Understanding the sun’s path
Every day, the sun traces an arc across the sky whose shape depends on latitude and date. This guide explains the concepts shown by SunPath 3D — sunrise, sunset, twilight, azimuth, altitude, shadow — and how they are calculated.
Azimuth and altitude: locating the sun
Two angles are enough to give the sun’s position as seen from a given place. Azimuth is the direction along the horizon, in degrees from north (90° = east, 180° = south, 270° = west). Altitude (or elevation) is the angle above the horizon, from 0° up to 90° at the zenith.
Light phases
| Phase | Sun altitude | What you see |
|---|---|---|
| Night | below −18° | Dark sky, no scattered sunlight. |
| Astronomical twilight | −18° to −12° | The sky starts to brighten; faint stars fade out. |
| Nautical twilight | −12° to −6° | The sea horizon becomes visible again. |
| Civil twilight | −6° to −0.833° | Bright enough for most activities without artificial light. |
| Sunrise / sunset | −0.833° | The upper edge of the sun touches the horizon. |
| Golden hour | −0.833° to 6° | Warm, raking light and very long shadows. |
| Daylight | above 6° | “Normal” daylight. |
Solstices and equinoxes 2026
These moments are the same everywhere on Earth (Universal Time, accurate to about a quarter of an hour); only their local time differs.
| Event | Date and time (UTC) | Paris: sunrise – sunset | Day length in Paris |
|---|---|---|---|
| March equinox | 20 March at 14:40 | 06:53 – 19:03 | 12h 10m |
| June solstice | 21 June at 08:26 | 05:46 – 21:57 | 16h 11m |
| September equinox | 23 September at 00:18 | 07:38 – 19:46 | 12h 08m |
| December solstice | 21 December at 20:56 | 08:41 – 16:56 | 8h 15m |
Calculating shadow length
On flat ground, shadow length = object height ÷ tan(sun altitude). For a 10 m object:
| Sun altitude | 60° | 45° | 30° | 15° | 5° |
|---|---|---|---|---|---|
| Shadow of a 10 m object | 5.8 m | 10.0 m | 17.3 m | 37.3 m | 114.3 m |
Reading the 3D view
- Globe view: the sun circles the Earth in 24 h. The golden arc shows the hours when it is up at your location, the dotted line the hours when it is down. The dotted orange and blue orbits are those of the June and December solstices.
- 3D, Horizon and Zenith views: a dome over the location shows the day’s path above the horizon, with the hours.
- Compass: the orange-red axis runs from east to west, the dotted line from north to south; the yellow and orange rays show the sunrise and sunset directions, the dark line the direction of the shadow.
- 3D shadows view: a street map of the location with an object casting its real shadow and, optionally, OpenStreetMap buildings in 3D with their shadows at the chosen time. Clicking the map measures the hours of direct sunlight that spot receives.
- Terrain and weather: actual sunrise and sunset behind the mountains, forecast cloud cover and UV index, estimated solar PV output.
- Real satellites (optional): the ISS and thousands of satellites positioned at the chosen time from the orbital elements published by CelesTrak, with the next visible ISS passes.
- Planets: the solar system at its real positions, and the planets visible from your location (altitude, rise, set, magnitude).
Method and accuracy
- Sun: SunCalc algorithm (J. Meeus’s formulas), apparent altitude with refraction. Times accurate to about 1 minute.
- Moon: same library; moonrise and moonset accurate to a few minutes.
- Solstices and equinoxes: ecliptic longitude of the sun, to within about 15 minutes.
- Eclipses and planets: Astronomy Engine library (accuracy on the order of an arcminute), local circumstances computed for your location.
- Time zones: IANA database (daylight saving time included), exact except within a few kilometres of a time zone boundary.
- Limitations: in Globe view, distances are not to scale (the real sun is about 23,000 times farther away than the orbit drawn); directions, however, are exact. The clouds on the globe are an illustrative image; the forecast cloud cover for your location comes from Open-Meteo.
Glossary
- Azimuth
- Horizontal direction of the sun, measured in degrees clockwise from north: 90° = east, 180° = south, 270° = west.
- Altitude (elevation)
- Angle of the sun above the horizon: 0° at the horizon, 90° at the zenith. A negative value means the sun is below the horizon.
- Sunrise / sunset
- The moment the upper edge of the sun touches the horizon, i.e. when the centre of the sun is 0.833° below the horizon, allowing for atmospheric refraction.
- Solar noon (culmination)
- The moment the sun reaches its highest altitude of the day. It rarely falls at 12:00 because of time zones, daylight saving time and the equation of time.
- Civil twilight
- Sun between 0.833° and 6° below the horizon: bright enough for most outdoor activities without artificial light.
- Nautical twilight
- Sun between 6° and 12° below the horizon: the sea horizon is still visible and bright stars appear.
- Astronomical twilight
- Sun between 12° and 18° below the horizon: the sky is not yet fully dark for astronomical observation.
- Golden hour
- Period when the sun is low (below 6° altitude in SunPath 3D): warm, raking light prized by photographers.
- Blue hour
- Part of twilight, often defined as the sun being between 4° and 6° below the horizon, when the sky turns deep blue. SunPath 3D does not calculate it separately.
- Solstice
- The moment the sun reaches its extreme declination (±23.44°): the longest day in one hemisphere and the shortest in the other.
- Equinox
- The moment the sun is directly above the equator: day and night are almost equal in length everywhere on Earth.
Frequently asked questions
Why doesn’t the longest day have the earliest sunrise?
Because of the equation of time: solar noon shifts by a few minutes over the year. In Paris in 2026, the earliest sunrise is on 16 June (05:46) and the latest sunset on 25 June (21:58), while the solstice falls on 21 June.
Why doesn’t the sun always rise due east?
Because the sun’s declination varies from −23.44° to +23.44° over the seasons. It only rises due east at the equinoxes. In Paris, the sunrise direction moves from about 52° (northeast) at the June solstice to 126° (southeast) at the December solstice.
How do you calculate the length of a shadow?
Shadow length = object height ÷ tangent of the sun’s altitude. On flat ground, a 10 m object casts a 10 m shadow when the sun is at 45°, a 17.3 m shadow at 30° and a 114 m shadow at 5°.
Do sunrise times take terrain into account?
The tables are calculated for a clear horizon at sea level, like most almanacs. The 3D map also calculates the actual sunrise and sunset behind the terrain (elevation model with a resolution of about 100 m); buildings and trees are not included.
How accurate are the times?
About one minute for sunrise, sunset and twilight at mid-latitudes, and a few minutes for the moon. Accuracy decreases near the polar circles, where the sun skims the horizon.
Is SunPath 3D free?
Yes, completely free, with no sign-up.
Sources
- V. Agafonkin, SunCalc (open-source library for sun and moon calculations).
- D. Cross, Astronomy Engine (eclipses, planets, moon phases).
- J. Meeus, Astronomical Algorithms, Willmann-Bell.
- NASA Earth Observatory, Blue Marble and Black Marble imagery.