Draw your sun path
Reading the diagram
The horizontal axis is the compass direction, from north through east, south and west back to north. The vertical axis is the height of the sun above the horizon. A curve therefore tells you two things at once: where to look and how high the sun will be at that moment.
Three curves matter more than the rest. The June solstice curve is the highest and widest the sun will ever be at your location; the December solstice curve is the lowest and shortest; the equinox curve sits between them and always rises due east and sets due west, everywhere on Earth. Any other date falls between the two solstice curves, so a roof overhang that shades the June curve and clears the December curve works for the whole year.
Typical noon altitudes
| Latitude | 21 Jun | Equinox | 21 Dec | Winter shadow of a 1 m post |
|---|
What the sun path tells you
Window and overhang design
A south-facing window in the northern hemisphere sees a high summer sun and a low winter sun. That is the whole idea behind passive solar design: an overhang deep enough to block the June arc still lets the December arc reach deep into the room. Read the June and December noon altitudes from the diagram, and the overhang depth follows from simple trigonometry — depth = window height ÷ tan(summer altitude).
Roof and array shading
Anything that pokes above the December curve will shade your panels in winter, when you can least afford it. Stand at the array position, note the elevation of the obstacle, and compare it with the winter curve: if the obstacle is higher, the array is in shadow at that time of day. The map tool does this numerically with its obstacle feature.
Photography and film
The diagram tells you when the sun will be behind, beside or in front of your subject. Combine it with the golden hour times to know both the direction and the quality of the light before you drive anywhere.
The maths behind the curve
Two angles fix the sun in the sky. Solar declination δ says how far the sun is north or south of the celestial equator on a given date; the hour angle H says how far the Earth has turned since solar noon, at 15° per hour. With your latitude φ they give:
- Altitude: sin(altitude) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H)
- Azimuth: measured from north, from the same two angles
This site evaluates those formulas with a solar series accurate to about 0.01°, adds atmospheric refraction near the horizon, and repeats the calculation every few pixels to draw a smooth curve. More detail is on the method page.
Questions
Frequently asked questions
What is a sun path diagram?
A sun path diagram plots the sun's altitude against its azimuth for a whole day. Each curve is one date; the family of curves between the June and December solstice covers everything the sun can do at that latitude. Architects use it to size overhangs, and photographers use it to know where the light will come from.
How does the sun path change with latitude?
Near the equator the sun climbs almost vertically and passes close to the zenith, so the arcs are steep and narrow. As latitude increases the arcs tilt, the summer path grows longer and flatter, and the winter path shrinks toward the southern horizon in the northern hemisphere. Above the polar circle the summer path never touches the horizon at all.
How high is the sun at solar noon?
At solar noon the altitude equals 90 degrees minus your latitude plus the solar declination of that date. Declination runs from +23.44 degrees on 21 June to -23.44 degrees on 21 December, so the noon sun swings through 46.9 degrees over the year at every location.
Why is the sun path not symmetrical around 12:00?
Clock noon and solar noon differ because of your position inside the time zone, daylight saving time and the equation of time, which shifts true solar noon by up to about 16 minutes over the year. The path itself is symmetrical around solar noon, not around 12:00 on the clock.