How are sunrise and sunset times calculated?

The tool uses the NOAA/Meeus solar-position algorithm. It computes the sun's ecliptic longitude, declination and the equation of time for the chosen Julian Day, then solves the hour-angle equation: cos(HA) = (cos(90.833°) − sin(lat)·sin(dec)) / (cos(lat)·cos(dec)). The 90.833° zenith accounts for standard atmospheric refraction (0.583°) plus the sun's apparent radius (0.25°). Solar noon minus/plus the hour angle gives sunrise and sunset in UTC, which is then offset by your chosen timezone.

What is civil twilight and why does it matter?

Civil twilight begins when the sun is 6° below the horizon (zenith angle 96°). At this point there is enough natural light to carry out outdoor activities without artificial lighting. Photographers use it as the practical start and end of the day — the sky is bright but the sun has not yet risen or has just set.

What is the golden hour?

Golden hour is the period just after sunrise and just before sunset when the sun is less than 6° above the horizon (zenith 84°). The light travels through more atmosphere, scattering blue wavelengths and leaving warm red and amber tones. It is the single most sought-after lighting condition in photography and film.

Why does solar noon differ from 12:00 on my clock?

Clock noon is defined by your civil timezone, which covers a wide band of longitudes. Solar noon — when the sun crosses the meridian — depends on your precise longitude and the equation of time (the accumulated difference between a perfectly regular clock and actual solar motion caused by Earth's elliptical orbit and axial tilt). The two can differ by up to ±30 minutes depending on your location and time of year.

What happens at very high latitudes in summer or winter?

Above roughly 66.5° N or S (the Arctic/Antarctic circle), the sun can remain above or below the horizon for the entire day. The calculator detects this and shows a Midnight Sun banner (sun never sets) or Polar Night banner (sun never rises) for affected dates.

How accurate is this calculator?

The algorithm matches NOAA's published solar calculator to within ±1 minute for latitudes between 70° N and 70° S and dates between 1901 and 2099. Accuracy degrades somewhat near the poles and at extreme historical or future dates because higher-order perturbation terms are not included. For everyday planning and photography purposes the results are accurate to within a minute or two.

Sunrise & Sunset Time Calculator

Whether you are a photographer hunting the perfect golden-hour light, a gardener planning when to water, or a traveller checking sunset times for a rooftop dinner reservation, knowing exactly when the sun will rise and set at a specific place on a specific date is surprisingly hard to look up. This tool solves it entirely in your browser — no API, no network request, just pure trigonometry applied to your latitude, longitude and the date.

What you get

Enter a location and a date and the calculator returns seven precise solar events:

Civil dawn — first usable daylight, 6° before sunrise
Sunrise — upper limb of sun clears the horizon
Golden hour end (morning) — sun reaches 6° altitude; warm directional light fades
Solar noon — sun at its highest point; shadows are shortest
Golden hour start (evening) — sun drops to 6° altitude; golden light returns
Sunset — upper limb of sun touches the horizon
Civil dusk — last usable daylight, 6° after sunset

You also get total day length (sunrise to sunset) and an interactive 24-hour day-arc diagram that shows the proportions of night, civil twilight, golden hour and full daylight at a glance.

How the formula works

The core of every solar calculator is the hour angle equation. Once you know the sun’s declination (its celestial latitude) and the observer’s latitude, you can work backwards from the desired solar zenith angle to find the time of day:

cos(HA) = (cos(z) − sin(lat) × sin(dec)) / (cos(lat) × cos(dec))

Where z is the target zenith angle (90.833° for sunrise — the extra 0.833° corrects for standard atmospheric refraction and the sun’s angular radius), lat is your latitude and dec is the sun’s declination on the chosen date.

Solving for HA gives the hour angle in degrees either side of solar noon. Converting that to clock time requires the equation of time — a wobble of up to ±16 minutes per year caused by Earth’s elliptical orbit and axial tilt — which the calculator also applies.

Worked example

Location: London (51.5074° N, −0.1278° E), Date: 21 June (summer solstice)

At the summer solstice the sun’s declination is approximately +23.44°. Substituting into the hour angle formula:

cos(HA) = (cos(90.833°) − sin(51.51°) × sin(23.44°)) / (cos(51.51°) × cos(23.44°))
cos(HA) ≈ (−0.01454 − 0.7826 × 0.3979) / (0.6225 × 0.9174)
cos(HA) ≈ −0.3257 / 0.5711 ≈ −0.5703
HA ≈ 124.8°

Solar noon in London on 21 June is approximately 13:02 BST (accounting for longitude and equation of time). Adding and subtracting 124.8° × 4 min/° = 499 min ≈ 8 h 19 min:

Sunrise: 13:02 − 8:19 = 04:43 BST
Sunset: 13:02 + 8:19 = 21:21 BST
Day length: 16 h 38 min — the longest day of the year

The calculator performs this calculation instantly for any latitude/longitude and date you enter.

Formula reference

Event	Zenith angle used
Sunrise / Sunset	90.833° (refraction + solar radius)
Civil twilight	96°
Golden hour boundary	84° (6° solar altitude)
Solar noon	Equation of time only (no hour angle)

All intermediate results (Julian Day, mean anomaly, ecliptic longitude, obliquity, right ascension, declination, equation of time) follow Jean Meeus’s Astronomical Algorithms (2nd edition), the same source used by NASA and NOAA.