Daylight Calculator
Calculate sunrise, sunset, and daylight duration for any location and date
Calculate Daylight Hours
Range: -90° (South) to +90° (North)
Range: -180° (West) to +180° (East)
Hours ahead (+) or behind (-) UTC
Example Calculation
Summer Solstice in London
Location: London, UK (51.5°N, 0.1°W)
Date: June 21st (Summer Solstice)
Solar Declination: +23.45°
Daylight Duration: ~16 hours 38 minutes
Sunrise: ~04:43
Sunset: ~21:21
Winter Solstice Formula
Hour Angle: ω = arccos(-tan(φ) × tan(δ))
Sunrise: 12 - ω × (12/π) - time_correction
Sunset: 12 + ω × (12/π) - time_correction
Where φ = latitude, δ = solar declination
Solar Phenomena
Equinoxes
March 20 & Sept 23
Equal day and night
Summer Solstice
June 21 (Northern)
Longest day of year
Winter Solstice
December 21 (Northern)
Shortest day of year
Daylight Facts
Equator receives ~12 hours daylight year-round
Arctic Circle: 24h daylight in summer, 0h in winter
Equation of time varies ±16 minutes throughout year
Earth's tilt (23.45°) causes seasonal daylight changes
Understanding Daylight Calculations
What Affects Daylight Hours?
Daylight duration at any location depends on several astronomical factors including Earth's axial tilt, orbital position, and the observer's latitude. The calculations involve complex trigonometric relationships between the sun's position and Earth's geometry.
Key Factors
- •Latitude: Distance from equator affects seasonal variation
- •Date: Earth's orbital position determines solar declination
- •Earth's Tilt: 23.45° axial tilt creates seasons
- •Longitude: Affects local solar time calculation
Mathematical Formulas
δ = 23.45° × sin(2π × (284 + n) / 365)
ω = arccos(-tan(φ) × tan(δ))
Daylight = 2 × ω × (24h / 2π)
- δ: Solar declination angle
- φ: Latitude of observer
- ω: Hour angle at sunrise/sunset
- n: Day of year (1-365)
Note: These formulas assume a perfectly spherical Earth and neglect atmospheric refraction effects.