General

The calculations in the Sunrise/Sunset and Solar Position Calculators are based on equations from Astronomical Algorithms, by Jean Meeus. The sunrise and sunset results have been verified to be accurate to within a minute for locations between +/- 72° latitude, and within 10 minutes outside of those latitudes.

Click here for a PDF file of low accuracy solar position equations.

Click here to see the higher accuracy JavaScript routines used in our improved calculators. These routines are based on Jean Meeus's book Astronomical Algorithms.

Historical Dates

For the purposes of these calculators the current Gregorian calendar is extrapolated backward through time. When using a date before 15 October, 1582, you will need to correct for this.

The year preceding year 1 in the calendar is year zero (0). The year before that is -1.

The approximations used in these programs are very good for years between 1800 and 2100. Results should still be sufficiently accurate for the range from -1000 to 3000. Outside of this range, results will be given, but the potential for error is higher.

Atmospheric Refraction Effects

For sunrise and sunset calculations, we assume 0.833° of atmospheric refraction. In the solar position calculator, atmospheric refraction is modeled as:

Solar Elevation	Approximate Atmospheric Refraction Correction (°)
85° to 90°	0
5° to 85°
-0.575° to 5°
< -0.575°

The effects of the atmosphere vary with atmospheric pressure, humidity and other variables. Therefore the solar position calculations presented here are approximate. Errors in sunrise and sunset times can be expected to increase the further away you are from the equator, because the sun rises and sets at a very shallow angle. Small variations in the atmosphere can have a larger effect.

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