Sun Angle Calculator
Calculate solar elevation, azimuth, shadow length, and inter-row spacing for any US location and date using NOAA algorithms — free solar design tool, no signup.
Sun Angle & Solar Position Calculator
Enter your location and date/time. Get solar altitude, azimuth, hour angle, declination, solar noon, sunrise/sunset times, and optimal panel tilt angle.
Not observed in AZ or HI
Height of obstruction near the array (tree, building, fence)
Row spacing calculated for no shade at winter solstice noon.
- 🌅 Sunrise--
- ☀ Solar Noon--
- 🌇 Sunset--
- 📏 Day Length--
- Noon Elevation--
| Metric | Summer (Jun 21) | Equinox (Mar 20) | Winter (Dec 21) |
|---|---|---|---|
| Noon Elevation | -- | -- | -- |
| Sunrise | -- | -- | -- |
| Sunset | -- | -- | -- |
| Day Length | -- | -- | -- |
| Shadow (10 ft obj) | -- | -- | -- |
| Time | Elevation | Azimuth | Shadow Len | Air Mass | Status |
|---|
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What This Tool Covers
The Sun Angle Calculator computes the precise position of the sun for any location, date, and time. It outputs solar altitude, azimuth, hour angle, declination, solar noon, sunrise/sunset times, and the optimal panel tilt for the selected date - giving installers and engineers the geometric data needed for shading analysis, panel orientation design, and site assessments.
Inputs You Provide
- • Latitude and longitude (decimal degrees)
- • Or select US state and city from dropdown
- • Date (month, day, year)
- • Time of day (local solar time)
Outputs You Get
- • Solar altitude angle (elevation above horizon)
- • Solar azimuth angle (compass direction)
- • Hour angle and solar declination
- • Solar noon time for the location and date
- • Sunrise and sunset times
- • Optimal panel tilt angle for that date
- • Panel production factor relative to optimal
Features
Goes beyond basic sunrise/sunset apps - outputs the engineering values needed for solar design calculations and shading assessments.
Altitude & Azimuth at Any Time
Calculate exact sun position for any minute of any day - essential for determining whether a specific obstruction casts shade on panels at critical times.
Solar Noon & Day Length
Find true solar noon (when the sun reaches maximum altitude) and total daylight hours - both vary by location and season and affect daily energy production windows.
Date-Optimal Tilt Angle
Outputs the ideal panel tilt for the selected date based on sun declination - useful for adjustable-tilt ground mount systems and seasonal tilt optimization guides.
How It Works
Uses astronomical algorithms (Spencer 1971, Iqbal 1983) to calculate sun position from latitude, longitude, and time.
Enter Location
Input latitude and longitude in decimal degrees, or select your US state and city. Longitude determines the offset between solar time and clock time at your location.
Select Date
Choose the date. Solar declination - the angle between the sun and Earth's equatorial plane - changes throughout the year, reaching +23.45° at the June solstice and −23.45° at the December solstice.
Select Time of Day
Enter local solar time (or clock time with timezone offset). The hour angle is calculated from solar noon - it is 0° at noon, −90° at sunrise, and +90° at sunset for an equatorial location.
Calculate Sun Position
The algorithm computes solar altitude (elevation) and azimuth from latitude, declination, and hour angle using spherical trigonometry. Results are accurate to within 0.1° for most practical applications.
Use Cases
Shading Obstruction Analysis
Determine exactly when a nearby tree, chimney, or building casts shade on a roof by comparing its obstruction angle with the sun's altitude and azimuth at that hour. Avoid panels in shade zones that lose significant winter production.
Optimal Tilt Angle Design
Find the best fixed tilt for a ground mount or flat roof installation. Run the calculator for the winter and summer solstice to determine the tilt that balances annual production across both seasons.
Solar Resource Verification
Verify that an installation site has sufficient unobstructed sun hours between 9am–3pm solar time, which accounts for the majority of daily energy production at most US latitudes.
Calculation Methodology
Standard astronomical solar position equations used in NREL tools, PVWatts, and IEC 61724.
Solar Declination
δ = 23.45 × sin(360/365 × (284 + Day of Year))
Declination is the angle of the sun north or south of Earth's equator. It drives all seasonal variation in sun position and optimal tilt angle.
