Sunrise Calculator
Calculate precise sunrise times using astronomical formulas and atmospheric refraction corrections
Calculate Sunrise Time
Location
Positive for North, negative for South (-90 to 90)
Positive for East, negative for West (-180 to 180)
Day of year: 288
Different definitions of sunrise based on sun angle
Sunrise Calculation Results
Calculation Details
288
-8.48°
83.75°
90.833°
200.12°
281.01°
Location Analysis
Example Calculations
New York City (Summer Solstice)
Location: 40.7128°N, 74.0060°W
Date: June 21st (Day 172)
Solar Declination: ~23.4° (maximum)
Sunrise Time: ~5:25 AM (earliest of the year)
Day Length: ~15 hours
Reykjavik, Iceland (Winter Solstice)
Location: 64.1466°N, 21.9426°W
Date: December 21st (Day 355)
Solar Declination: ~-23.4° (minimum)
Sunrise Time: ~11:22 AM (latest of the year)
Day Length: ~4 hours
Types of Dawn
Apparent Sunrise
Sun's edge touches horizon (90.833°)
Standard sunrise time with refraction
Civil Twilight
Sun 6° below horizon (96°)
Outdoor activities possible
Nautical Twilight
Sun 12° below horizon (102°)
Horizon visible at sea
Astronomical Twilight
Sun 18° below horizon (108°)
Complete astronomical darkness
Quick Locations
Key Formulas
Hour Angle
ha = arccos((cos(z) - sin(δ)·sin(φ))/(cos(δ)·cos(φ)))
Solar Declination
δ = arcsin(0.39782 · sin(L))
True Longitude
L = M + 1.916·sin(M) + 0.020·sin(2M) + 282.634
Mean Anomaly
M = 0.9856 · t - 3.289
Understanding Sunrise Calculations
What is Sunrise?
Sunrise is the moment when the upper edge of the Sun appears above the eastern horizon. This definition accounts for atmospheric refraction, which bends sunlight and makes the Sun appear slightly higher than its geometric position.
Types of Dawn
- •Civil dawn: Sun 6° below horizon - outdoor activities possible
- •Nautical dawn: Sun 12° below horizon - horizon visible at sea
- •Astronomical dawn: Sun 18° below horizon - complete darkness ends
Atmospheric Refraction
Earth's atmosphere bends sunlight by approximately 0.58°, making the Sun appear higher than its true position. Combined with the Sun's apparent radius (0.25°), this gives us the standard refraction correction of 0.833°.
Calculation Variables
The Calculation Process
1. Initial Setup
Convert coordinates to proper units, calculate day of year, and estimate initial sunrise time based on longitude.
2. Solar Position
Calculate the Sun's mean anomaly, true longitude, right ascension, and declination using astronomical formulas.
3. Final Time
Compute hour angle, apply atmospheric corrections, and adjust for time zone and daylight saving time.
Applications and Accuracy
Real-World Uses
- • Photography and cinematography planning
- • Solar panel installation and optimization
- • Agriculture and gardening schedules
- • Navigation and outdoor activities
- • Religious and cultural observances
Accuracy Notes
- • ±2 minutes accuracy for most locations
- • Weather and local topology can affect visibility
- • Calculations assume clear, unobstructed horizon
- • Polar regions may experience polar day/night
- • Atmospheric conditions can vary results slightly