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Category Time & Date

Date Select calculation date

Latitude Degrees (positive = North)

Longitude Degrees (positive = East)

Timezone (UTC) Local timezone offset

Presets:

Enter location and date to calculate daylight times

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About

Accurate daylight calculations require solving the spherical trigonometry of Earth's rotation relative to the Sun. This calculator implements the standard astronomical algorithms from Jean Meeus' Astronomical Algorithms, computing the Sun's declination via the obliquity of the ecliptic (ε ≈ 23.44°) and applying the hour angle formula to derive sunrise and sunset times. Civil twilight begins when the Sun's geometric center is 6° below the horizon; nautical twilight at 12°; astronomical twilight at 18°. Polar regions experience perpetual daylight or darkness when the Sun's declination exceeds the complementary latitude.

The Equation of Time correction accounts for Earth's elliptical orbit and axial tilt, causing solar noon to drift by up to ±16 minutes from mean noon throughout the year. This tool calculates true solar time, not civil time approximations. Atmospheric refraction (0.833°) is applied to sunrise/sunset, meaning the Sun is geometrically below the horizon when visually touching it.

Formulas

The hour angle H at sunrise/sunset is derived from the solar zenith angle equation. For a horizon angle of 90.833° (including refraction and solar disk radius):

cos(H) = cos(z) − sin(φ) ⋅ sin(δ)cos(φ) ⋅ cos(δ)

Where z = 90.833° is the zenith angle, φ is the observer's latitude, and δ is the Sun's declination. The declination is computed from:

δ = 23.44° ⋅ sin(360°365 ⋅ (N + 284))

Where N is the day of the year. Sunrise time t_rise and sunset time t_set are computed as:

t_rise = 12h − H15°/h − E − λ15°/h + TZ

Where E is the Equation of Time (minutes), λ is longitude, and TZ is the timezone offset in hours. The Equation of Time corrects for orbital eccentricity:

E = 9.87 ⋅ sin(2B) − 7.53 ⋅ cos(B) − 1.5 ⋅ sin(B)

Where B = 360°365 ⋅ (N − 81). For twilight calculations, replace the zenith angle: Civil twilight uses z = 96°, Nautical uses z = 102°, and Astronomical uses z = 108°.

Reference Data

Location	Latitude	Longest Day	Shortest Day	Variation
Equator	0°	12h 7m	12h 7m	0m
Miami, USA	25.76°N	13h 45m	10h 32m	3h 13m
Cairo, Egypt	30.04°N	14h 4m	10h 5m	3h 59m
Tokyo, Japan	35.68°N	14h 35m	9h 45m	4h 50m
Rome, Italy	41.90°N	15h 14m	9h 7m	6h 7m
New York, USA	40.71°N	15h 6m	9h 15m	5h 51m
Paris, France	48.86°N	16h 10m	8h 14m	7h 56m
London, UK	51.51°N	16h 38m	7h 50m	8h 48m
Berlin, Germany	52.52°N	16h 49m	7h 40m	9h 9m
Moscow, Russia	55.76°N	17h 34m	7h 0m	10h 34m
Stockholm, Sweden	59.33°N	18h 37m	6h 5m	12h 32m
Helsinki, Finland	60.17°N	18h 57m	5h 49m	13h 8m
Reykjavik, Iceland	64.15°N	21h 5m	4h 7m	16h 58m
Tromsø, Norway	69.65°N	24h 0m	0h 0m	Polar Day/Night
North Cape	71.17°N	24h 0m	0h 0m	Polar Day/Night
Sydney, Australia	33.87°S	14h 24m	9h 54m	4h 30m
Cape Town, SA	33.93°S	14h 25m	9h 53m	4h 32m
Buenos Aires	34.60°S	14h 30m	9h 48m	4h 42m
Ushuaia, Argentina	54.80°S	17h 18m	7h 12m	10h 6m
McMurdo Station	77.85°S	24h 0m	0h 0m	Polar Day/Night

Frequently Asked Questions

Differences arise from atmospheric refraction models, which vary with local pressure and temperature. This calculator uses the standard refraction correction of 0.833° at sea level. Altitude, humidity, and temperature inversions can shift apparent sunrise by 1 - 3 minutes. Official sources like NOAA may use different algorithms or local corrections.

When the Sun's declination (δ ≈ ±23.44° at solstices) exceeds the co-latitude (90° − φ), the hour angle equation has no real solution. The Sun never crosses the horizon. This occurs poleward of latitude 66.56° (the Arctic/Antarctic circles).

The Equation of Time causes solar noon to drift from clock noon by up to ±16 minutes throughout the year. The maximum deviation occurs around February 11 (+14min) and November 3 (−16min). This is why sundials require correction tables.

Civil twilight (Sun 0° to 6° below horizon) provides enough light for outdoor activities without artificial lighting. Nautical twilight (6° to 12°) allows horizon visibility for marine navigation. Astronomical twilight (12° to 18°) marks when the sky becomes dark enough for all astronomical observations.

Yes. At higher altitudes, the geometric horizon is depressed, allowing the observer to see the Sun earlier at sunrise and later at sunset. At 1000m elevation, sunrise occurs approximately 3 minutes earlier than at sea level. This calculator assumes sea level; add altitude corrections for mountainous locations.

The rate of change of daylight follows a sinusoidal pattern. Near solstices, the Sun's declination is at its maximum or minimum, changing slowly. Near equinoxes, declination changes most rapidly (approximately 0.4°/day), causing daylight duration to shift by up to 4 minutes per day at mid-latitudes.