Below is the geometrically derived formula for estimating day length based on latitude and time of year:

Formula for Day Length

The day length DDD in hours can be estimated using:

D=24πcos⁡−1(−tan⁡(ϕ)tan⁡(δ))D = \frac{24}{\pi} \cos^{-1}(-\tan(\phi) \tan(\delta))D=π24​cos−1(−tan(ϕ)tan(δ))

where:

• ϕ\phiϕ is the latitude of the location.
• δ\deltaδ is the solar declination angle, which varies throughout the year.

Solar Declination Angle (δ\deltaδ)

The solar declination angle δ\deltaδ can be approximated by:

δ=23.44∘⋅sin⁡(360∘365⋅(N+10))\delta = 23.44^\circ \cdot \sin\left(\frac{360^\circ}{365} \cdot (N + 10)\right)δ=23.44∘⋅sin(365360∘​⋅(N+10))

where NNN is the day of the year (1 for January 1, 2 for January 2, etc.).

Calculation Steps

This formula captures the variation in day length due to Earth's axial tilt and orbit around the Sun.

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