Calculate The Position of The Sun in The Sky

Understanding the sun's position in the sky is essential for solar energy applications, astronomy, and everyday life. This calculator determines the solar azimuth (compass direction), altitude (angle above horizon), and day length based on your location and time.

How to Calculate the Sun's Position

The position of the sun in the sky depends on several factors including your geographic coordinates, the date, and the time of day. The calculation involves converting these inputs into solar angles using astronomical algorithms.

Key Parameters

Latitude: Your location's north-south position (e.g., 40.7128° for New York)
Longitude: Your location's east-west position (e.g., -74.0060° for New York)
Date: The day of interest (month and day)
Time: The specific hour and minute of day

Calculation Steps

Convert the date and time to Julian Day (a continuous count of days)
Calculate the solar declination (angle between Earth's rotational axis and the sun)
Determine the equation of time (difference between solar time and clock time)
Compute the hour angle (angular distance of the sun from solar noon)
Calculate the solar altitude (angle above the horizon)
Determine the solar azimuth (compass direction of the sun)

Note: This calculator uses the standard solar position algorithms developed by the National Renewable Energy Laboratory (NREL).

Formula Used

The solar position is calculated using the following formulas:

Solar Altitude (θ)

θ = arcsin(sin(φ) * sin(δ) + cos(φ) * cos(δ) * cos(ω))

Where:

φ = latitude
δ = solar declination
ω = hour angle

Solar Azimuth (γ)

γ = arctan2(sin(ω) * cos(δ), cos(ω) * cos(δ) * sin(φ) - sin(δ) * cos(φ))

Where:

φ = latitude
δ = solar declination
ω = hour angle

The solar declination and hour angle are calculated using more complex formulas involving the Julian Day and equation of time.

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).

Convert date/time to Julian Day: 2459345.0
Calculate solar declination: 23.44°
Determine equation of time: 0 minutes
Compute hour angle: 0° (noon)
Calculate solar altitude: 73.5°
Determine solar azimuth: 180° (south)

At solar noon on June 21, the sun is directly overhead (altitude = 90°) at the Tropic of Cancer (23.44° N). In New York, it reaches 73.5° altitude from the south.

Interpreting Results

The calculator provides three key outputs:

Solar Altitude: Angle above the horizon (0° = horizon, 90° = overhead)
Solar Azimuth: Compass direction (0° = north, 90° = east, 180° = south, 270° = west)
Day Length: Duration of daylight for the selected date

These values help determine solar energy potential, optimal panel angles, and astronomical observations.

FAQ

What is solar azimuth?: Solar azimuth is the compass direction from which the sun appears to be coming. It ranges from 0° (north) to 360°.
What is solar altitude?: Solar altitude is the angle of the sun above the horizon, measured from 0° (horizon) to 90° (overhead).
How accurate is this calculator?: The calculator uses standard astronomical algorithms with an accuracy of ±1° for most locations and times.
Can I use this for solar panel installation?: Yes, the solar altitude and azimuth angles help determine optimal panel tilt and orientation for maximum energy production.
Does this account for atmospheric refraction?: The calculator includes a small correction for atmospheric refraction (≈0.57°) to improve accuracy near sunrise and sunset.