How this calculator works
The NOAA approximation estimates declination and the equation of time for local noon. The chosen horizon depression gives the morning and evening hour angles. Longitude and UTC offset convert those angles to local clock times. A 0.833 degree depression approximates the upper solar limb and typical refraction at a level sea horizon. Mountain skylines, elevation and changing refraction are excluded. High-latitude seasons can have no crossing. Times are rounded to the nearest minute, with day offsets shown when needed.
Formula
cos(H) = [-sin(depression)-sin(latitude)sin(declination)]/[cos(latitude)cos(declination)]. Solar noon minutes = 720 - 4 longitude_degrees - equation_of_time + 60 UTC_offset. Rise/set = noon minus/plus 4 H_degrees.
Worked example
On the equator with a zero-degree geometric horizon, the Sun is above that horizon for 12 hours in this daily approximation. A 0.833 degree depression makes the estimated apparent day slightly longer.
Advertisement
Frequently asked questions
Can I calculate twilight?
Yes. Enter a depression of 6 degrees for civil, 12 for nautical or 18 for astronomical twilight.
Why is no sunrise returned?
The Sun can remain above or below the chosen horizon all day at high latitudes.
Do these times include daylight saving?
Only when you select the extra-hour adjustment. Use your standard UTC offset in the numeric field.