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Sunrise Sunset On A Date Calculator

Work out sunrise sunset on a date instantly with clear inputs, formula shown and shareable results.

About Sunrise Sunset On A Date Calculator

Sunrise and sunset are symmetrical about solar noon, separated by twice the sunrise hour angle whose cosine is -tan(latitude)tan(declination). At 51.5 degrees north on the June solstice the half-day is 8.18 hours, so the Sun rises at 03:49 and sets at 20:11 in local solar time - which clock time then shifts by longitude and the equation of time.

Formulas

Sunrise hour angle

cos(H) = -tan(latitude) x tan(declination)

Sunrise and sunset

solar noon minus and plus H/15 hours

Worked example

With the default values below, Sunrise Sunset On A Date Calculator returns Day Length of 16.404. Change any input above and every figure here is recalculated in your browser.

Inputs used

Latitudeaccepts -66–66 deg
51.5 deg
Date
2026-06-21
UTC offsetaccepts -12–14 h
1 h

Results

Day Length
16.404 h
Sunrise In Local Solar Time
3.80 h
Sunset In Local Solar Time
20.20 h
Solar Noon
12.0 h

Step by step

  1. 1Values used
  2. 2Sunrise hour angle
  3. 3Sunrise and sunset
  4. 4Day Length= 16.404 h
  5. 5Sunrise In Local Solar Time= 3.80 h
  6. 6Sunset In Local Solar Time= 20.20 h
  7. 7Solar Noon= 12.0 h

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do these differ from published times?

Published times use clock time rather than solar time, and allow for atmospheric refraction and the Sun's disc, which adds about three minutes at each end.

What happens above the Arctic Circle?

The cosine goes out of range, meaning the Sun never rises or never sets. Latitude is limited to 66 degrees here for that reason.

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Sunrise Sunset On A Date Calculator – Calculate Day Length