Solar Position Calculator

Calculate the sun's exact position including azimuth, elevation, and solar angles for any location and time.

Determine the sun's position in the sky using precise astronomical calculations. Essential for solar energy systems, architectural design, agriculture, and navigation applications.

Examples

Click on any example to load it into the calculator.

New York City - Summer Solstice

newyork

Calculate sun position for New York City during summer solstice at noon.

Latitude: 40.7128°

Longitude: -74.0060°

Date: 2024-06-21

Time: 12:00

Timezone: -5h

London - Winter Solstice

london

Calculate sun position for London during winter solstice at sunrise.

Latitude: 51.5074°

Longitude: -0.1278°

Date: 2024-12-21

Time: 08:00

Timezone: 0h

Tokyo - Spring Equinox

tokyo

Calculate sun position for Tokyo during spring equinox at sunset.

Latitude: 35.6762°

Longitude: 139.6503°

Date: 2024-03-20

Time: 18:00

Timezone: 9h

Sydney - Autumn Equinox

sydney

Calculate sun position for Sydney during autumn equinox at midday.

Latitude: -33.8688°

Longitude: 151.2093°

Date: 2024-09-22

Time: 12:00

Timezone: 10h

Other Titles
Understanding Solar Position Calculation: A Comprehensive Guide
Master the science of solar positioning and learn how to calculate the sun's exact location in the sky for any time and place. Essential knowledge for solar energy, architecture, agriculture, and navigation.

What is Solar Position Calculation?

  • Core Concepts
  • Why It Matters
  • Astronomical vs. Solar Time
Solar position calculation is the mathematical process of determining the sun's exact location in the sky at any given time and location on Earth. This involves calculating two primary angles: the azimuth angle (horizontal direction from north) and the elevation angle (vertical height above the horizon). These calculations are based on fundamental astronomical principles including Earth's rotation, orbital motion around the sun, and the tilt of Earth's axis.
The Importance of Solar Position
Understanding solar position is crucial for numerous applications. Solar energy systems need to track the sun's movement to maximize energy collection. Architects use solar position data to design buildings that optimize natural lighting and heating. Farmers rely on sun position for crop planning and irrigation timing. Navigators use solar position for celestial navigation. Even everyday activities like photography and outdoor recreation benefit from knowing the sun's position.
Key Solar Position Parameters
The solar position is defined by several interconnected parameters. The azimuth angle measures the sun's horizontal position relative to true north, ranging from 0° (north) through 90° (east), 180° (south), and 270° (west). The elevation angle measures the sun's height above the horizon, from 0° (horizon) to 90° (directly overhead). The solar angle combines both to give a complete 3D position vector. Additionally, day length calculations determine sunrise and sunset times.
Astronomical vs. Solar Time
Solar position calculations must account for the difference between clock time and true solar time. Earth's elliptical orbit and axial tilt cause variations in solar time throughout the year. The Equation of Time correction adjusts for these variations, ensuring accurate solar position calculations regardless of the date. This is why the same clock time on different dates can result in significantly different solar positions.

Solar Position Applications:

  • Solar Energy: Optimizing panel orientation and tracking systems for maximum energy production
  • Architecture: Designing buildings with optimal natural lighting and passive solar heating
  • Agriculture: Planning crop planting, irrigation, and harvesting based on solar patterns
  • Navigation: Using celestial navigation techniques for maritime and aviation applications
  • Photography: Planning outdoor shoots with optimal lighting conditions

Step-by-Step Guide to Using the Calculator

  • Gathering Location Data
  • Inputting Time Information
  • Interpreting Results
Using the solar position calculator requires accurate input data to ensure precise results. Follow these steps carefully to obtain reliable solar position information for your specific needs.
1. Determine Your Exact Location
Start by finding your precise latitude and longitude coordinates. Use GPS devices, online mapping services, or geographic databases to obtain coordinates in decimal degrees format. Latitude ranges from -90° (South Pole) to +90° (North Pole), while longitude ranges from -180° (Western Hemisphere) to +180° (Eastern Hemisphere). Ensure you're using the WGS84 coordinate system for maximum accuracy.
2. Specify the Date and Time
Enter the date in YYYY-MM-DD format and the time in 24-hour HH:MM format. Use local time for your location, as the calculator will apply the appropriate timezone offset. Consider the specific application: for solar energy systems, you might want multiple calculations throughout the day; for architectural design, you might focus on specific seasons or times of day.
3. Set the Correct Timezone
Enter your timezone offset from UTC (Coordinated Universal Time). This is crucial for accurate calculations, as solar position depends on true solar time, not clock time. Common offsets include EST (-5), CET (+1), JST (+9), and AEST (+10). The calculator uses this offset to convert your local time to the appropriate astronomical time for calculations.
4. Analyze and Apply the Results
The calculator provides comprehensive solar position data. The azimuth angle tells you the sun's compass direction, useful for orienting solar panels or planning outdoor activities. The elevation angle indicates the sun's height, affecting shadow length and solar intensity. The solar angle combines both for complete positioning. Day length information helps with planning activities and understanding seasonal variations.

