Calculate solar altitude, azimuth, zenith angle, and shadow length for any location, date, and time. Includes hourly sun path table.
The position of the sun in the sky is determined by three factors: your latitude, the time of day, and the day of the year. The solar altitude (elevation angle) measures how high the sun sits above the horizon, while the azimuth indicates its compass direction. Together, these angles define shadows, solar panel tilt, building orientation, and daylight quality.
At solar noon, the sun reaches its highest altitude, which equals 90° minus the latitude plus or minus the solar declination (±23.45° over the year). In summer at 40°N latitude, the sun reaches about 73°; in winter, only 27°. This dramatic difference drives seasonal heating patterns and is the reason buildings need different shading strategies for summer vs. winter.
The equation of time — a correction up to ±16 minutes — accounts for Earth's elliptical orbit and axial tilt, which cause solar noon to differ from clock noon. This calculator computes precise solar angles at any location and time, useful for architects, solar engineers, photographers, and anyone who works with natural light.
Architects use sun angles for shading design and natural lighting. Solar installers optimize panel tilt and orientation. Photographers plan golden-hour shoots. Gardeners determine sunny vs. shaded areas. This calculator serves all these needs with precise solar geometry.
This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Solar declination: δ = 23.45° × sin(360/365 × (284+N)). Hour angle: H = 15°(t − t_solar_noon). Altitude: sin(α) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H). Azimuth: cos(Az) = (sin(δ) − sin(φ)sin(α))/(cos(φ)cos(α)).
Result: Altitude: 72.5°, Azimuth: 177°
In New York on June 21 (summer solstice) at noon: declination ≈ 23.45°, maximum altitude = 90 − 40.71 + 23.45 ≈ 72.7°. Near solar noon, sun is almost due south.
Use consistent units throughout your calculation and verify all assumptions before treating the output as final. For professional or academic work, document your input values and any conversion standards used so results can be reproduced. Apply this calculator as part of a broader workflow, especially when the result feeds into a larger model or report.
Most mistakes come from mixed units, rounding too early, or misread labels. Recheck each final value before use. Pay close attention to sign conventions — positive and negative inputs often produce very different results. When working with multiple related calculations, keep intermediate values available so you can trace discrepancies back to their source.
Enter the most precise values available. Use the worked example or presets to confirm the calculator behaves as expected before entering your real data. If a result seems unexpected, compare it against a manual estimate or a known reference case to catch input errors early.
A correction factor (±16 minutes) that accounts for Earth's elliptical orbit and 23.45° axial tilt. It's why a sundial doesn't match a clock exactly.
Panels produce maximum power when perpendicular to sunlight. The optimal tilt angle approximately equals your latitude so panels face the sun at noon in equinoxes.
Jan 1 = 1, Feb 1 = 32, Mar 21 (equinox) ≈ 80, Jun 21 (solstice) ≈ 172, Sep 22 (equinox) ≈ 265, Dec 21 (solstice) ≈ 355. Use this as a practical reminder before finalizing the result.
The horizontal compass direction of the sun, measured clockwise from true North. 0° = North, 90° = East, 180° = South, 270° = West.
Only between the tropics (23.45°N to 23.45°S). At these latitudes, the sun passes through zenith (altitude = 90°) twice per year.
Air mass describes how much atmosphere sunlight passes through. AM1 = sun at zenith, AM1.5 = altitude 42° (standard for solar testing), AM2 = altitude 30°.