Sunrise and Sunset Calculator
Sunrise, sunset, solar noon and the length of the day for any latitude, longitude and date.
The Sun’s position is computed from the date (its mean anomaly and ecliptic longitude), which gives its declination and the equation of time; the hour angle at which its upper edge crosses the horizon — allowing 0.
How the sunrise and sunset calculator works
The Sun’s position is computed from the date (its mean anomaly and ecliptic longitude), which gives its declination and the equation of time; the hour angle at which its upper edge crosses the horizon — allowing 0.833° for refraction — then sets sunrise and sunset either side of solar noon. Times are within a minute or two of the almanac. Enter the UTC offset that applies on that date, daylight saving included.
Formula: cos ω₀ = (sin −0.833° − sin φ · sin δ) ÷ (cos φ · cos δ); sunrise = solar noon − ω₀ ÷ 15°
Worked examples
| Inputs | Sunrise | Note |
|---|---|---|
| Southern-hemisphere midsummer: 33.9° S, 151.2° E (UTC+11) | 05:47 | about 05:47 to 20:10, 14 h 23 min |
| London, midsummer (BST, +1) | 04:43 | about 04:43 to 21:21 |
| New York, midwinter (EST, −5) | 07:16 | about 07:17 to 16:32 |
FAQFrequently asked questions
How accurate are the times?
Within a minute or two for most places and dates; the formula uses a simplified solar model with standard refraction. Very high latitudes near the polar day-and-night boundary are less certain.
Which UTC offset should I use?
The one in force on that date, daylight saving included: London is +1 in summer and 0 in winter, New York −4 and −5, and southern-hemisphere cities that observe daylight saving add their hour from October to April.
What is solar noon?
The moment the Sun is highest, halfway between sunrise and sunset. It is rarely 12:00 on the clock because of your position within the time zone and the equation of time.
Why is the day longer than 12 hours at the equinox?
Refraction bends sunlight over the horizon and sunrise is timed from the Sun’s upper edge, so every day is about seven minutes longer than pure geometry gives — the equinox has about 12 h 07 min.
Where these figures come from
- ISO 8601 — Date and time — Representations for information interchange — the yyyy-mm-dd format and the week-numbering rules used here
- US Naval Observatory — Calendars — the Gregorian leap-year rule
- GOV.UK — bank holidays — bank holidays by nation (not applied here)
Last checked: September 2026. The Gregorian calendar rules do not change; working-day counts exclude Saturdays and Sundays only.