Sunrise & Sunset

Location

Today — —

About the Calculation

The calculations use the JavaScript library SunCalc by Vladimir Agafonkin, which is based on Jean Meeus' standard work Astronomical Algorithms (2nd edition, 1998).

1. Julian Date & Epoch J2000.0

All calculations internally use the Julian Date (JD) — a continuous day count from 1 January 4713 BC. The reference point is the epoch J2000.0 (1 January 2000, 12:00 UTC = JD 2,451,545.0). The number of days since J2000.0 is called d.

2. Sun Position

The ecliptic longitude of the Sun is computed via the mean anomaly:

M  = 357.5291° + 0.98560028° × d        (mean anomaly)
C  = 1.9148·sin(M) + 0.0200·sin(2M) + 0.0003·sin(3M)   (equation of centre)
λ  = M + C + 180° + 102.9372°           (ecliptic longitude)

The Sun's declination (its angle to the celestial equator) follows:

sin(δ) = sin(λ) · sin(23.4397°)         (23.4397° = axial tilt)

3. Solar Noon

Solar noon at a given longitude:

J_transit = 2,451,545.5 + λ_geo/360 + 0.0009
           + 0.0053·sin(M) − 0.0069·sin(2λ)

where λ_geo is the observer's geographic longitude.

4. Hour Angle & Sunrise Time

Sunrise and sunset occur when the Sun reaches a certain altitude h above the horizon. From the spherical triangle zenith–pole–Sun:

cos(ω₀) = (sin(h) − sin(φ)·sin(δ)) / (cos(φ)·cos(δ))

φ is the geographic latitude, ω₀ the hour angle of rise or set. Sunrise time is solar noon − ω₀/360, sunset is solar noon + ω₀/360.

5. Altitude Corrections by Event

The threshold h varies by event:

Accuracy

The model is an approximation accurate to ±1 minute for practical purposes. High-precision astronomical calculations (e.g. eclipse predictions) require more elaborate perturbation methods. Atmospheric refraction at the horizon also depends on air pressure and temperature — these are approximated here with standard values (1013 hPa, 10 °C).