Sunrise & Sunset Calculator — NOAA Solar Position Algorithm, Any Lat/Lon, Any Date
Get exact local sunrise, sunset, solar noon, day length and all three twilight bands (civil, nautical, astronomical) for any place on Earth and any date. Uses the standard NOAA Solar Position Algorithm with atmospheric refraction (0.833 deg below horizon). The live sun-arc SVG shows the Sun's instantaneous altitude and azimuth. Today, May 27, 2026 in Mumbai, sunrise is ~05:59, sunset ~19:07.
Quick Conversion
Formula: hour_angle_hr = degrees / 15
Sun Arc & Live Solar Position
Dawn / Dusk Phases
| Phase | Sun altitude | Dawn | Dusk |
|---|---|---|---|
| Astronomical | -18 deg | 04:39 | 20:31 |
| Nautical | -12 deg | 05:08 | 20:02 |
| Civil | -6 deg | 05:37 | 19:34 |
| Sunrise / Sunset | -0.833 deg | 06:01 | 19:10 |
City Presets
NOAA Solar Position — Key Formulas
cos(H) = (sin(-0.833°) - sin(lat) × sin(decl)) / (cos(lat) × cos(decl))solar_noon = 12 - lon/15 + tz - EoT/60sunrise = solar_noon - H/15, sunset = solar_noon + H/15Worked: Mumbai (19.076°N, 72.878°E, UTC+5.5) on 2026-05-27: N = 147, decl = 21.45°, EoT = 2.84 min, solar_noon = 12 - 4.858 + 5.5 - 0.047 = 12:36, H = arccos((sin(-0.833°) - sin(19.076°)×sin(21.45°)) / (cos(19.076°)×cos(21.45°))) = 95.31° = 6.354 hr, sunrise = 12:36 - 6:21 = ~06:15.
Day Length at June Solstice by Latitude
| Latitude | Day length (hr) | Note |
|---|---|---|
| 0° N | 12.12 | Equator |
| 15° N | 12.95 | Mumbai band |
| 30° N | 13.93 | New Delhi / Cairo |
| 40° N | 14.97 | NYC / Madrid |
| 50° N | 16.36 | London / Berlin |
| 60° N | 18.88 | Helsinki / Oslo |
| 66.56° N | 24.00 | Arctic Circle - first midnight sun |
| 70° N | 24.00 | Tromso - polar day |
| 90° N | 24.00 | North Pole |
Need civil-time conversion across cities? Time-zone converter.
Saved Lookups
How To Use the Calculator — 5 Steps
- Step 1. Pick a date. Use any date between 1900-2100 with full accuracy.
- Step 2. Pick a city preset, or enter your own latitude, longitude and time-zone offset (e.g. 5.5 for India IST).
- Step 3. Read sunrise, sunset, solar noon and day length. For dark-sky planning read the astronomical twilight band.
- Step 4. Drag the local clock-hour input to see the sun's altitude and azimuth move along the arc SVG.
- Step 5. Click Save lookup to keep the result in browser storage for later.
A Brief History of Solar Position
In 2026, a cadastral surveyor in Mumbai needs to know the exact sunrise time at the Arabian Sea coast to time a plane-table traverse before the heat haze rolls in. The Mumbai preset above returns ~06:00 — and the civil-twilight band tells the field party they have light enough to start setting up by 05:35. This is exactly the kind of question the NOAA Solar Position Algorithm was designed to answer.
The mathematics behind sunrise dates back to Hipparchus (c. 120 BCE), who built the first table of solar declination. Ptolemy's Almagest (c. 150 CE) refined the model and held the standard for 1300 years. Tycho Brahe's 1580s observations from Uraniborg, processed by Johannes Kepler in 1609, finally replaced the geocentric tables — and yielded the elliptical orbit that produces our 16-minute equation of time swing.
The Gregorian calendar reform of October 1582 (Pope Gregory XIII) recalibrated civil dates to the seasons but left solar position computation to almanacs. Nathaniel Bowditch's American Practical Navigator(first edition 1802) put sunrise tables into every captain's hand. Naval-Almanac-Office tables remained the gold standard until digital computation took over in the 1970s.
The NOAA Solar Position Algorithm, distributed by the Earth System Research Laboratory in Boulder, uses the 1992 USNO simplifications of Meeus 1991 Astronomical Algorithms. It is accurate to within +/- 0.5 minute for years 1900-2100 at all latitudes between -65 and +65 deg, with degraded accuracy beyond. This calculator implements the NOAA SPA verbatim, with Spencer 1971 Fourier-series declination and Roger 1996 EoT.
The three twilight bands — civil (-6 deg), nautical (-12 deg) and astronomical (-18 deg) — were codified in 1842 by the British Hydrographic Office for naval star-sight timing. Civil twilight is when the brightest stars become visible. Nautical twilight is when the horizon is still visible against the sky, enabling sextant sights. Astronomical twilight is when even the faintest stars (mag 6) become observable.
The 0.833 deg correction below the geometric horizon accounts for two physical effects: standard atmospheric refraction at the horizon (34 arcmin, per the ICAO standard atmosphere) plus the Sun's apparent semi-diameter (16 arcmin). Above the Arctic Circle (66.56 deg N) the Sun no longer crosses this threshold for parts of the year — producing the midnight sun (around June solstice) and polar night (around December solstice). The Tromso preset above demonstrates both.
For lunar timing pair this with Moon Phase; for civil-time conversions use Time-Zone Converter.
Trusted by surveyors, photographers, professors and event planners
“I need exact local sunrise for plane-table surveys near the Arabian Sea. The Mumbai preset matches my GNSS receiver almanac to within 30 seconds. The civil twilight band tells me when I can pack up.”
“The blue-hour and golden-hour timings save me hours of trial-and-error in the field. The altitude/azimuth-right-now widget lets me preposition for low-angle backlight on cheetahs at first light.”
“I teach the Norse seasonal year. Showing students the Tromso polar-night/midnight-sun output makes the ~66 deg cutoff visceral. Better than any textbook diagram.”
“Couples pick sunset ceremonies. I pull sunset + civil dusk for the venue lat/lon, then plan the photographer's golden hour and the band start time. Indispensable.”
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