Solar Position
Sun position from latitude, date, and time. Elevation α from sin(α)=sin(φ)sin(δ)+cos(φ)cos(δ)cos(h). Declination δ varies ±23.45° yearly. Shadow length = H/tan(α).
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Declination ±23.45°: solstices. Optimal panel tilt ≈ latitude ± seasonal. Golden hour: elevation 0–6°. Air mass 2: ~25% less radiation.
Ready to run the numbers?
Why: Solar position determines panel tilt, shadow analysis, photography timing, and solar energy potential. Declination causes seasons.
How: Declination from day of year. Hour angle from local solar time. Elevation and azimuth from spherical trigonometry. Equation of time corrects clock vs. solar time.
Run the calculator when you are ready.
⚙️ Input Parameters
Location
Date & Time
Optional
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Elevation: angle above horizon
— Solar position
Declination: Sun angular distance from equator
— Astronomy
Shadow length = height/tan(elevation)
— Geometry
Air mass: path length through atmosphere
— Atmospheric optics
Key Takeaways
- •Solar elevation ranges from -90° (below horizon) to 90° (zenith). At solar noon, elevation = 90° - |latitude - declination|
- •Solar declination varies ±23.45° throughout the year, causing seasons. Maximum on June 21 (summer solstice), minimum on December 21 (winter solstice)
- •Shadow length = object height / tan(elevation). Longer shadows occur at lower elevations (morning/evening and winter)
- •Air mass measures atmospheric path length. AM = 1 at zenith, increases as elevation decreases, affecting solar radiation intensity
- •Optimal solar panel tilt ≈ latitude ± seasonal adjustment. For year-round: latitude; for summer: latitude - 15°; for winter: latitude + 15°
Did You Know?
☀️ Solar Noon Variation
Solar noon (when sun reaches highest point) can differ from clock noon by up to 16 minutes due to the equation of time. This is caused by Earth's elliptical orbit and axial tilt!
🌍 Polar Day/Night
Above the Arctic Circle (66.5°N), the sun never sets during summer solstice and never rises during winter solstice. This creates 24-hour daylight or darkness!
📸 Golden Hour Magic
Golden hour occurs when solar elevation is between 0° and 6° above horizon. The low angle creates warm, diffused light perfect for photography - typically 1 hour after sunrise and 1 hour before sunset!
🔋 Solar Panel Efficiency
Solar panels produce maximum power when sunlight hits perpendicularly (elevation = 90° - panel tilt). At 30° elevation, power drops to ~50% compared to perpendicular incidence!
🏗️ Architecture Shadow Analysis
Buildings cast shadows 3-5× longer in winter than summer at mid-latitudes. Understanding sun angles helps architects design for natural lighting and energy efficiency!
🌡️ Air Mass Impact
When solar elevation is 30°, air mass = 2.0, meaning sunlight passes through twice the atmosphere compared to zenith. This reduces solar radiation intensity by ~25%!
How It Works
The sun angle calculator uses spherical trigonometry to determine the Sun's position in the sky based on location (latitude/longitude), date, and time. The algorithm follows the standard solar position equations verified by NOAA and astronomical references.
1. Solar Declination Calculation
Declination (δ) represents the Sun's angular distance from the celestial equator. It varies sinusoidally throughout the year: δ = 23.45° × sin(360/365 × (284 + day_of_year)). This accounts for Earth's 23.45° axial tilt.
2. Equation of Time
Due to Earth's elliptical orbit and axial tilt, solar time differs from clock time. The equation of time correction accounts for this difference, which can be up to ±16 minutes.
3. Hour Angle
Hour angle (h) measures how far the Sun has moved from solar noon. h = 15° × (local_solar_time - 12). At solar noon, h = 0°; morning is negative, afternoon is positive.
4. Solar Elevation
Elevation angle (α) is calculated using: sin(α) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(h), where φ is latitude, δ is declination, and h is hour angle. This formula comes from spherical trigonometry.
5. Solar Azimuth
Azimuth angle (A) indicates compass direction: cos(A) = [sin(δ) - sin(α)sin(φ)] / [cos(α)cos(φ)]. Azimuth is measured clockwise from North (0° = North, 90° = East, 180° = South, 270° = West).
