Paritian

Science

Sun Position and Shadow Length Calculator

Height and direction of the Sun at any clock time, place and day, the length of a shadow, and the Sun's path through the day drawn against the solstices.

Results

Sun elevation above the horizon 55.33 °
Sun azimuth (from north, clockwise) 218.00 °
Shadow length 1.25 m
Sun above the horizon? Yes
Solar noon (clock time) 13.613 h
Sun elevation at solar noon 60.76 °
Solar declination 9.481 °
Equation of time -0.24 min
The shape, to scale
Sun Position and Shadow Length CalculatorSun Position and Shadow Length Calculator: Shadow length = 1.25 m, Object height = 1.80 m, 55.33°Shadow length = 1.25 mObject height = 1.80 m55.33°
How it changes
Sun elevation above the horizonClock time (hours, 14.5 = 14:30) 0 – 24. On the chosen day: -36.7907 → -36.7907; 21 June: -23.7356 → -23.7356; 21 December: -64.7817 → -64.7817On the chosen day21 June21 December-100-5005010005101520Clock time (hours, 14.5 = 14:30) (h)

The dashed line marks the value you entered.

What this tool does

The Sun's height follows from three numbers: your latitude, the Sun's declination that day and how far it is from solar noon. Clock time is not solar time — the time zone, summer time, your longitude within the zone and the equation of time (up to about 16 minutes either way through the year) all shift it — so the calculator converts your clock time first. A shadow is the object's height divided by the tangent of the Sun's elevation: at 45° it equals the height, and below 10° it is more than five times longer. Day of year: 1 January is 1, 21 June is 172 and 21 December is 355 in a normal year.

Formula

sin α = sin φ sin δ + cos φ cos δ cos h · h = 15° × (solar time − 12) · shadow = height ÷ tan α

Variables

SymbolMeaningUnit
laLatitude°
loLongitude (east positive)°
tzClock offset from UTC (with summer time)h
ndDay of the year—
hrClock time (hours, 14.5 = 14:30)h
hhObject heightm
ELSun elevation above the horizon°
AZSun azimuth (from north, clockwise)°
SHShadow lengthm
UPSun above the horizon?—
SNSolar noon (clock time)h
NESun elevation at solar noon°
DCSolar declination°
EQEquation of timemin

Worked example

  • Latitude38.72 °
  • Longitude (east positive)-9.14 °
  • Clock offset from UTC (with summer time)1 h
  • Day of the year105
  • Clock time (hours, 14.5 = 14:30)15 h
  • Object height1.8 m
  • Sun elevation above the horizon55.33 °
  • Sun azimuth (from north, clockwise)218.00 °
  • Shadow length1.25 m
  • Sun above the horizon?Yes
  • Solar noon (clock time)13.613 h
  • Sun elevation at solar noon60.76 °
  • Solar declination9.481 °
  • Equation of time-0.24 min

Limitations

  • Declination and the equation of time come from Spencer's 1971 series, good to a small fraction of a degree. Atmospheric refraction, which lifts the Sun by about half a degree at the horizon, is not included.
  • The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.