Solar Altitude / Winter-Design Sun Elevation
The sun's elevation angle above the horizon.
Example
You enter
- Latitude (deg, + north) 40
- Day of year (1-365; 355 = winter solstice) 355
You get
- Solar altitude (elevation) 26.55
- Declination (deg) -23.45
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method.
Details, formula, and sources
Scopesin(altitude) = sin(lat) sin(dec) + cos(lat) cos(dec) cos(H), declination from Cooper's dec = 23.45 sin(360 (284+n)/365), hour angle H = 15 x (hours from solar noon); at solar noon altitude = 90 - |lat - dec|. At 40 deg N on the winter solstice the noon sun reaches only 26.6 deg and by 3 p.m. about 14 deg -- the winter-design elevation a shading, solar-access, tree, or setback study turns on. Feed it into a shadow length or PV row spacing. A negative value means the sun is below the horizon. True solar time and a flat horizon assumed; the Clock Time to Solar Time calculator converts a clock reading, and refraction is separate. The actual sun path governs.
Formula or tabledec = 23.45 sin(360 (284 + n)/365); H = 15 (hours from solar noon); sin(altitude) = sin(lat) sin(dec) + cos(lat) cos(dec) cos(H); at noon altitude = 90 - |lat - dec|.
Source and editionThe solar altitude (elevation) angle from the standard NOAA/ASHRAE solar-geometry relation, with the declination from Cooper's equation, by name.
Free accessThe solar-position equations are public-domain solar geometry (NOAA/ASHRAE); the latitude, date, and time are the user's own site inputs.
What governsEstimate. AHJ and licensed professional govern.
API field nameslatitude_deg, day_of_year, altitude_deg, declination_deg
- Altitude sin(altitude) = sin(lat) sin(dec) + cos(lat) cos(dec) cos(H)NOAA/ASHRAE solar geometry
- Declination dec = 23.45 sin(360 (284 + n)/365) (Cooper's equation)Cooper (1969)
- Hour angle H = 15 x (hours from solar noon); solar-noon form altitude = 90 - |lat - dec|solar geometry
- Scope true solar time, flat horizon; solar-time-correction converts a clock time; refraction is separatescope of this tile; solar-time-correction