Download your PDF
Sunrise and Sunset from Solar Geometry result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Sunrise and Sunset from Solar Geometry — result sheet
Estimate sunrise, sunset, daylight duration, and solar noon from latitude, declination, longitude, time zone, and equation of time.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: cos H₀ = (cos 90.833° − sin φ sin δ)/(cos φ cos δ); solar noon = 720 − 4λ − E + 60·TZ minutes, sunrise/noon/sunset = noon ± 4H₀ minutes.
This planning calculator finds the sunrise and sunset hour angle for the standard apparent-sunrise altitude of −0.833°. It then applies longitude, time-zone offset, and equation-of-time corrections to express approximate local standard-clock times.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Location latitude — °; minimum -90; maximum 90
- Solar declination — °; minimum -90; maximum 90
- Location longitude — °; minimum -180; maximum 180
- Standard time-zone offset — hours from UTC; minimum -14; maximum 14
- Equation of time — min; minimum -30; maximum 30
Worked example
| Input | Value |
|---|---|
| Location latitude | 26.07 |
| Solar declination | 10 |
| Location longitude | 50.55 |
| Standard time-zone offset | 3 |
| Equation of time | -5 |
The example location has approximately 11.58 hours of daylight, with sunrise near 05:09, solar noon near 11:40, and sunset near 16:18 standard time.
Assumptions and limits
- The entered declination and equation of time correspond to the date being planned; the calculator does not infer a date or time zone from a place name.
- The standard apparent sunrise/sunset zenith of 90.833° includes a common refraction and solar-radius allowance.
- Results are local standard time and do not apply daylight-saving rules; polar day or night is reported when no crossing exists.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.