How to use the sun path calculator
Where the sun sits in the sky drives a building's daylight, heat gain, shading and the shadows it throws onto neighbours. This calculator gives the sun's position for any place, date and time using the NOAA solar equations, so you can orient a plan, size an overhang or answer a neighbour's question about overshadowing without opening modelling software.
- Pick a city preset or enter the site's latitude and longitude in decimal degrees. North and east are positive; south and west are negative.
- Set the UTC offset the clock shows on that date, including daylight saving time. Presets fill in the standard-time offset.
- Choose the date and clock time you want to test, such as a solstice afternoon.
- Enter an object height, for example a building, wall or tree, to get the length of its shadow on level ground.
The results show altitude, azimuth, compass direction, shadow ratio and length, sunrise, solar noon, sunset and day length, followed by a table of the sun's position for every hour of daylight.
Sun position formulas
sin(altitude) = sin φ × sin δ + cos φ × cos δ × cos h
Hour angle h = (true solar time ÷ 4) − 180°
Shadow length = height ÷ tan(altitude)
Overhang depth ≈ window height ÷ tan(noon altitude)
φ is the latitude, δ the sun's declination for the date (between −23.44° and +23.44°), and h the hour angle, which is zero at solar noon and changes by 15° per hour. True solar time corrects your clock for longitude, time zone and the equation of time, which is why solar noon is rarely exactly 12:00. Sunrise and sunset include the standard allowance for atmospheric refraction.
| Sun altitude | Shadow length ÷ height |
|---|---|
| 60° | 0.58 |
| 45° | 1.00 |
| 30° | 1.73 |
| 15° | 3.73 |
| 5° | 11.4 |
Worked examples
Midsummer in London
On 21 June at 13:00 British Summer Time (UTC+1), the sun in London is at about 62° altitude and 179° azimuth, almost due south. A 10 m building casts a shadow of only about 5.3 m. The sun rises at about 04:43 and sets at about 21:22, giving roughly 16.6 hours of daylight.
Midwinter in London
On 21 December at 12:00 (UTC+0) the sun reaches only about 15° above the horizon. The same 10 m building now casts a shadow of about 37 m, which is why winter overshadowing dominates rights-of-light and planning discussions in northern cities, and day length falls to about 7.8 hours.
A west facade in New York
On 21 June at 15:00 EDT (UTC−4) the sun in New York is at about 59° altitude and 245° azimuth, west-southwest. Low afternoon sun from this direction is hard to block with horizontal overhangs, so vertical fins or external blinds suit west glazing better.
Southern hemisphere check
In Sydney at noon on 21 December (UTC+11), the sun is at about 74° altitude and 52° azimuth, to the northeast. South of the equator the midday sun is to the north, so living spaces and solar panels face north instead.
Who this calculator helps
- Architects orienting buildings, placing glazing and sizing shading at concept stage.
- Landscape architects placing gardens, terraces and planting that need sun or shade.
- Planning consultants giving quick overshadowing answers before a full study.
- Solar installers and engineers checking sun angles for panels and obstructions.
- Photographers and visualisers matching render lighting to a real time and place.
Tips for designing with the sun
- Size south-facing overhangs (north-facing in the southern hemisphere) from the summer noon altitude so they shade in summer but let low winter sun in.
- Pair sun angles with the window-to-wall ratio calculator to keep glazing on east and west facades in check.
- Remember that daylight and sunlight are different: check diffuse daylight with the daylight factor calculator.
- Use the shadow length with the setback calculator to see how close a tall block can sit to a neighbour's garden.
- Check the winter solstice for the worst case and an equinox for a fair average before presenting results.
Want to show a client the same scene at golden hour? Turn a daytime exterior photo into an evening view with Day to Dusk.
