Calculator Inputs
Example Data Table
| Place | Latitude | Longitude | Date | Time | Time Zone | Expected Use |
|---|---|---|---|---|---|---|
| Lahore | 31.5204 | 74.3587 | 2026-06-21 | 12:00 | 5 | Summer noon solar check |
| London | 51.5072 | -0.1276 | 2026-12-21 | 12:00 | 0 | Winter shadow planning |
| Sydney | -33.8688 | 151.2093 | 2026-03-21 | 10:30 | 11 | Morning panel angle review |
Formula Used
Solar declination: δ = 23.44 × sin((360 / 365) × (N − 81))
Equation of time: E = 9.87sin(2B) − 7.53cos(B) − 1.5sin(B)
Time correction: TC = 4 × (Longitude − Standard Meridian) + E
Local solar time: LST = Local Time + TC / 60
Hour angle: H = 15 × (LST − 12)
Altitude angle: α = sin⁻¹(sinφsinδ + cosφcosδcosH)
Zenith angle: θz = 90 − α
Shadow length: Shadow = Object Height / tan(Apparent Altitude)
How to Use This Calculator
Enter latitude with north as positive and south as negative.
Enter longitude with east as positive and west as negative.
Add the local date, clock time, and time zone offset.
Use object height when you want a shadow estimate.
Set panel tilt and azimuth to compare sunlight on a surface.
Click Calculate to show results below the header and above the form.
Use CSV or PDF buttons to save the current result set.
Understanding Sun Altitude Angle
Sun Altitude Angle
Sun altitude angle describes how high the sun appears above the horizon. It is measured in degrees. A value near zero means the sun is close to sunrise or sunset. A value near ninety means the sun is almost overhead. This calculator helps students, surveyors, builders, gardeners, and solar designers estimate that angle from practical inputs.
Why The Angle Matters
Sun height controls shadow length, roof exposure, panel output, daylight access, and outdoor comfort. A low sun creates long shadows and weaker direct radiation. A high sun creates shorter shadows and stronger overhead light. Because the earth tilts, the same location receives different solar paths across the year. Noon altitude is higher in summer and lower in winter. Latitude also matters. Places closer to the equator often see higher solar altitude during many months.
How Time Changes The Result
Clock time is not always solar time. The calculator adjusts local clock time with longitude, time zone, and the equation of time. Longitude correction handles the difference between your location and the standard meridian for the time zone. The equation of time handles changes caused by earth orbit shape and axial tilt. These corrections give local solar time. The hour angle then tells how far the sun is from solar noon.
Useful Planning Details
The tool also estimates zenith angle, azimuth, daylight length, sunrise, sunset, air mass, shadow length, and panel incidence. Zenith is the complement of altitude. Azimuth shows compass direction. Air mass gives a simple measure of atmosphere crossed by sunlight. Panel incidence compares the sun ray with a tilted surface. These results support early design checks for skylights, greenhouses, solar panels, lessons, and field notes.
Best Input Practice
Use east longitude as positive and west longitude as negative. Use north latitude as positive and south latitude as negative. Pick the correct time zone offset for the chosen date, including daylight saving time when used. For highest accuracy, compare the result with a professional solar ephemeris. For most educational and planning tasks, the formulas provide a clear and useful estimate. Keep units consistent when entering object height. Review apparent altitude near the horizon, because refraction changes low sun readings more strongly there today for planning.
FAQs
What is sun altitude angle?
It is the angle between the sun and the local horizon. Zero degrees is on the horizon. Ninety degrees is directly overhead.
Is altitude angle the same as zenith angle?
No. Zenith angle is measured from the vertical sky point. Altitude is measured upward from the horizon. They add to ninety degrees.
Why does longitude affect the result?
Longitude shifts local solar time away from clock time. The calculator uses longitude and time zone offset to estimate that correction.
What does solar azimuth mean?
Solar azimuth is the compass direction of the sun. This calculator reports it in degrees from north, moving clockwise.
Can I use this for solar panels?
Yes. Enter surface tilt and surface azimuth. The tool estimates incidence angle and direct light factor for that panel direction.
Why is refraction included?
Atmospheric refraction bends sunlight near the horizon. It can slightly lift the apparent sun position during sunrise and sunset periods.
Why is shadow length unavailable sometimes?
Shadow length is unavailable when the sun is below the horizon. A negative or zero altitude cannot produce a normal daylight shadow.
How accurate is this calculator?
It is useful for education and planning. For navigation, legal surveys, or precision solar engineering, compare results with professional ephemeris software.