Advanced Solar Geometry Calculator

Calculator inputs

Angles use true north by default. East longitude values are positive.

Calculation mode

Analysis mode

Range start date

Range end date

Location

Location preset

Location name

Coordinate display

Latitude (−90 to 90)

Longitude (−180 to 180)

Elevation above sea level (m)

Degrees, minutes, seconds input

Latitude degrees

Latitude minutes

Latitude seconds

Latitude direction

Longitude degrees

Longitude minutes

Longitude seconds

Longitude direction

Date and time

Calendar date

Local clock time

UTC offset

Daylight saving

Time format

Surface and tracking

Surface tilt angle

Surface azimuth

Preferred tracking mode

Single-axis tilt

Single-axis azimuth

Ground reflectance

Azimuth north reference

Magnetic declination, east positive

Roof rise

Roof run

Shadow and output settings

Object height

Length unit

Angle unit

Decimal precision

Saved calculation history

No saved calculations yet.

Formula used

Fractional year: γ = 2π / 365 × (n − 1 + (hour − 12) / 24)

Solar declination: NOAA trigonometric series using fractional year γ.

Equation of time: EoT = 229.18 × (0.000075 + 0.001868 cosγ − 0.032077 sinγ − 0.014615 cos2γ − 0.040849 sin2γ)

Solar time: LST = local clock time + [EoT + 4(longitude − 15 × UTC offset)] / 60

Hour angle: H = 15° × (LST − 12)

Zenith: cos θz = sinφ sinδ + cosφ cosδ cosH

Elevation: α = 90° − θz

Incidence: cos θi = cosθz cosβ + sinθz sinβ cos(γs − γp)

Day length: N = 2 cos⁻¹(−tanφ tanδ) / 15

Shadow length: L = object height / tanα

These formulas estimate geometric solar position. They exclude clouds and local obstructions. Atmospheric refraction matters near the horizon for precision.

Calculation steps

Convert the selected date into the year’s day number.
Calculate fractional year, equation of time, and declination.
Correct clock time into local apparent solar time.
Calculate hour angle, zenith, elevation, and azimuth.
Resolve surface incidence for fixed and tracking systems.
Estimate sunrise, sunset, daylight, shadows, and irradiance geometry.

How to use

Select a calculation mode first. Enter coordinates and the matching UTC offset. Then provide the local date and clock time.

Set panel tilt and azimuth next. Add tracker axis values when needed. Enter object height to calculate shadow length and direction.

Choose output units and precision. Submit the form to view detailed results. Export or save results using the available controls.

Example data

Scenario	Latitude	Longitude	Date	Time	Tilt	Azimuth
Equator at solar noon	0	0	2026-03-20	12:00	0°	180°
London summer solstice	51.5074	−0.1278	2026-06-21	12:00	35°	180°
Sydney winter solstice	−33.8688	151.2093	2026-06-21	12:00	34°	0°
New York equinox	40.7128	−74.0060	2026-09-22	12:00	41°	180°
High-latitude polar day	69.6492	18.9553	2026-06-21	00:00	55°	180°

Solar angle meanings

Elevation measures the Sun above the horizon. Zenith measures from the vertical direction. Together, both angles always total ninety degrees.

Azimuth is measured clockwise from true north. East is ninety degrees and south is 180 degrees. Surface azimuth follows the same directional convention.

Incidence measures sunlight against the surface normal. Zero degrees means direct alignment with sunlight. Larger angles reduce direct-beam geometric capture.

Assumptions and limitations

The model calculates geometric solar position and extraterrestrial irradiance. It does not forecast weather or shading. Buildings and terrain require separate obstruction modelling.

Sunrise uses a geometric horizon approximation. Refraction can shift observed sunrise and sunset. Precise surveying may require specialised ephemeris software.

Optimal tilt values use simple latitude guidance. Energy optimisation also depends on climate and tariffs. Detailed projects need measured irradiance and engineering review.

Frequently asked questions

What is solar geometry?

Solar geometry describes the Sun’s apparent position. It connects location, date, and solar time. These relationships support shading and solar-energy calculations.

What is the difference between solar time and clock time?

Clock time follows time zones and civil rules. Solar time follows the Sun’s local position. Longitude and equation of time create differences.

Which azimuth convention is used?

This calculator measures clockwise from true north. East equals ninety degrees and south equals 180 degrees. West equals 270 degrees under this convention.

Why can sunrise be unavailable?

High latitudes may experience polar conditions. The Sun can remain above or below. The calculator reports polar day or night.

What does incidence angle mean?

Incidence compares sunlight with the panel normal. Lower values indicate stronger direct alignment. Zero degrees represents ideal direct alignment.

Is extraterrestrial irradiance actual panel output?

No, it represents radiation before atmospheric losses. Clouds and aerosols reduce ground irradiance. Panel efficiency also changes electrical output.

How is shadow direction calculated?

A shadow points opposite the solar azimuth. Its length depends on elevation angle. Low sunlight creates much longer shadows.

What is air mass?

Air mass estimates atmospheric path length. Values rise as the Sun approaches the horizon. It becomes undefined below the horizon.

Can this calculator design a complete solar system?

It supports geometry and orientation analysis. Complete design needs weather and electrical data. Professional review remains important for final projects.