Sunrise Sunset Calculator

NOAA daily approximation evaluated at noon, using a 90.833° sunrise/sunset zenith for a non-leap year. Inputs without daily rise/set are rejected. Terrain, actual refraction and elevation are not modeled; include daylight saving in the UTC offset.

How to use this tool

Check the units, enter your values, and run the tool. Results follow the assumptions and method below.

Calculation method

Sunrise local decimal hour

mod(((720-4*longitude-(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+0)))-0.032077*sin((2*pi/365*(day-1+0)))-0.014615*cos(2*(2*pi/365*(day-1+0)))-0.040849*sin(2*(2*pi/365*(day-1+0)))))+60*zone)-4*(acos((cos(90.833*pi/180)/(cos(latitude*pi/180)*cos((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0))))))-tan(latitude*pi/180)*tan((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0)))))))*180/pi)),1440)/60

Sunset local decimal hour

mod(((720-4*longitude-(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+0)))-0.032077*sin((2*pi/365*(day-1+0)))-0.014615*cos(2*(2*pi/365*(day-1+0)))-0.040849*sin(2*(2*pi/365*(day-1+0)))))+60*zone)+4*(acos((cos(90.833*pi/180)/(cos(latitude*pi/180)*cos((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0))))))-tan(latitude*pi/180)*tan((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0)))))))*180/pi)),1440)/60

Sunrise day offset

floor(((720-4*longitude-(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+0)))-0.032077*sin((2*pi/365*(day-1+0)))-0.014615*cos(2*(2*pi/365*(day-1+0)))-0.040849*sin(2*(2*pi/365*(day-1+0)))))+60*zone)-4*(acos((cos(90.833*pi/180)/(cos(latitude*pi/180)*cos((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0))))))-tan(latitude*pi/180)*tan((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0)))))))*180/pi))/1440)

Sunset day offset

floor(((720-4*longitude-(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+0)))-0.032077*sin((2*pi/365*(day-1+0)))-0.014615*cos(2*(2*pi/365*(day-1+0)))-0.040849*sin(2*(2*pi/365*(day-1+0)))))+60*zone)+4*(acos((cos(90.833*pi/180)/(cos(latitude*pi/180)*cos((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0))))))-tan(latitude*pi/180)*tan((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0)))))))*180/pi))/1440)

Daylight duration

8*(acos((cos(90.833*pi/180)/(cos(latitude*pi/180)*cos((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0))))))-tan(latitude*pi/180)*tan((0.006918-0.399912*cos((2*pi/365*(day-1+0)))+0.070257*sin((2*pi/365*(day-1+0)))-0.006758*cos(2*(2*pi/365*(day-1+0)))+0.000907*sin(2*(2*pi/365*(day-1+0)))-0.002697*cos(3*(2*pi/365*(day-1+0)))+0.00148*sin(3*(2*pi/365*(day-1+0)))))))*180/pi)/60

Solar noon local decimal hour

mod((720-4*longitude-(229.18*(0.000075+0.001868*cos((2*pi/365*(day-1+0)))-0.032077*sin((2*pi/365*(day-1+0)))-0.014615*cos(2*(2*pi/365*(day-1+0)))-0.040849*sin(2*(2*pi/365*(day-1+0)))))+60*zone),1440)/60

References

https://gml.noaa.gov/grad/solcalc/solareqns.PDF