Calculator Form
Plotly Graph
The graph below shows azimuth variation across daylight solar hours for the current latitude and declination.
Example Data Table
| Latitude (°) | Day Number | Solar Time (h) | Hour Angle (°) | Declination (°) | Azimuth (°) | Altitude (°) |
|---|---|---|---|---|---|---|
| 0.0 | 81 | 9.00 | -45.00 | 0.00 | 90.00 | 45.00 |
| 23.5 | 172 | 12.00 | 0.00 | 23.45 | 180.00 | 89.95 |
| 35.0 | 172 | 15.00 | 45.00 | 23.45 | 265.93 | 49.43 |
| 51.5 | 266 | 10.00 | -30.00 | -1.01 | 144.02 | 31.69 |
These rows demonstrate how azimuth changes with location, season, and solar time.
Formula Used
δ = 23.45 × sin[ 360 × (284 + n) / 365 ]
H = 15 × (Tsolar − 12)
sin(α) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H)
A = [ atan2(sin(H), cos(H)sin(φ) − tan(δ)cos(φ)) + 180° ] mod 360°
Where:
- φ = latitude
- δ = solar declination
- H = hour angle
- α = solar altitude
- A = solar azimuth angle
- n = day number of the year
How to Use This Calculator
- Choose a method: automatic mode or direct mode.
- Enter latitude and your preferred decimal precision.
- For automatic mode, provide day number and local solar time.
- For direct mode, enter declination and hour angle directly.
- Press the calculate button to generate the azimuth result.
- Review azimuth, altitude, zenith, and compass direction.
- Use the graph to inspect daily azimuth behavior visually.
- Download the current result as CSV or PDF.
Frequently Asked Questions
1) What is the solar azimuth angle?
Solar azimuth is the sun’s horizontal direction on the horizon. It is usually measured clockwise from true north, where east is 90°, south is 180°, and west is 270°.
2) Why does the calculator use solar time?
Solar time aligns calculations with the sun’s actual position in the sky. Clock time may differ because of time zones, longitude offsets, and daylight saving adjustments.
3) What is the difference between azimuth and altitude?
Azimuth describes the sun’s compass direction across the horizon. Altitude describes how high the sun is above the horizon. Both are needed for complete solar position analysis.
4) Can I use this for solar panel planning?
Yes. Azimuth is useful when checking panel orientation, shading direction, and sun path studies. It helps designers understand where sunlight arrives from throughout the day.
5) What does a negative hour angle mean?
A negative hour angle means the time is before solar noon. Positive hour angles mean the time is after solar noon. Zero hour angle occurs exactly at solar noon.
6) Why does azimuth change during the day?
The Earth rotates continuously, so the sun appears to move across the sky. This apparent motion changes the sun’s compass direction from morning to evening.
7) Is the declination value always required?
Not always. In automatic mode, declination is estimated from the day number. In direct mode, you enter declination yourself when accurate solar geometry data is already available.
8) What if the sun is below the horizon?
The calculator still computes the geometric position, but the altitude becomes zero or negative. That means the sun is not visibly above the horizon at that moment.