Sunrise Sunset Calculator
Calculate precise sunrise and sunset times using astronomical formulas for any location and date
Calculate Sunrise and Sunset Times
Select any date to calculate sunrise and sunset times
North positive, South negative (-90° to 90°)
East positive, West negative (-180° to 180°)
Sunrise & Sunset Results
Calculation Details
Day of Year: 0
Solar Declination: 0.00°
Civil Twilight Start:
Civil Twilight End:
Astronomical Formulas
Hour Angle (ω)
ω = arccos[(cos z - sin δ sin φ) / (cos δ cos φ)]
Where z = 90.833° (accounts for atmospheric refraction and sun's radius)
Solar Declination (δ)
δ = arcsin[0.39782 × sin(L)]
Where L is the sun's true longitude
Variables
- ω: Hour angle
- δ: Solar declination
- φ: Latitude
- z: Zenith angle
- L: Sun's true longitude
Constants
- 90.833°: Official sunrise/sunset
- 96°: Civil twilight
- 102°: Nautical twilight
- 108°: Astronomical twilight
Quick Location Selection
Twilight Phases
Seasonal Effects
Day length varies throughout the year due to Earth's tilt
Summer solstice: longest day in Northern Hemisphere
Winter solstice: shortest day in Northern Hemisphere
Equinoxes: equal day and night everywhere
Polar regions experience midnight sun and polar night
Understanding Sunrise and Sunset Calculations
What Causes Sunrise and Sunset?
Sunrise and sunset occur due to Earth's rotation on its axis. As Earth rotates at 15° per hour, different parts of the planet face toward or away from the Sun, creating the cycle of day and night.
Key Factors
- •Earth's Rotation: 15° per hour creates day/night cycle
- •Axial Tilt: 23.45° tilt causes seasonal variations
- •Latitude: Distance from equator affects day length
- •Atmospheric Refraction: Bends light, making sun appear higher
Applications
- 1Solar Energy: Plan solar panel efficiency and energy collection
- 2Photography: Golden hour and blue hour timing for optimal lighting
- 3Agriculture: Planning farm activities and crop management
- 4Navigation: Traditional celestial navigation and timekeeping
- 5Circadian Rhythms: Understanding natural light cycles
Note: These calculations account for atmospheric refraction and the sun's angular diameter for practical sunrise and sunset times that match observations.
Atmospheric Effects on Sunrise and Sunset
Atmospheric Refraction
Earth's atmosphere bends sunlight, making the sun appear 0.83° higher than its true position. This extends daylight by about 4 minutes.
Sun's Angular Size
The sun's diameter appears as 0.5° in the sky. Sunrise begins when the sun's edge touches the horizon, not when the center crosses it.
Elevation Effects
Higher elevations see sunrise earlier and sunset later. The horizon appears lower, extending the visible day length.