Model sun bearing precisely for any latitude. Use date-time inputs or supply declination directly fast. Get azimuth, zenith, and compass direction with confidence always.
This tool computes the solar azimuth angle (clockwise from true north) using latitude (φ), solar declination (δ), and hour angle (H). When you choose the date/time mode, δ and H are estimated from the day of year, longitude, and local time.
| Declination (approx.) | δ ≈ 23.45° · sin( 360° · (284 + n) / 365 ) |
| Equation of time (min) | EoT ≈ 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B), B = 360°(n−81)/364 |
| Time correction (min) | TC = 4(λ − LSTM) + EoT, LSTM = 15° · TZ |
| Hour angle | H = 15° · (LST − 12) |
| Zenith angle | cos θz = sinφ·sinδ + cosφ·cosδ·cosH |
| Azimuth (north‑based) | Az = ( atan2( sinH, cosH·sinφ − tanδ·cosφ ) + 180° ) mod 360° |
Notes: Approximations are suitable for engineering calculations. Use true‑north references for best alignment.
| Latitude (deg) | Longitude (deg) | Date | Time | TZ | Expected azimuth (deg) |
|---|---|---|---|---|---|
| 24.8607 | 67.0011 | 2026-01-13 | 12:00 | +5 | ~180 (near solar noon) |
| 40.7128 | -74.0060 | 2026-06-21 | 09:30 | -5 | East‑southeast |
| -33.8688 | 151.2093 | 2026-12-21 | 15:00 | +10 | West‑northwest |
| 51.5074 | -0.1278 | 2026-03-20 | 06:30 | 0 | Near east |
Example azimuths are qualitative. Exact values depend on solar time and corrections.
Solar azimuth is the compass direction of the Sun on the horizon plane. It is reported as an angle measured clockwise from true north, so it connects sky position to real‑world orientation for design and analysis.
This calculator uses the common engineering convention: north = 0°, east = 90°, south = 180°, west = 270°, and values wrap to 0–360°. The result also includes a 16‑point compass label (N, NNE, NE …) for quick reading.
Latitude (φ) should be between −90° and +90°, and longitude between −180° and +180°. When you select the declination/hour‑angle mode, declination (δ) is typically within ±23.44° over a year, and hour angle (H) is usually within about ±180° for a full day.
In date/time mode, the tool estimates solar time from your clock time using time‑zone offset, longitude, and a standard equation‑of‑time correction. Solar time matters because the Sun’s direction is governed by Earth’s rotation relative to the Sun, not by local wall‑clock time.
Declination describes how far the Sun is north or south of the equatorial plane. It drifts slowly through the seasons, reaching about +23.44° near the June solstice and −23.44° near the December solstice. That shift changes sunrise/sunset directions and the daily azimuth curve.
Hour angle converts time into rotation: H ≈ 15° × (solar time − 12). Negative H indicates morning (Sun east of the meridian) and positive H indicates afternoon (Sun west). Correct sign handling prevents mirrored azimuths.
Azimuth supports photovoltaic array alignment, solar thermal collectors, shading studies, daylighting, building orientation, and outdoor photography planning. Combined with solar elevation, it defines the full Sun vector needed for incidence angles on tilted surfaces.
For best results, use coordinates from a reliable map source, ensure the time‑zone offset matches the selected date, and interpret outputs in true‑north coordinates. If you need sub‑degree precision, consider adding atmospheric refraction and higher‑order ephemeris models.
It is the Sun’s horizontal direction, measured clockwise from true north. It tells you where to face to look toward the Sun at a specific moment and location.
A compass points to magnetic north, while solar azimuth here is referenced to true north. Local magnetic declination can cause noticeable differences, especially at higher latitudes.
Yes, if you want a better estimate. Longitude shifts solar time relative to clock time, which directly affects hour angle and therefore azimuth.
Use your UTC offset for the date you are analyzing (for example, +5). If your region changes offset seasonally, apply the correct offset for that specific day.
Azimuth can change rapidly when the Sun is low. Small time or coordinate errors may cause larger azimuth shifts, so use precise inputs and consider pairing with elevation to confirm the geometry.
It can still compute a geometric azimuth, but the Sun is not visible. For practical use, check the elevation output (if available) or use sunrise/sunset times to confirm visibility.
Compare the Sun’s azimuth with your panel’s facing direction to understand incidence and shading. For fixed systems, evaluate azimuth across key hours and seasons to optimize orientation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.