Daylight Calculator

What Is Daylight Duration?

Daylight duration is the time between sunrise and sunset at a given location on a given date. It varies with latitude and season: summer days are longer at mid-latitudes, while equatorial locations see relatively stable day lengths year-round.

Approximate Daylight Formula

This calculator uses a simplified solar geometry model. First, solar declination $\delta$ is estimated from the day of year $n$:

$$\delta = 23.45° \times \sin\left(\frac{2\pi}{365}(n - 81)\right)$$

Daylight hours at latitude $\phi$ are then:

$$\text{Daylight} = \frac{24}{\pi} \arccos(-\tan\phi \cdot \tan\delta)$$

Example: at 40°N on June 21 (day 172), declination is about +23.45° and daylight is roughly 15 hours.

Real-World Applications

Daylight calculations help gardeners plan growing seasons, photographers schedule golden-hour shoots, solar installers estimate panel exposure, and travelers compare seasonal conditions at different latitudes.

Frequently Asked Questions

How accurate is this daylight calculator?

It uses an approximate astronomical formula suitable for planning. Actual sunrise and sunset times also depend on atmospheric refraction, elevation, and horizon obstructions.

Can I use latitude south of the equator?

Yes. Enter negative latitude for the Southern Hemisphere. Seasons are reversed relative to the Northern Hemisphere.

What is day of year?

Day of year counts from January 1 as day 1 through December 31 as day 365 (or 366 in leap years). June 21 is typically around day 172.

Why are some days 24 hours of daylight or darkness?

Inside the polar circles, the sun may not set (polar day) or not rise (polar night) when $|\tan\phi \cdot \tan\delta| \geq 1$.

Does this account for time zones?

No. The result is the astronomical duration of daylight in hours, independent of local clock time or time zone.

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What Is Daylight Duration?

Approximate Daylight Formula

Real-World Applications

Frequently Asked Questions

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