Sun Elevation Calculator

Accurately determine the Sun’s elevation angle above the horizon for any given date, time, and geographical coordinates.

Calculate Sun Elevation

Hourly Sun Elevation and Related Angles for Current Date

Time (HH:MM)	Elevation Angle (°)	Zenith Angle (°)	Declination Angle (°)	Hour Angle (°)

What is a Sun Elevation Calculator?

A Sun Elevation Calculator is a specialized tool designed to determine the angle of the Sun above the horizon at a specific geographical location, date, and time. This angle, known as the solar elevation angle, is crucial for understanding how much direct sunlight an area receives. It’s a fundamental concept in solar geometry, providing insights into the Sun’s apparent path across the sky.

The Sun’s elevation angle varies significantly throughout the day and year, influenced by factors such as latitude, the Earth’s tilt, and its orbit around the Sun. At solar noon, the Sun reaches its highest point in the sky for that day, resulting in the maximum elevation angle. At sunrise and sunset, the elevation angle is approximately 0 degrees (ignoring atmospheric refraction), and it becomes negative when the Sun is below the horizon.

Who Should Use a Sun Elevation Calculator?

• Solar Energy Professionals: For optimizing solar panel placement and tilt angles to maximize energy capture.
• Architects and Builders: To design energy-efficient buildings, plan window placements, and manage natural lighting and shading.
• Photographers and Filmmakers: To predict lighting conditions, golden hour, and blue hour for outdoor shoots.
• Gardeners and Farmers: To understand sun exposure for plant growth and crop planning.
• Astronomers and Hobbyists: For tracking solar events, planning observations, or simply understanding celestial mechanics.
• Urban Planners: To assess shadow impacts of new constructions on public spaces and neighboring properties.

Common Misconceptions About Sun Elevation

• “The Sun is always highest at 12:00 PM local time.” This is a common misconception. Solar noon, the time when the Sun reaches its highest elevation, rarely coincides exactly with 12:00 PM local clock time due to factors like the Equation of Time, longitude within a time zone, and daylight saving time.
• “Sun elevation is the same everywhere on the same day.” Incorrect. Latitude is a primary determinant of sun elevation. Locations closer to the equator generally experience higher sun elevation angles throughout the year compared to those at higher latitudes.
• “Atmospheric refraction doesn’t matter.” While small, atmospheric refraction can slightly increase the apparent sun elevation, especially near the horizon. A precise Sun Elevation Calculator often includes this correction.

Sun Elevation Calculator Formula and Mathematical Explanation

The calculation of the Sun’s elevation angle involves several astronomical concepts and formulas. Our Sun Elevation Calculator uses a widely accepted simplified algorithm, often based on principles from the NOAA Solar Position Algorithm (SPA), to provide accurate results. Here’s a step-by-step breakdown of the core mathematical process:

Step-by-Step Derivation:

1. Day of Year (N): First, the calculator determines the day number (N) for the given date, counting from January 1st (e.g., January 1 = 1, February 1 = 32). This is crucial for tracking the Earth’s position in its orbit.
2. Solar Declination Angle (δ): This is the angle between the plane of the Earth’s equator and the line joining the center of the Earth to the center of the Sun. It varies throughout the year due to the Earth’s axial tilt. The formula involves a series of trigonometric functions based on the day of the year (N) to approximate the Sun’s position relative to the celestial equator.

   δ ≈ 0.006918 - 0.399912 cos(γ) + 0.070257 sin(γ) - 0.006758 cos(2γ) + 0.000907 sin(2γ) - 0.002697 cos(3γ) + 0.00148 sin(3γ)

   Where γ = (2π / 365) * (N - 1) (in radians, N is day of year).

3. Equation of Time (EoT): This value accounts for the discrepancy between mean solar time (what a clock shows) and apparent solar time (what a sundial shows). It arises from the Earth’s elliptical orbit and axial tilt. EoT is typically expressed in minutes.

   EoT ≈ 229.18 * (0.000075 + 0.001868 cos(γ) - 0.032077 sin(γ) - 0.014615 cos(2γ) - 0.040849 sin(2γ))

4. True Solar Time (TST): This is the actual time based on the Sun’s position, adjusted for longitude and the Equation of Time. It’s calculated by taking the local clock time, adjusting for the longitude’s deviation from the time zone’s standard meridian, and then applying the Equation of Time.

   TST (minutes) = Local Time (minutes) + (4 * Longitude) + EoT - (60 * Time Zone Offset)

   Where Longitude is in degrees, and Time Zone Offset is in hours from UTC.

