Day length changes through the year because Earth’s axis is tilted. Near the poles the Sun may not set in summer or rise in winter. The 0.833° in the formula accounts for atmospheric refraction and the Sun’s radius.
How to use the Sunrise and Sunset Calculator
- Latitude (° N positive)
- Longitude (° E positive)
- Date
- Time zone (UTC offset in hours)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the latitude and longitude, the date and the UTC offset of your local time (including daylight saving).
Inputs explained
| Field | What to enter |
|---|---|
| Latitude (° N positive) | A number |
| Longitude (° E positive) | A number |
| Date | A date |
| Time zone (UTC offset in hours) | A number |
What each result means
- Equation of time = 4×(mod([L] – deg(atan2(cos([eps])×sin([lambda]), cos([lambda]))) + 540, 360) – 180)
- Solar declination = deg(asin(sin([eps])×sin([lambda])))
- Sunrise = (720 – 4×([Longitude (° E positive)] + [ha0]) – [Equation of time] + 60×[Time zone (UTC offset in hours)])÷60
- Solar noon = (720 – 4×[Longitude (° E positive)] – [Equation of time] + 60×[Time zone (UTC offset in hours)])÷60
- Sunset = (720 – 4×([Longitude (° E positive)] – [ha0]) – [Equation of time] + 60×[Time zone (UTC offset in hours)])÷60
Formula
cos(ha₀) = cos(90.833°)/(cos φ cos δ) − tan φ tan δ, sunrise = 720 − 4(λ + ha₀) − EoT + 60·tz (minutes)
sunset = 720 − 4(λ − ha₀) − EoT + 60·tz, solar noon = 720 − 4λ − EoT + 60·tz
Worked example
Inputs — Latitude (° N positive): 51.5074; Longitude (° E positive): -0.1278; Date: 2026-10-25; Time zone (UTC offset in hours): 0.
Results — Equation of time = 15.934 min; Solar declination = -12.1954 °; Sunrise = 06:42; Solar noon = 11:45; Sunset = 16:47; Day length = 10 h 5 min; Polar condition = Normal day.
Key terms
- Day length
- Time between sunrise and sunset.
Frequently asked questions
Why do sunrise times differ across a time zone?
Longitude changes solar time by 4 minutes per degree.
What is solar noon?
When the Sun is highest – rarely exactly 12:00.
Why is 90.833° used?
It includes refraction (0.567°) and the Sun's radius (0.267°).
How accurate is it?
Within about a minute at mid-latitudes.