Expert Tips
💡 Solar Panel Installation
Set panel tilt = latitude for year-round optimization. Adjust ±15° seasonally: subtract for summer, add for winter. Face panels true south (not magnetic south) in Northern Hemisphere.
📸 Photography Timing
Golden hour: elevation 0-6° (1 hour after sunrise/before sunset). Blue hour: elevation -4° to -6° (20-30 min before sunrise/after sunset). Use sun angle calculator to plan shoots!
🏗️ Architecture Design
Calculate shadow lengths at different times/seasons to optimize window placement, overhangs, and building orientation. Winter shadows are longest - design accordingly for passive solar heating.
🌱 Agriculture & Gardening
Use sun path diagrams to plan crop spacing, greenhouse orientation, and shade structures. Maximize sunlight exposure during growing season by understanding daily sun paths.
Solar Angles Comparison
| Location | Summer Solstice Noon | Winter Solstice Noon | Equinox Noon |
|---|---|---|---|
| Equator (0°) | 66.55° | 66.55° | 90° ✅ |
| New York (40.7°N) | 72.85° ✅ | 25.85° | 49.3° |
| London (51.5°N) | 62° | 15° | 38.5° |
| Sydney (33.9°S) | 32.45° | 79.35° ✅ | 56.1° |
Frequently Asked Questions
Q1: What is the difference between solar elevation and solar altitude?
Solar elevation and solar altitude are the same thing - both refer to the angle between the Sun and the horizon. Elevation ranges from -90° (directly below) to 90° (directly overhead at zenith).
Q2: How accurate is this calculator?
This calculator uses algorithms verified against NOAA and US Naval Observatory standards. Accuracy is typically within ±0.1° for elevation and ±0.5° for azimuth. For precise astronomical work, consider atmospheric refraction corrections.
Q3: Why does solar noon differ from clock noon?
Solar noon (when sun reaches highest point) can differ from clock noon by up to 16 minutes due to the equation of time. This accounts for Earth's elliptical orbit and axial tilt. The calculator includes this correction automatically.
Q4: What is air mass and why does it matter?
Air mass (AM) measures how much atmosphere sunlight passes through. AM = 1 at zenith (sun directly overhead), increases as elevation decreases. Higher air mass reduces solar radiation intensity - AM 2.0 reduces intensity by ~25% compared to AM 1.0.
Q5: How do I find the optimal solar panel tilt angle?
For year-round optimization: tilt = latitude. For summer: tilt = latitude - 15°. For winter: tilt = latitude + 15°. Use this calculator to find maximum elevation at different times, then set panel perpendicular to that angle.
Q6: Can I use this for photography planning?
Yes! Golden hour occurs when elevation is 0-6° (typically 1 hour after sunrise/before sunset). Blue hour is at -4° to -6° elevation. Use the calculator to find exact times for your location and date.
Q7: Why are shadows longer in winter?
Shadows are longer when solar elevation is lower. In winter, declination is negative in Northern Hemisphere, reducing maximum elevation. At 30° elevation, shadows are ~1.73× object height; at 15°, shadows are ~3.73× height!
By the Numbers
Official Sources
- •NOAA Solar Calculator- Official NOAA solar position calculator
- •US Naval Observatory- Official sunrise/sunset data
- •Solar Energy International- Solar energy education and training
- •PV Education- Photovoltaic education resource
- •Astronomical Algorithms- Jean Meeus reference algorithms
Disclaimer
Important: This calculator provides theoretical solar position calculations for educational and planning purposes. For critical applications:
- Results are accurate to within ±0.1° for elevation and ±0.5° for azimuth under standard conditions
- Atmospheric refraction (typically 0.5-0.6° at horizon) is not included in calculations
- For precise astronomical observations, consult professional astronomical software
- Solar panel installations should account for local terrain, shading, and microclimates
- Architectural shadow analysis should consider surrounding structures and topography
This calculator uses algorithms verified against NOAA and US Naval Observatory standards, but results are provided "as-is" without warranty.
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