5. Hour Angle (H): The hour angle represents the angular displacement of the Sun east or west of the local meridian. It’s 0 degrees at solar noon, negative before noon, and positive after noon.

   H = 15 * (TST (hours) - 12)

6. Zenith Angle (θ): This is the angle between the Sun and the vertical (directly overhead). It’s calculated using the observer’s latitude, the solar declination, and the hour angle.

   cos(θ) = sin(Latitude) * sin(δ) + cos(Latitude) * cos(δ) * cos(H)

   All angles (Latitude, δ, H) must be in radians for trigonometric functions. The result θ is then converted back to degrees.

7. Sun Elevation Angle (α): Finally, the elevation angle is simply 90 degrees minus the zenith angle.

   α = 90° - θ

8. Atmospheric Refraction Correction: For greater accuracy, especially when the Sun is near the horizon, a small correction for atmospheric refraction is applied. This makes the Sun appear slightly higher than it actually is.

Variable Explanations and Units:

Variable	Meaning	Unit	Typical Range
Latitude	Geographical latitude of the observer	Degrees (°)	-90 to +90
Longitude	Geographical longitude of the observer	Degrees (°)	-180 to +180
Date	Specific date of observation	YYYY-MM-DD	Any valid date
Time	Local time of observation	HH:MM	00:00 to 23:59
Time Zone Offset	Difference from Coordinated Universal Time (UTC)	Hours	-12 to +14
N	Day of the year	Integer	1 to 366
δ (Declination Angle)	Angle of the Sun north or south of the equator	Degrees (°)	-23.45 to +23.45
EoT (Equation of Time)	Difference between apparent and mean solar time	Minutes	-14 to +16
H (Hour Angle)	Angular distance of the Sun from the local meridian	Degrees (°)	-180 to +180
θ (Zenith Angle)	Angle between the Sun and the vertical	Degrees (°)	0 to 180
α (Elevation Angle)	Angle between the Sun and the horizontal	Degrees (°)	-90 to +90

Practical Examples of Using the Sun Elevation Calculator

Example 1: Solar Panel Optimization in Phoenix, Arizona

A homeowner in Phoenix, Arizona, wants to install solar panels and needs to understand the Sun’s elevation throughout the year to optimize their tilt angle. They are particularly interested in the peak sun angle during summer and winter.

• Location: Phoenix, Arizona
• Latitude: 33.4484° N
• Longitude: -112.0740° W
• Time Zone Offset: -7 hours (MST, no daylight saving in most of AZ)

Scenario A: Summer Solstice (June 21st, 12:00 PM local time)

• Date: 2024-06-21
• Time: 12:00
• Inputs: Latitude: 33.4484, Longitude: -112.0740, Date: 2024-06-21, Time: 12:00, Time Zone Offset: -7
• Outputs (approximate):
  • Sun Elevation Angle: ~79.5°
  • Zenith Angle: ~10.5°
  • Declination Angle: ~23.4°
  • Hour Angle: ~-0.5° (very close to solar noon)
• Interpretation: The Sun is very high in the sky, almost directly overhead. Solar panels should be tilted at a shallow angle (or even flat) to capture maximum summer sun.

Scenario B: Winter Solstice (December 21st, 12:00 PM local time)

• Date: 2024-12-21
• Time: 12:00
• Inputs: Latitude: 33.4484, Longitude: -112.0740, Date: 2024-12-21, Time: 12:00, Time Zone Offset: -7
• Outputs (approximate):
  • Sun Elevation Angle: ~32.7°
  • Zenith Angle: ~57.3°
  • Declination Angle: ~-23.4°
  • Hour Angle: ~-0.5°
• Interpretation: The Sun is much lower in the sky during winter. Solar panels would benefit from a steeper tilt angle to be more perpendicular to the Sun’s rays and maximize winter energy production.

Example 2: Architectural Shading in Sydney, Australia

An architect is designing a building in Sydney and needs to ensure adequate shading for south-facing windows during the summer months to prevent overheating, while allowing winter sun for warmth.

• Location: Sydney, Australia
• Latitude: -33.8688° S
• Longitude: 151.2093° E
• Time Zone Offset: +10 hours (AEST)

Scenario A: Summer (January 15th, 2:00 PM local time)

• Date: 2025-01-15
• Time: 14:00
• Inputs: Latitude: -33.8688, Longitude: 151.2093, Date: 2025-01-15, Time: 14:00, Time Zone Offset: +10
• Outputs (approximate):
  • Sun Elevation Angle: ~60.1°
  • Zenith Angle: ~29.9°
  • Declination Angle: ~-21.0°
  • Hour Angle: ~30.0°
• Interpretation: In the Southern Hemisphere, the Sun is high in the northern sky during summer. A high elevation angle means deep overhangs or vertical fins would be effective for shading south-facing windows (which face north in the Southern Hemisphere).