Optimal Solar Panel Angles by Season:

  • Spring (March-May): Tilt angle = latitude × 0.93 - 21°
  • Summer (June-August): Tilt angle = latitude × 0.93 - 2.3°
  • Autumn (September-November): Tilt angle = latitude × 0.93 + 21°
  • Winter (December-February): Tilt angle = latitude × 0.93 + 29°

Real-World Applications and Practical Uses

  • Solar Energy Systems
  • Architectural Design
  • Agricultural Planning
Solar position calculations have numerous practical applications that impact our daily lives and technological systems. Understanding these applications helps optimize various processes and systems for maximum efficiency and effectiveness.
Solar Energy System Optimization
Solar photovoltaic and thermal systems rely heavily on accurate solar position data. Fixed solar panels are typically oriented to maximize annual energy production, often facing south in the Northern Hemisphere with a tilt angle approximately equal to the local latitude. Tracking systems use real-time solar position data to continuously adjust panel orientation, potentially increasing energy production by 25-40%. The calculator helps determine optimal fixed orientations and validate tracking system performance.
Architectural and Building Design
Architects use solar position data to design buildings that maximize natural lighting while minimizing unwanted heat gain. This includes positioning windows, designing overhangs and shading devices, and planning building orientation. Passive solar design principles rely on understanding seasonal solar patterns to optimize heating and cooling. The calculator helps architects model solar access throughout the year and design accordingly.
Agricultural and Horticultural Applications
Farmers and horticulturists use solar position data for crop planning, irrigation scheduling, and greenhouse management. Understanding solar patterns helps optimize planting times, determine crop spacing for maximum light exposure, and plan irrigation systems that work with natural solar cycles. Greenhouse operators use solar position data to optimize glazing angles and shading systems for year-round production.

Common Misconceptions and Solar Myths

  • Seasonal Variations
  • Geographic Differences
  • Time Zone Effects
Several misconceptions exist about solar position and its calculation. Understanding these myths helps ensure accurate calculations and proper application of solar position data.
Myth: The Sun is Always Directly South at Noon
This is only true at the equator during equinoxes. Due to Earth's axial tilt and elliptical orbit, the sun's position at solar noon varies throughout the year and by latitude. In the Northern Hemisphere, the sun appears south of the zenith (directly overhead point) except during summer months at high latitudes. The Equation of Time correction accounts for these variations, ensuring accurate solar position calculations.
Myth: Solar Position is the Same Everywhere at the Same Time
Solar position varies significantly with geographic location. Even small differences in latitude and longitude can result in noticeable variations in solar angles. This is why precise coordinates are essential for accurate calculations. Additionally, local atmospheric conditions, terrain, and elevation can affect the apparent solar position, though these are typically minor factors in most applications.
Myth: Daylight Saving Time Affects Solar Position
Daylight saving time changes clock time but doesn't affect the actual solar position. The sun's position is determined by astronomical factors, not human timekeeping conventions. However, daylight saving time does affect when we observe the sun at specific clock times. The calculator accounts for this by using the timezone offset to convert between local clock time and true solar time.

Expert Tip:

  • For maximum accuracy in solar energy applications, consider calculating solar position at multiple times throughout the day and year to account for seasonal variations and optimize system performance.

Mathematical Derivation and Advanced Concepts

  • Astronomical Algorithms
  • Coordinate Transformations
  • Precision Considerations
Solar position calculations are based on sophisticated astronomical algorithms that account for Earth's complex orbital and rotational dynamics. Understanding the underlying mathematics helps appreciate the precision and limitations of solar position calculations.
Fundamental Astronomical Parameters
Solar position calculations begin with fundamental astronomical parameters including Earth's orbital elements, axial tilt (obliquity), and rotational characteristics. The Julian Day Number provides a continuous time scale for astronomical calculations, while the Equation of Time accounts for variations in solar time due to Earth's elliptical orbit and axial tilt. These parameters are used to calculate the sun's apparent position in the sky.
Coordinate System Transformations
Solar position calculations involve transformations between different coordinate systems. The sun's position is first calculated in celestial coordinates (right ascension and declination), then transformed to horizontal coordinates (azimuth and elevation) for a specific location and time. This requires knowledge of the observer's latitude, longitude, and the local sidereal time, which relates Earth's rotation to the celestial sphere.
Precision and Accuracy Considerations
Solar position calculations can achieve high precision, typically within 0.01° for most applications. However, accuracy depends on the quality of input data and the specific algorithm used. Factors affecting accuracy include atmospheric refraction (especially near the horizon), parallax effects, and variations in Earth's orbital parameters. For most practical applications, the precision provided by standard algorithms is more than adequate.

Key Mathematical Formulas:

  • Solar Declination: δ = 23.45° × sin(360° × (284 + day_of_year) / 365)
  • Hour Angle: H = 15° × (solar_time - 12)
  • Elevation Angle: α = arcsin(sin(φ) × sin(δ) + cos(φ) × cos(δ) × cos(H))
  • Azimuth Angle: A = arctan2(sin(H), cos(H) × sin(φ) - tan(δ) × cos(φ))