Solar Altitude (Elevation)
sin(α) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H)
Where φ = latitude, δ = declination, H = hour angle. Altitude of 0° is the horizon; 90° is directly overhead (only at equatorial locations at equinox solar noon).
Solar Azimuth
cos(Az) = (sin(δ) − sin(α)sin(φ)) ÷ (cos(α)cos(φ))
Azimuth is the compass direction of the sun measured from true north. South is 180° in the Northern Hemisphere. The sun traces an arc from east to west each day.
Optimal Tilt for Date
Optimal Tilt = Latitude − Declination
This gives the tilt that maximizes irradiance on the given date. In summer (positive declination), optimal tilt is lower than latitude; in winter (negative), it is higher.
Pro Tips
Check December 21 at 9am and 3pm for Worst-Case Shading
The winter solstice gives the lowest sun altitude of the year. If there's no shading issue on December 21 at 9am and 3pm solar time, the site is clear year-round. This is the standard check for northern installations.
Solar Noon Is Rarely at 12:00 PM Clock Time
Solar noon occurs when the sun crosses the local meridian - which almost never coincides with 12:00 PM on the clock due to timezone boundaries and daylight saving time. Use the calculator's solar noon output, not clock noon, when timing site visits for shading checks.
Altitude Below 10° Contributes Little Energy
When solar altitude is below 10°, the sun passes through 5–10× more atmosphere (high air mass), dropping irradiance dramatically. Don't stress over shading during the first and last hour of the day - that production is minimal.
Use the Equinox Date for Year-Round Average Tilt
Run the calculator on March 21 (spring equinox) to find the tilt that best represents year-round average sun position. At the equinox, declination is 0°, so optimal tilt equals latitude - confirming the common rule of thumb.
Frequently Asked Questions
What is solar altitude angle?
Solar altitude (also called solar elevation) is the angle between the sun and the horizon. At 0°, the sun is on the horizon (sunrise/sunset). At 90°, the sun is directly overhead. In the US, maximum altitude at solar noon ranges from about 25° in winter (Alaska) to 85° in summer (southern states).
What is solar azimuth angle?
Solar azimuth is the compass direction of the sun, measured clockwise from true north. East is 90°, south is 180°, west is 270°. In the Northern Hemisphere, the sun always transits through the southern sky. An azimuth below 180° means the sun is in the southeast (morning); above 180° means southwest (afternoon).
What is the difference between solar time and clock time?
Solar time is based on the actual position of the sun. Clock time is a standardized zone offset from UTC. The difference depends on your longitude within the timezone and the equation of time (a calendar correction). Solar noon can differ from 12:00 PM clock time by 15–45 minutes depending on location.
Why does optimal tilt change by season?
The sun is higher in the sky in summer (up to 23.45° north of the equator) and lower in winter (up to 23.45° south of the equator). To point panels perpendicular to the sun - maximum irradiance - tilt must increase in winter and decrease in summer. Fixed-tilt systems use an annual average; adjustable systems capture seasonal gains.
What is hour angle?
Hour angle measures how far the sun has traveled across the sky from solar noon. It advances 15° per hour (360° in 24 hours). At solar noon, hour angle = 0°. At 9:00 AM solar time, hour angle = −45°. At 3:00 PM solar time, hour angle = +45°. Hour angle is used directly in altitude and azimuth calculations.
How does this differ from a shading analysis tool?
The Sun Angle Calculator gives you the position of the sun for a specific time and date - it's an input to shading analysis. A full shading analysis tool takes 3D site geometry (tree heights, building distances, panel positions) and computes how much shade falls on panels throughout the year. Use the sun angle data here to manually assess specific obstructions.
Can this tool help me determine if a site will meet the 4-hour rule?
Yes. Some utilities and incentive programs require at least 4 peak sun hours of unobstructed exposure between 9am–3pm solar time. Use the altitude and azimuth outputs to check whether obstructions fall within the sun's path during those hours on the critical dates (winter solstice for worst-case).
Related Tools
Shading Analysis Tool
Estimate production loss from shading obstructions at your site.
Solar Power Calculator
Calculate energy production for a system at any tilt and azimuth.
Irradiance Estimator
Look up monthly irradiance and peak sun hours by location.
Roof Pitch Calculator
Convert roof pitch to degrees for tilt angle input.
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