Scenario B: Winter (July 15th, 10:00 AM local time)

• Date: 2025-07-15
• Time: 10:00
• Inputs: Latitude: -33.8688, Longitude: 151.2093, Date: 2025-07-15, Time: 10:00, Time Zone Offset: +10
• Outputs (approximate):
  • Sun Elevation Angle: ~26.5°
  • Zenith Angle: ~63.5°
  • Declination Angle: ~21.5°
  • Hour Angle: ~-30.0°
• Interpretation: During winter, the Sun is much lower in the northern sky. The lower elevation angle means that the same overhangs that provided summer shade would allow beneficial winter sun to penetrate, aiding passive heating.

How to Use This Sun Elevation Calculator

Our Sun Elevation Calculator is designed for ease of use, providing quick and accurate results. Follow these simple steps to get your solar elevation angle:

Step-by-Step Instructions:

1. Enter Latitude (degrees): Input the geographical latitude of your location. Positive values are for the Northern Hemisphere, negative for the Southern Hemisphere. You can find this using online maps or GPS.
2. Enter Longitude (degrees): Input the geographical longitude of your location. Positive values are for East of the Prime Meridian, negative for West.
3. Select Date: Use the date picker to choose the specific date for which you want to calculate the Sun’s elevation.
4. Enter Time (HH:MM): Input the local time in 24-hour format (e.g., 14:30 for 2:30 PM).
5. Enter Time Zone Offset (hours from UTC): Provide your local time zone’s offset from Coordinated Universal Time (UTC). For example, Eastern Standard Time (EST) is -5, Central European Time (CET) is +1. Remember to adjust for Daylight Saving Time if applicable (e.g., EDT is -4).
6. View Results: As you enter or change values, the calculator will automatically update the “Sun Elevation Angle” and other intermediate values in real-time.
7. Use Reset Button: If you wish to clear all inputs and start over with default values, click the “Reset” button.
8. Copy Results: Click the “Copy Results” button to copy the main result, intermediate values, and key assumptions to your clipboard for easy sharing or record-keeping.

How to Read Results:

• Sun Elevation Angle: This is the primary result, indicating the angle of the Sun above the horizon. A positive value means the Sun is visible, 0° means it’s at the horizon (sunrise/sunset), and a negative value means it’s below the horizon.
• Zenith Angle: The angle from directly overhead (zenith) to the Sun. It’s 90° minus the elevation angle. A smaller zenith angle means the Sun is higher in the sky.
• Declination Angle: Shows how far north or south of the celestial equator the Sun is. Positive in Northern Hemisphere summer, negative in Southern Hemisphere summer.
• Hour Angle: Represents the angular distance of the Sun from your local meridian. 0° at solar noon, negative before noon, positive after noon.
• Equation of Time: The difference between clock time and solar time, in minutes.

Decision-Making Guidance:

The results from the Sun Elevation Calculator can inform various decisions:

• Solar Panel Installation: Aim for the highest average elevation angle during peak energy demand seasons.
• Building Design: Use high summer elevation angles to design effective shading, and low winter angles to maximize passive solar heating.
• Photography: Plan shoots around specific elevation angles for desired lighting effects (e.g., low angles for dramatic shadows).
• Gardening: Understand sun exposure patterns to place plants that thrive in full sun or partial shade.

Key Factors That Affect Sun Elevation Calculator Results

The Sun’s elevation angle is a dynamic value influenced by several astronomical and geographical factors. Understanding these factors is key to interpreting the results from any Sun Elevation Calculator.

• Latitude:

  This is the most significant geographical factor. Locations closer to the equator (0° latitude) experience higher average sun elevation angles throughout the year, with the Sun often passing directly overhead (zenith angle of 0°, elevation of 90°). As you move towards the poles (90° N or S), the maximum sun elevation angle decreases, leading to longer shadows and less direct sunlight. For example, at the poles, the maximum elevation is never more than 23.45 degrees.

• Date (Day of Year):

  The Earth’s axial tilt (approximately 23.45°) and its orbit around the Sun cause the solar declination angle to change throughout the year. This change directly impacts the Sun’s elevation. The Sun is highest in the sky during the summer solstice (around June 21st in the Northern Hemisphere, December 21st in the Southern Hemisphere) and lowest during the winter solstice (around December 21st in the Northern Hemisphere, June 21st in the Southern Hemisphere).

