Sun Elevation Calculator

Sun’s Path for the Day

Chart showing the sun’s elevation angle throughout the selected day.

Hourly Sun Position Data

Time	Elevation (°)	Azimuth (°)

Table of sun elevation and azimuth angles at hourly intervals for the specified location and date.

What is a sun elevation calculator?

A sun elevation calculator is a tool used to determine the sun’s angular height above the horizon at a specific geographic location and time. The elevation angle is 0° at sunrise and sunset, and it reaches its maximum at solar noon. This calculator also provides the sun’s azimuth, which is its directional position along the horizon (e.g., east, south, west). Understanding the sun’s position is critical for various fields, including solar energy system design, architecture (for building orientation and shadow analysis), photography (for lighting conditions), agriculture, and astronomy. For anyone needing to know the precise location of the sun, a sun elevation calculator is an indispensable tool. A negative elevation indicates the sun is below the horizon.

Sun Elevation Formula and Explanation

The calculation of the sun’s elevation angle (α) is a complex process involving several astronomical variables. The primary formula is:

α = asin( sin(δ) * sin(φ) + cos(δ) * cos(φ) * cos(HRA) )

Where the variables are derived from your location and the specific time. Each component plays a crucial role in pinpointing the sun’s location.

Variables in the Sun Elevation Formula

Variable	Meaning	Unit	Typical Range
α (Alpha)	Sun Elevation Angle	Degrees	-90° to +90°
φ (Phi)	Observer’s Latitude	Degrees	-90° to +90°
δ (Delta)	Solar Declination Angle	Degrees	-23.45° to +23.45°
HRA	Hour Angle	Degrees	-180° to +180°

The Solar Declination (δ) is the angle of the sun relative to the Earth’s equatorial plane, which changes based on the day of the year. The Hour Angle (HRA) converts the local time of day into an angular measurement, where solar noon is 0°.

Practical Examples

Example 1: Summer in Los Angeles

Let’s calculate the sun elevation for a summer afternoon in Los Angeles.

• Inputs: Latitude: 34.05° N, Longitude: -118.24° W, Date: July 21st, Time: 2:00 PM (14:00), Timezone: UTC-7 (Daylight Saving)
• Results: The sun elevation calculator would show a high elevation angle, approximately 65.5°, with an azimuth of about 255° (in the west-southwest sky). This high angle is typical for a summer afternoon and is a key factor for a photovoltaic efficiency tool.

Example 2: Winter in Stockholm

Now consider a winter morning in a high-latitude city like Stockholm, Sweden.

• Inputs: Latitude: 59.33° N, Longitude: 18.06° E, Date: December 21st, Time: 10:00 AM, Timezone: UTC+1
• Results: The calculator would reveal a much lower sun elevation angle, around 5.2°, with an azimuth of about 150° (in the southeast). This demonstrates the dramatic effect of latitude and season on the sun’s path, a crucial concept for architects creating an architectural sun study tool.

How to Use This sun elevation calculator

Using this calculator is a straightforward process:

1. Enter Latitude: Input the latitude of your location. Use positive values for the Northern Hemisphere and negative values for the Southern Hemisphere.
2. Enter Longitude: Input the longitude of your location. Use positive values for East of the Prime Meridian and negative for West.
3. Select Date and Time: Choose the exact date and time for which you want to calculate the sun’s position.
4. Set Timezone: Select the correct UTC offset for your location. Remember to account for Daylight Saving Time if it’s in effect.
5. Interpret Results: The calculator will instantly update the sun’s Elevation and Azimuth angles. The chart and table provide a broader overview for the entire day. The elevation helps you understand the sun’s height, while the azimuth tells you its compass direction.

Key Factors That Affect Sun Elevation

Several factors interact to determine the sun’s position in the sky. A good sun elevation calculator must account for all of them.

• Geographic Latitude: This is the most significant factor. The closer you are to the equator, the higher the sun can get in the sky.
• Day of the Year: The Earth’s axial tilt of 23.45° causes the seasons and changes the sun’s declination angle daily. This is why the sun is higher in summer and lower in winter.
• Time of Day: The sun’s elevation changes continuously from sunrise (0°) to solar noon (maximum elevation) to sunset (0°).
• Timezone and Longitude: These determine your local solar time. Solar noon, when the sun is highest, rarely aligns perfectly with 12:00 PM on your clock due to time zone conventions and the Equation of Time.
• Atmospheric Refraction: Our atmosphere bends light, making the sun appear slightly higher than it geometrically is, especially near sunrise and sunset. This calculator performs geometric calculations.
• Observer’s Altitude: Being at a higher altitude (e.g., on a mountain) can slightly alter the time of sunrise and sunset, but has a negligible effect on the measured elevation angle against the horizon. For more details, see our guide on understanding solar declination.

Frequently Asked Questions (FAQ)

What is the difference between sun elevation and azimuth?

Elevation is the sun’s vertical angle from the horizon (up/down). Azimuth is the sun’s horizontal angle along the horizon, typically measured clockwise from North (0°). A solar noon calculator can find when the sun reaches its highest point.

Why is the calculated elevation negative?

A negative elevation angle means the sun is below the horizon at the selected time and location. It’s nighttime.

How accurate is this sun elevation calculator?

This calculator provides highly accurate geometric positions. It does not account for atmospheric refraction, which can make the sun appear about 0.5° higher when it is on the horizon.

Can I use this for positioning solar panels?

Absolutely. This is a perfect tool for determining the optimal tilt angle for solar panels. By finding the sun’s elevation at different times of the year, you can find the best average angle to maximize energy capture.

What is the maximum possible sun elevation?

The maximum elevation is 90°, which occurs when the sun is directly overhead (at the zenith). This only happens in the tropics (between the Tropic of Cancer and Tropic of Capricorn).

Does my altitude above sea level affect the calculation?

For the purpose of calculating the angle relative to the horizon, your altitude has a negligible effect and is not considered in standard formulas.

What is Solar Declination?

It is the angle between the Earth’s equatorial plane and the sun’s rays. It varies from +23.45° on the June solstice to -23.45° on the December solstice.

Why does the chart shape change with latitude?

At higher latitudes, the sun’s path is more slanted, leading to longer days in summer and shorter days in winter. Near the equator, the sun’s path is more perpendicular to the horizon, resulting in more consistent day lengths throughout the year. Explore this with our sun path chart generator.