs button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; width: 100%; box-sizing: border-box; transition: background-color 0.3s ease; } .calculator-inputs button:hover { background-color: #0056b3; } .calculator-results { margin-top: 20px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 4px; color: #155724; } .calculator-results h3 { color: #155724; margin-top: 0; } .calculator-results p { margin: 5px 0; } .calculator-results strong { color: #000; } .error { color: #dc3545; background-color: #f8d7da; border-color: #f5c6cb; padding: 10px; border-radius: 4px; }

Understanding the Solar Elevation Angle

The solar elevation angle, also known as the solar altitude angle, is a fundamental concept in solar geometry. It represents the angle between the horizon and the center of the sun's disk. When the sun is directly overhead, the elevation angle is 90 degrees. When it's on the horizon, the angle is 0 degrees. A negative elevation angle indicates that the sun is below the horizon.

Why is the Solar Elevation Angle Important?

This angle has significant implications across various fields:

  • Solar Energy: For solar panel installations, knowing the sun's elevation angle throughout the day and year is crucial for optimizing panel tilt and orientation to maximize energy capture.
  • Architecture and Building Design: Architects use this information to design buildings that maximize natural light, minimize heat gain in summer, and maximize passive solar heating in winter. Overhangs, window placement, and shading devices are all influenced by solar angles.
  • Photography and Filmmaking: Understanding the sun's position helps photographers plan shoots, predict lighting conditions, and avoid harsh shadows or glare.
  • Agriculture and Gardening: The amount of sunlight a plant receives is directly related to the solar elevation angle. Gardeners and farmers use this to plan crop placement and optimize growing conditions.
  • Astronomy and Navigation: Historically, solar elevation was used for navigation (e.g., with a sextant) and remains a key parameter in astronomical observations.
  • Climate and Weather: The solar elevation angle influences the intensity of solar radiation reaching the Earth's surface, which in turn affects local temperatures and weather patterns.

Factors Influencing Solar Elevation Angle

The sun's elevation angle is dynamic and depends on several key factors:

  1. Latitude: Your geographical position north or south of the equator significantly impacts the sun's path. Locations closer to the equator generally experience higher solar elevation angles throughout the year.
  2. Date (Day of the Year): Due to the Earth's axial tilt (approximately 23.5 degrees), the sun's apparent path across the sky changes with the seasons. The highest elevation angles occur around the summer solstice, and the lowest around the winter solstice.
  3. Time of Day: The sun's elevation angle is lowest at sunrise and sunset, gradually increasing to its peak at solar noon (when the sun is at its highest point in the sky for that day).
  4. Longitude and Time Zone: While longitude doesn't directly affect the sun's *path*, it determines when solar noon occurs relative to your local clock time. The time zone offset from UTC is essential for accurately converting local time to the universal time used in astronomical calculations.

How to Use the Calculator

Our Solar Elevation Angle Calculator simplifies these complex astronomical calculations. To use it:

  1. Latitude (degrees): Enter your location's latitude. Positive values for Northern Hemisphere, negative for Southern Hemisphere (e.g., 34.05 for Los Angeles, -33.86 for Sydney).
  2. Longitude (degrees): Enter your location's longitude. Positive values for East of the Prime Meridian, negative for West (e.g., -118.25 for Los Angeles, 151.21 for Sydney).
  3. Date: Select the specific date for which you want the calculation.
  4. Time (HH:MM): Enter the local time in 24-hour format (e.g., 14:30 for 2:30 PM).
  5. Time Zone Offset from UTC (hours): Input your local time zone's offset from Coordinated Universal Time (UTC). For example, Eastern Standard Time (EST) is -5, Pacific Daylight Time (PDT) is -7, Central European Time (CET) is +1.

Click "Calculate Solar Angles" to get the results.

Interpreting the Results

  • Solar Elevation Angle: This is the primary output, indicating how high the sun is above the horizon. A higher angle means more direct sunlight.
  • Solar Zenith Angle: This is the complementary angle to the elevation angle (90° – Elevation Angle). It's the angle between the sun and the zenith (the point directly overhead).
  • Solar Azimuth Angle: This indicates the sun's direction along the horizon. It's typically measured clockwise from North (0°). So, East is 90°, South is 180°, and West is 270°. If the sun is below the horizon, the azimuth angle is undefined.

Use these values to make informed decisions for your solar projects, architectural designs, or any application where understanding the sun's position is critical.

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