calculate angle of sun

Calculate the precise solar altitude, azimuth, and zenith angles for any location and time.

Hourly Solar Data Table

Time	Altitude (°)	Azimuth (°)	Status

What is a Sun Angle Calculator?

A Sun Angle Calculator is a specialized tool used to determine the exact position of the sun in the sky relative to a specific geographic location on Earth. By inputting latitude, longitude, date, and time, the Sun Angle Calculator provides critical data points such as solar altitude (elevation) and solar azimuth.

Who should use a Sun Angle Calculator? This tool is indispensable for solar energy engineers, architects, photographers, and agricultural scientists. Architects use it to design passive solar heating systems, while solar installers rely on it to optimize the tilt and orientation of photovoltaic panels. Common misconceptions include the belief that the sun is always directly overhead at noon; in reality, this only occurs between the Tropics of Cancer and Capricorn on specific days.

Sun Angle Calculator Formula and Mathematical Explanation

The mathematics behind the Sun Angle Calculator involves spherical trigonometry. The primary goal is to find the altitude angle (α) and the azimuth angle (A).

The step-by-step derivation involves calculating the Solar Declination (δ), which is the angle between the rays of the sun and the plane of the Earth's equator. This changes daily due to the Earth's axial tilt of approximately 23.45°.

Variable	Meaning	Unit	Typical Range
L	Latitude	Degrees	-90° to 90°
δ	Solar Declination	Degrees	-23.45° to 23.45°
H	Hour Angle	Degrees	-180° to 180°
α	Solar Altitude	Degrees	0° to 90°

The Core Formulas

1. Declination (δ): δ = 23.45 * sin(360/365 * (284 + n)), where n is the day of the year.

2. Hour Angle (H): H = 15° * (Time – 12). This represents the sun's movement across the sky (15 degrees per hour).

3. Altitude (α): sin(α) = sin(L)sin(δ) + cos(L)cos(δ)cos(H).

Practical Examples (Real-World Use Cases)

Example 1: Solar Panel Installation in New York

Suppose a technician uses the Sun Angle Calculator for a site in New York City (Lat: 40.71°) on the Summer Solstice (June 21) at 12:00 PM. The calculator would show a solar altitude of approximately 72.7°. This information helps the technician decide that a lower tilt angle for the panels is optimal for summer energy production.

Example 2: Architectural Shading in London

An architect designing a building in London (Lat: 51.50°) wants to ensure that a window is shaded during the hottest part of a July afternoon. By using the Sun Angle Calculator, they find that at 3:00 PM, the sun's azimuth is roughly 238° (West-Southwest) and the altitude is 45°. They can then design a horizontal overhang of the correct depth to block the sun.

How to Use This Sun Angle Calculator

1. Enter Coordinates: Input your Latitude and Longitude. Use positive numbers for North/East and negative for South/West.
2. Select Date: Choose the specific calendar day you wish to analyze.
3. Set Time: Use the 24-hour format to specify the exact moment.
4. Review Results: The Sun Angle Calculator will instantly update the Altitude, Azimuth, and Zenith angles.
5. Analyze the Chart: Look at the SVG chart to see how the sun's elevation changes throughout that specific day.

Key Factors That Affect Sun Angle Calculator Results

• Latitude: The further you are from the equator, the lower the maximum solar altitude generally is.
• Time of Year: The Earth's tilt causes the sun to appear higher in summer and lower in winter.
• Time of Day: Solar altitude peaks at "Solar Noon," which may differ from 12:00 PM local clock time.
• Longitude: Affects the timing of solar noon relative to your local time zone.
• Equation of Time: Small variations in Earth's orbit speed cause the sun to be slightly "fast" or "slow" throughout the year.
• Atmospheric Refraction: Near the horizon, the atmosphere bends light, making the sun appear slightly higher than its geometric position.

Frequently Asked Questions (FAQ)

1. What is the difference between Altitude and Zenith?

Altitude is the angle measured up from the horizon (0° to 90°). Zenith is the angle measured down from directly overhead. They are complementary: Altitude + Zenith = 90°.

2. Why does the Sun Angle Calculator show a negative altitude?

A negative altitude means the sun is below the horizon (nighttime). Our Sun Angle Calculator displays these values to help you determine how far below the horizon the sun is during twilight.

3. Does this calculator account for Daylight Savings Time?

This Sun Angle Calculator uses the local time you input. You should adjust your input time manually if you are currently observing DST to get the most accurate results.

4. How accurate is the solar azimuth?

The azimuth is highly accurate for general engineering and architectural purposes, typically within 0.1 degrees of astronomical tables.

5. Can I use this for any location on Earth?

Yes, the Sun Angle Calculator works for all latitudes from the North Pole to the South Pole.

6. What is Solar Noon?

Solar noon is the moment when the sun reaches its highest point in the sky for a specific day at a specific location.

7. How does the date affect the declination?

The declination varies from +23.45° in June to -23.45° in December, crossing 0° during the equinoxes in March and September.

8. Why is the azimuth 180° at noon in the Northern Hemisphere?

In the Northern Hemisphere (outside the tropics), the sun is due South at solar noon, which corresponds to an azimuth of 180°.