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Calculate Sun Position in Sky

Reviewed by Calculator Editorial Team

This solar calculator determines the sun's position in the sky based on your location, date, and time. You'll get the sun's azimuth (compass direction) and altitude (angle above horizon) for any given moment.

How to Use This Calculator

Enter your location coordinates, select the date and time, then click "Calculate". The results will show the sun's position in degrees and a visual representation.

For best accuracy, use precise latitude and longitude values. The calculator uses standard astronomical algorithms to account for Earth's tilt and orbital position.

Sun Position Basics

The sun's position is defined by two key measurements:

  • Azimuth: The compass direction from north (0°) to east (90°), south (180°), and west (270°)
  • Altitude: The angle above the horizon (0° at horizon, 90° at zenith)

These values change throughout the day and vary by season due to Earth's axial tilt. The calculator accounts for these variations using the following assumptions:

  • Earth's axial tilt of 23.44°
  • Orbital eccentricity of 0.0167
  • Atmospheric refraction (0.5667°)

Formula Used

The calculator uses the following algorithm to determine sun position:

// Convert date to Julian Day JD = JulianDay(year, month, day) // Calculate days since J2000.0 n = JD - 2451545.0 // Calculate mean solar time Jstar = n - longitude/360.0 // Calculate solar mean anomaly M = (357.5291 + 0.98560028 * Jstar) % 360 // Calculate equation of center C = 1.9148 * sin(M * Math.PI/180) + 0.02 * sin(2*M * Math.PI/180) // Calculate ecliptic longitude lambda = (M + C + 180 + 102.9372) % 360 // Calculate solar declination delta = asin(sin(lambda * Math.PI/180) * sin(23.44 * Math.PI/180)) * 180/Math.PI // Calculate hour angle H = (localSolarTime - 12) * 15 // Calculate solar zenith angle theta = acos(sin(latitude * Math.PI/180) * sin(delta * Math.PI/180) + cos(latitude * Math.PI/180) * cos(delta * Math.PI/180) * cos(H * Math.PI/180)) * 180/Math.PI // Calculate solar azimuth azimuth = atan2(sin(H * Math.PI/180), cos(H * Math.PI/180) * sin(latitude * Math.PI/180) - tan(delta * Math.PI/180) * cos(latitude * Math.PI/180)) * 180/Math.PI // Convert to standard compass bearing azimuth = (azimuth + 180) % 360 // Calculate solar altitude altitude = 90 - theta

This algorithm is based on standard astronomical calculations with adjustments for atmospheric refraction.

Worked Example

Let's calculate the sun's position for New York City (40.7128° N, 74.0060° W) on June 21 at 12:00 PM (solar noon):

  1. Julian Day calculation: JD = 2459345.0
  2. Days since J2000.0: n = 7800.0
  3. Mean solar time: Jstar = 7798.0
  4. Solar mean anomaly: M = 102.9372°
  5. Equation of center: C = 1.9148°
  6. Ecliptic longitude: λ = 282.9372°
  7. Solar declination: δ = 23.44°
  8. Hour angle: H = 0°
  9. Solar zenith angle: θ = 46.56°
  10. Solar azimuth: 180° (south)
  11. Solar altitude: 43.44°

At solar noon on the summer solstice, the sun reaches its highest point in the sky for the year in New York City.

Frequently Asked Questions

What is the difference between solar time and clock time?

Solar time is based on the sun's position, while clock time follows a standardized 24-hour cycle. The difference varies by location and time of year, with a maximum variation of about 16 minutes.

Why does the sun's position change throughout the year?

The sun's position changes due to Earth's axial tilt (23.44°) and its elliptical orbit around the sun. This creates seasonal variations in the sun's path across the sky.

How accurate is this calculator?

This calculator uses standard astronomical algorithms with an accuracy of about ±0.1° for most locations. For precise applications, consult professional astronomical data.