Daylight Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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Sunrise, sunset, and daylight are geometry problems wrapped in calendar and clock conventions. Daylight Calculator estimates daylight duration from the solar model used on this page, while separating astronomical geometry from local-horizon effects.

What this calculator does

The Daylight Calculator centers on daylight duration using the fields that are actually present here: Day of year, Hemisphere (N/S), Latitude (φ), Hemisphere (E/W), Longitude (λ). Rather than treating every box as an independent input, use the equation below to identify the driving quantities and read the remaining fields as derived or supporting values when appropriate.

How to use it

Enter day of year and latitude, then choose the north/south hemisphere. The longitude, east/west, and time-zone controls are not part of this duration calculation.

How the calculation works

The page estimates solar declination from day of year, δ ≈ 23.44°·sin[2π(284 + N)/365], then uses the sunrise hour-angle relation cos H₀ = −tan φ tan δ. Daylight duration is 2H₀/15 when H₀ is expressed in degrees, with polar-day and polar-night limits handled separately.

Example

Around day 172 (near the June solstice), a latitude of 40° N gives roughly 14.8 hours of daylight in this geometric model. At the same latitude near the December solstice, the result falls to roughly 9.2 hours.

How to interpret the result

For Daylight Calculator, read daylight duration in the context of the equation above. Interpret the clock or duration as a modeled solar event for the entered date/location assumptions. A one-hour time-zone change should shift the displayed clock time by roughly one hour, while changing latitude or season changes the underlying solar geometry itself.

Limitations and notes

Only day of year, latitude, and north/south hemisphere drive this daylight calculation. Longitude, east/west hemisphere, and time-zone controls do not alter the duration here. It is a solar-geometry estimate and does not model terrain, observer elevation, atmospheric refraction, the solar disk, or civil clock conventions.