Sunrise Calculator — Sunrise Time by Location & Date
Enter a latitude, longitude, date and your UTC offset to calculate the precise local sunrise time, solar noon, sunset and total daylight duration — from the equator to the polar circles.
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Sunrise at 17:47 local time
How does this calculator work?
Sunrise time = Solar noon − hour angle/15°. The hour angle ω₀ = arccos[(sin(−0.833°) − sin φ · sin δ) / (cos φ · cos δ)], where φ is latitude and δ is solar declination. Declination ranges ±23.44° with the seasons. At high latitudes the sun may not rise in winter (polar night) or not set in summer (midnight sun).
Formula
How this is calculated
Sunrise occurs when the geometric centre of the Sun's disc crosses the observer's mathematical horizon, adjusted for atmospheric refraction (+0.583°) and the Sun's apparent semi-diameter (0.25°) — a combined correction of −0.833° below the true horizontal plane. This calculator uses the NOAA simplified solar position algorithm (accurate to within a few minutes for dates 1901–2099), which chains four steps: (1) compute the Julian date offset from J2000.0 to fix the Earth's position in its orbit; (2) calculate the Sun's ecliptic longitude via the mean anomaly and equation of the centre; (3) derive the solar declination δ — the latitude of the sub-solar point — from the ecliptic longitude; and (4) solve the horizon equation for the hour angle ω₀, which gives the angular distance (in time) from solar noon to sunrise.
The Sun rises earlier in summer and later in winter because the declination δ moves with the seasons (±23.44°). At the equinoxes (δ ≈ 0°), every latitude on Earth experiences sunrise close to 6:00 local solar time. Near the poles, |sin φ · tan δ| can exceed 1, meaning the horizon equation has no real solution — this is polar day (midnight sun) or polar night.
The result is in local solar time converted to your timezone via the UTC offset you enter. Daylight saving time is not applied automatically — add 1 hour to the UTC offset when DST is in effect in your location.
Frequently asked questions
Official tables use the full VSOP87 planetary theory (accurate to seconds) and apply precise topographic corrections. This calculator uses a simplified algorithm accurate to ±2 minutes. Cloud cover, elevation above sea level, and the exact definition of the horizon also shift the visual sunrise from the computed civil one.
Declination is the latitude of the point on Earth directly beneath the Sun — it ranges from +23.44° at the June solstice to −23.44° at the December solstice. When declination equals your latitude, the Sun passes closest to the zenith at solar noon.
Converting a city name to coordinates and timezone requires an external geocoding API, which cannot be used here. Enter your latitude/longitude (from a map app) and your current UTC offset (e.g. UTC+2 for Central European Summer Time). Add 1 h to the standard offset when DST is active.
Also known as
TG we-Calculate Editorial Team. (2026). Sunrise Calculator — Sunrise Time by Location & Date [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sunrise-calculator
TG we-Calculate Editorial Team. "Sunrise Calculator — Sunrise Time by Location & Date." TG we-Calculate. 2026. https://we-calculate.com/calculator/sunrise-calculator.
TG we-Calculate Editorial Team, "Sunrise Calculator — Sunrise Time by Location & Date," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sunrise-calculator
@misc{wecalculate_sunrise_calculator, title = {Sunrise Calculator — Sunrise Time by Location & Date}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sunrise-calculator}}, year = {2026}, note = {TG we-Calculate} }
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