How to use
- Pick a date. It starts as today.
- Choose a city, tap Use my location, or type the latitude and longitude. South and west are negative.
- Check the time zone. Daylight saving time is applied for that date.
- Read sunrise, sunset, day length and twilight. Open Show every day of the month for a table.
How sunrise and sunset are calculated
The calculator uses the equations behind NOAA’s Solar Calculator, which come from Jean Meeus’s Astronomical Algorithms.
- For the date, work out the sun’s declination δ (how far north or south of the equator it is) and the equation of time.
- Solar noon, in minutes after midnight UTC, is 720 − 4 × longitude − equation of time.
- The hour angle H when the sun reaches a zenith angle z, at latitude φ, is found from:
cos H = cos z ÷ (cos φ × cos δ) − tan φ × tan δ
- Sunrise is solar noon − 4H minutes and sunset is solar noon + 4H. Each is recalculated at its own time for accuracy.
| Event | The sun’s centre is | Zenith angle z |
|---|---|---|
| Sunrise and sunset | 0.833° below the horizon | 90.833° |
| Civil twilight | 6° below | 96° |
| Nautical twilight | 12° below | 102° |
| Astronomical twilight | 18° below | 108° |
If cos H comes out above 1, the sun never climbs to that angle that day (polar night). Below −1, it never sinks to it (midnight sun).
Examples
- New York, 21 October 2026: sunrise 7:14 AM, sunset 6:07 PM (daylight time), so 10 h 53 min of daylight. Civil twilight lasts from 6:46 AM to 6:35 PM.
- Karachi, 21 October 2026: sunrise 6:33 AM and sunset 6:00 PM, giving 11 h 27 min of daylight.
- Reykjavík, 21 June 2026: sunrise 2:55 AM and sunset 12:04 AM the next day, and it never gets darker than civil twilight.
- Tromsø, Norway: the sun doesn’t set on 21 June 2026 and doesn’t rise on 21 December 2026.
Day length at the solstices (2026)
| City | 21 June | 21 December |
|---|---|---|
| London | 16 h 39 min | 7 h 49 min |
| New York | 15 h 6 min | 9 h 15 min |
| Karachi | 13 h 41 min | 10 h 36 min |
| Dubai | 13 h 42 min | 10 h 35 min |
| Singapore | 12 h 12 min | 12 h 3 min |
| Sydney | 9 h 54 min | 14 h 24 min |
| Reykjavík | 21 h 9 min | 4 h 7 min |
Accuracy and the limits of the method
- NOAA says sunrise and sunset from these equations are accurate to within a minute between 72° north and south, and within 10 minutes nearer the poles.
- The 0.833° allows for the sun’s radius and average refraction, the bending of light by air. Real refraction changes with temperature and pressure, so what you see can differ.
- Times assume a level horizon, as the US Naval Observatory’s definition does. Hills, buildings and your height change what you see.
- We checked our results against NOAA’s own spreadsheet for nine places. Sunrise and sunset agree to within a few seconds.
City coordinates come from GeoNames (CC BY 4.0). To write the times on a 24-hour clock, try the military time converter.