Sun Position in Sky Calculator

The sun's position in the sky changes throughout the day and year, affecting solar energy collection, photography, and astronomy. This calculator determines the sun's altitude and azimuth angles for any location and time.

What is Sun Position in Sky?

The sun's position in the sky is defined by two key angles:

Altitude (Elevation): The angle between the sun and the horizon, measured from 0° (on the horizon) to 90° (directly overhead).
Azimuth: The compass direction of the sun, measured clockwise from north (0°) to east (90°), south (180°), and west (270°).

These angles depend on:

Location (latitude and longitude)
Date and time
Time zone
Daylight saving time (if applicable)

Note

The sun's position changes rapidly near sunrise and sunset. The calculator provides accurate results for most practical applications but may have slight variations for extreme conditions.

How to Calculate Sun Position

Calculating the sun's position involves several steps:

Convert the date and time to Julian Day
Calculate the solar declination angle
Determine the hour angle
Compute the solar altitude and azimuth angles

The calculations use standard astronomical algorithms that account for Earth's elliptical orbit and axial tilt.

Formula Used

Solar Altitude (θ)

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

Where:

φ = latitude
δ = solar declination angle
ω = hour angle

Solar Azimuth (A)

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

Where:

φ = latitude
δ = solar declination angle
ω = hour angle

The full calculation involves additional steps to determine the solar declination and hour angle based on the date and time.

Worked Example

Example Calculation

For a location at 40°N latitude on June 21 at 12:00 PM local time:

Solar declination (δ) ≈ 23.44°
Hour angle (ω) = 0° (noon)
Solar altitude (θ) ≈ 73.44°
Solar azimuth (A) ≈ 180° (south)

This means the sun is directly overhead at this location on the summer solstice at noon.

FAQ

What is the difference between solar altitude and azimuth?

Solar altitude measures how high the sun is in the sky, while solar azimuth measures the compass direction the sun is coming from.

How does the sun's position change throughout the day?

The sun rises in the east, reaches its highest point (solar noon) in the south, and sets in the west. The altitude increases until noon and decreases afterward.

What factors affect the sun's position?

The sun's position depends on your location, date, time, and whether daylight saving time is in effect.