Formula Used
The calculator uses a NOAA style solar position method. It first calculates the fractional year.
gamma = 2 pi / days_in_year * (day_of_year - 1 + (standard_hour - 12) / 24)
Equation of time is estimated in minutes.
E = 229.18 * (0.000075 + 0.001868 cos(gamma) - 0.032077 sin(gamma) - 0.014615 cos(2 gamma) - 0.040849 sin(2 gamma))
Solar declination is estimated in radians.
delta = 0.006918 - 0.399912 cos(gamma) + 0.070257 sin(gamma) - 0.006758 cos(2 gamma) + 0.000907 sin(2 gamma) - 0.002697 cos(3 gamma) + 0.00148 sin(3 gamma)
True solar time uses longitude, time zone, and equation of time.
TST = local_standard_minutes + E + 4 * longitude - 60 * utc_offset
Hour angle converts true solar time into solar rotation.
H = TST / 4 - 180
Solar zenith is calculated by spherical trigonometry.
cos(Z) = sin(latitude) sin(delta) + cos(latitude) cos(delta) cos(H)
Solar elevation is the complement of zenith.
elevation = 90 - Z
Shadow length uses apparent elevation.
shadow_length = object_height / tan(apparent_elevation)
Panel incidence compares the solar beam with the panel normal.
cos(I) = cos(Z) cos(tilt) + sin(Z) sin(tilt) cos(solar_azimuth - panel_azimuth)
What This Solar Tool Does
A solar position estimate explains where the sun appears in the sky for a selected place and clock time. It is useful for physics lessons, field surveys, solar panel planning, shade studies, photography, crop checks, and daylight review. This calculator follows a practical NOAA style workflow. It converts date, time, latitude, longitude, and zone data into solar angles. The main outputs are elevation, apparent elevation, zenith, azimuth, solar noon, sunrise, sunset, daylight length, shadow length, and panel incidence.
Why Solar Angles Matter
Elevation tells how high the sun is above the horizon. Zenith is the matching angle measured down from overhead. Azimuth gives direction clockwise from north. Together, these values describe the solar beam. A higher elevation usually means shorter shadows and stronger direct radiation. A lower elevation produces longer shadows and larger atmospheric effects. The refraction correction adjusts the geometric elevation near the horizon. That is important around sunrise and sunset, where the atmosphere bends light visibly.
How The Estimate Is Built
The method first finds the day of year and fractional year. It then estimates equation of time and solar declination. Equation of time adjusts for the difference between clock time and apparent solar time. Declination describes the sun's seasonal north south position. Longitude, zone offset, and daylight saving choice convert clock time into true solar time. The hour angle then measures how far the sun is from local solar noon. Trigonometric formulas combine latitude, declination, and hour angle to find zenith, elevation, and azimuth.
Practical Use Notes
Enter east longitudes as positive values and west longitudes as negative values. Enter zone offset east of UTC, such as 5 for Pakistan or -5 for Eastern Standard Time. Use the daylight saving box only when the clock time includes a summer one hour shift. Results are estimates, not legal or survey grade evidence. Weather, terrain, buildings, refraction changes, and local horizon height can move observed events. For best planning, compare several dates and times. Export the table when you need records for reports, worksheets, or design notes. Check both standard time and daylight time inputs when source records are unclear. Small time errors can shift azimuth quickly near sunrise, sunset, and noon also locally.
FAQs
What does this calculator estimate?
It estimates solar elevation, azimuth, zenith, solar noon, sunrise, sunset, daylight length, shadow length, and panel incidence for a selected location and time.
Which longitude format should I enter?
Enter east longitude as positive and west longitude as negative. For example, Karachi is positive, while New York is negative.
What does UTC offset mean?
UTC offset is the standard time difference from UTC. Pakistan uses 5. Eastern Standard Time uses -5. Use the daylight saving checkbox separately.
What is solar azimuth?
Solar azimuth is the sun direction measured clockwise from north. East is near 90 degrees. South is near 180 degrees. West is near 270 degrees.
What is solar elevation?
Solar elevation is the angle of the sun above the horizon. Positive values mean the sun is above the horizon. Negative values indicate twilight or night.
Why is apparent elevation different?
Apparent elevation includes an atmospheric refraction correction. Refraction is most important near sunrise and sunset, where light bends through dense air.
Can I use the result for legal evidence?
No. Treat results as planning estimates. Local terrain, weather, refraction, and horizon obstructions can change observed sunrise, sunset, and shadow behavior.
Why include panel tilt and azimuth?
Panel tilt and azimuth estimate incidence angle. A smaller incidence angle means the panel faces the sun more directly at that moment.