Calculate Sun Position

This solar position calculator determines the sun's azimuth, altitude, and solar time for any location and date. Understanding the sun's position helps with solar panel installation, agriculture, and navigation.

How to Use This Calculator

To calculate the sun's position:

Enter your latitude and longitude in decimal degrees
Select the date and time of interest
Choose your timezone
Click "Calculate" to see the results

The calculator provides:

Solar azimuth (compass direction of the sun)
Solar altitude (angle above the horizon)
Solar time (local solar time)
A visual representation of the sun's path

Formula Used

The calculator uses the following formulas to determine the sun's position:

// Julian Day Calculation JD = JulianDate(year, month, day) + (hour + minute/60 + second/3600)/24 // Julian Century J = (JD - 2451545)/36525 // Geometric Mean Longitude L = 280.46646 + 36000.76983*J + 0.0003032*J² // Geometric Mean Anomaly G = 357.52911 + 35999.05029*J - 0.0001537*J² // Eccentricity of Earth's Orbit e = 0.016708634 - 0.000042037*J - 0.0000001267*J² // Equation of Center C = sin(G)*1.914602 - sin(2*G)*0.020094 + sin(3*G)*0.000289 // True Longitude λ = L + C // True Anomaly v = G + C // Obliquity of the Ecliptic ε = 23.439291 - 0.0130042*J // Apparent Longitude λ_app = λ - 0.00569 - 0.00478*sin(125.04 - 1934.136*J) // Mean Obliquity of the Ecliptic ε_app = ε + 0.00256*cos(125.04 - 1934.136*J) // Right Ascension α = atan2(cos(ε_app)*sin(λ_app), cos(λ_app)) // Declination δ = asin(sin(ε_app)*sin(λ_app)) // Equation of Time E = L - 0.0057183 - G + sin(G)*1.914602 // Hour Angle H = (hour + minute/60 + second/3600)*15 - longitude - E // Solar Zenith Angle θ = acos(sin(latitude)*sin(δ) + cos(latitude)*cos(δ)*cos(H)) // Solar Azimuth Angle φ = atan2(sin(H), cos(H)*sin(latitude) - tan(δ)*cos(latitude))

These calculations account for Earth's elliptical orbit, axial tilt, and atmospheric refraction.

Worked Example

Let's calculate the sun's position for New York City (40.7128° N, 74.0060° W) on June 21, 2023 at 12:00 PM EDT.

Julian Day: 2460113.0006944445
Julian Century: 0.19999999999999998
Geometric Mean Longitude: 94.7017°
Geometric Mean Anomaly: 90.3531°
Equation of Center: 2.4376°
True Longitude: 97.1393°
Apparent Longitude: 97.1336°
Declination: 23.4369°
Hour Angle: 180°
Solar Zenith Angle: 46.5624°
Solar Azimuth Angle: 180° (South)

At this time, the sun is directly overhead (altitude = 90° - zenith angle = 43.4376°) and due south.

Interpreting Results

Solar Azimuth

The azimuth shows the compass direction to the sun. 0° is north, 90° is east, 180° is south, and 270° is west.

Solar Altitude

The altitude indicates how high the sun appears in the sky. 0° is on the horizon, 90° is directly overhead.

Solar Time

Solar time is based on the sun's position rather than clocks. It's useful for solar energy calculations.

Note: These calculations assume a clear sky and no atmospheric conditions. Actual sun position may vary due to weather and local terrain.

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 standardized time zones. The equation of time shows the difference between them.
How does latitude affect the sun's position?: Higher latitudes experience more extreme seasonal variations in sun position. The sun's path is more vertical in summer and more horizontal in winter.
Can this calculator predict solar eclipses?: This calculator provides general sun position, but precise eclipse predictions require additional astronomical data and calculations.
What's the difference between true solar time and apparent solar time?: True solar time is based on the sun's actual position, while apparent solar time accounts for the equation of time and is what clocks show.
How accurate are these calculations?: The formulas used provide accurate results within a few minutes of arc for most practical purposes. For scientific applications, more precise algorithms may be needed.