About

Precise knowledge of solar timing is not just a convenience; it is a necessity for architectural planning, agricultural scheduling, and outdoor cinematography. While standard weather applications provide a binary sunrise/sunset time, they often fail to account for the geometric nuances of twilight phases or the sun's varying elevation. This tool bridges that gap by using astronomical algorithms to map the sun's exact trajectory relative to a specific geographic point.

We calculate not only the visible daylight but also the Shadow Ratio (crucial for solar panel installation and urban planning) and the Solar Noon altitude. The calculator distinguishes between Civil, Nautical, and Astronomical twilight, ensuring that users strictly adhere to legal definitions of "daytime" for aviation and construction mandates. The output is corrected for atmospheric refraction and standard solar radius.

Formulas

To determine the daylight duration D, we first calculate the Sun's declination δ and the observer's latitude φ. The hour angle ω at sunrise/sunset is derived from the spherical law of cosines:

cosω = sinα − sinφ sinδcosφ cosδ

Where α is the altitude of the sun's center (-0.833° for refraction correction). The total daylight duration in hours is calculated as:

D = 2 ⋅ ω15°

Reference Data

Solar Event	Sun Elevation (α)	Visual Characteristics	Use Case
Solar Noon	Max°	Shortest shadows, highest intensity.	Solar Energy alignment, Vitamin D.
Golden Hour	6° to -4°	Soft, diffused, warm light.	Portrait photography, Cinematography.
Civil Twilight	-0.8° to -6°	Streetlights on. Horizon clear.	Aviation (VFR), Construction safety.
Nautical Twilight	-6° to -12°	Horizon visible at sea. Stars appear.	Marine navigation, Military ops.
Astronomical Twilight	-12° to -18°	Sky trace illumination. Point sources only.	Astrophotography, Telescope calibration.
Night	< -18°	No solar interference.	Deep space observation.

Frequently Asked Questions

The Shadow Ratio indicates the length of a shadow relative to the object's height. A ratio of 2.0 means a 10-meter tree will cast a 20-meter shadow. This is critical for architects to avoid blocking light to neighboring buildings and for photographers planning shoot angles.

Vitamin D synthesis generally requires the sun to be at an elevation greater than 45° (when UV index is sufficient). In winter months or at high latitudes, the sun may never reach this altitude, resulting in no natural Vitamin D production window for that day.

The calculations are performed in local time relative to the timezone offset provided by your browser or the selected location. While we adjust for standard offsets, verify specific DST transitions if you are planning events months in advance near changeover dates.

Geometric sunrise occurs when the sun's center crosses the horizon. Visible sunrise considers atmospheric refraction, which bends light, making the sun appear about 0.5 degrees higher than it actually is. This tool uses the standard visible sunrise definition (-0.833 degrees altitude).