• Time of Day:

  The Sun’s elevation angle changes continuously throughout the day. It is 0° at sunrise, gradually increases to its maximum at solar noon, and then decreases back to 0° at sunset. Before sunrise and after sunset, the elevation angle is negative, indicating the Sun is below the horizon.

• Longitude:

  While latitude determines the general height of the Sun, longitude affects the precise timing of solar events like solar noon. Because time zones are broad, your specific longitude within a time zone determines how much your local clock time deviates from true solar time. This is accounted for in the “True Solar Time” calculation within the Sun Elevation Calculator.

• Time Zone Offset (from UTC):

  This factor is crucial for converting your local clock time into a universal time reference (like UTC) and then back into true solar time. An incorrect time zone offset will lead to inaccurate hour angle calculations and thus incorrect elevation angles, especially regarding the timing of solar noon.

• Atmospheric Refraction:

  The Earth’s atmosphere bends sunlight, making celestial objects appear slightly higher in the sky than they actually are. This effect is most pronounced when the Sun is near the horizon. While small, a precise Sun Elevation Calculator includes a correction for atmospheric refraction to provide more accurate results, particularly for sunrise and sunset times.

Frequently Asked Questions (FAQ) About Sun Elevation

Q1: What is the difference between Sun Elevation and Solar Azimuth?

A1: Sun Elevation (or solar altitude) is the vertical angle of the Sun above the horizon (0° to 90°). Solar Azimuth is the horizontal angle of the Sun’s position, measured clockwise from true North (0° to 360°). Both are needed to fully describe the Sun’s position in the sky.

Q2: Why is the Sun’s elevation not always highest at 12:00 PM local time?

A2: Solar noon, the moment of highest sun elevation, rarely aligns with 12:00 PM local clock time due to three main reasons: 1) The Equation of Time, which accounts for variations in Earth’s orbital speed and axial tilt. 2) Your specific longitude within your time zone. 3) Daylight Saving Time adjustments.

Q3: Can this Sun Elevation Calculator predict sunrise and sunset times?

A3: While this calculator directly calculates the elevation angle, you can infer sunrise and sunset by finding the times when the elevation angle is approximately 0 degrees. However, dedicated Sunrise Sunset Times calculators are optimized for this specific task and often include more precise atmospheric refraction models.

Q4: How does the Earth’s tilt affect sun elevation?

A4: The Earth’s axial tilt of about 23.45 degrees is the primary reason for seasons and the annual variation in solar declination. This tilt causes different parts of the Earth to receive more direct sunlight at different times of the year, directly impacting the maximum sun elevation angle experienced at any given latitude.

Q5: Is the Sun Elevation Calculator accurate for all locations, including the poles?

A5: Yes, the underlying astronomical formulas are generally valid for all latitudes. However, at extreme latitudes (near the poles), the Sun may remain above or below the horizon for extended periods (polar day/night), and the concept of “sunrise” or “sunset” becomes less distinct for certain times of the year.

Q6: What is the significance of a negative sun elevation angle?

A6: A negative sun elevation angle means the Sun is below the horizon. While not directly visible, the sky can still be illuminated (twilight) even with negative elevation angles, depending on how far below the horizon the Sun is (e.g., civil, nautical, astronomical twilight).

Q7: How often should I use a Sun Elevation Calculator for solar panel planning?

A7: For initial planning, calculating elevation for solstices (summer and winter) and equinoxes (spring and autumn) provides a good overview of seasonal variations. For fine-tuning, you might check monthly or even hourly data for critical periods to ensure optimal performance of your solar panel angle.

Q8: Can I use this calculator to determine shadow lengths?

A8: Yes, the sun elevation angle is a direct input for calculating shadow lengths. The formula is typically `Shadow Length = Object Height / tan(Elevation Angle)`. You can use the elevation angle from this calculator in conjunction with a Shadow Length Calculator.

Related Tools and Internal Resources

Explore our other specialized calculators and resources to further your understanding of solar geometry and related topics:

• Solar Azimuth Calculator: Determine the Sun’s horizontal direction (azimuth) for any location and time.
• Solar Noon Calculator: Find the exact time when the Sun reaches its highest point in the sky for your location.
• Day Length Calculator: Calculate the duration of daylight hours for any given date and location.
• Sunrise Sunset Times Calculator: Get precise sunrise and sunset times, including twilight phases.
• Solar Panel Angle Calculator: Optimize the tilt angle of your solar panels for maximum energy generation.
• Shadow Length Calculator: Calculate the length of shadows cast by objects based on sun elevation.