Why solar noon is not at 12:00
Time zones, daylight saving and the equation of time: why the sun peaks at 14:16 in Madrid in June.
The basics
Two numbers for one point in the sky
Every position of the sun can be written as a direction and a height. Navigators, surveyors and solar engineers all use the same pair of angles, and so does every tool on this site.
Azimuth is the compass bearing of the sun, measured clockwise from true north: 0° is north, 90° east, 180° south and 270° west. A sun at azimuth 135° stands in the south-east. Because it is a bearing, it tells you which way a window, a roof or a camera has to face to catch the sun.
Elevation, also called altitude or the sun angle, is the height of the sun above the horizon: 0° when its centre is on the horizon, 90° when it is straight overhead. Below the horizon it turns negative, and those negative values are what define twilight: civil twilight lasts until the sun is 6° down, nautical twilight until 12°, astronomical until 18°.
Solar engineers often quote the zenith angle instead, which is simply 90° minus the elevation. A sun 30° above the horizon has a zenith angle of 60°.
A worked example: in London on 15 October 2026 at 14:00 local time (13:00 UTC) the sun stands at azimuth 200.7°, a little west of south, and elevation 27.8°. A one-metre stick casts a shadow 1.9 metres long, pointing to azimuth 20.7°, north-north-east.
Through the day
How the two angles move from sunrise to sunset
At sunrise the elevation is zero and the azimuth is somewhere on the eastern half of the compass. As the morning goes on the sun climbs and swings towards the south (in the northern hemisphere). At solar noon it reaches its highest elevation of the day and crosses the meridian: its azimuth is exactly 180° north of the tropics, or exactly 0° south of them. The afternoon is the mirror image of the morning.
The two angles do not change at a steady pace. The azimuth turns fastest around noon, and faster the higher the sun climbs: in the tropics, on the days the sun passes almost through the zenith, the azimuth swings from east to west in a few minutes either side of noon. The elevation changes fastest near sunrise and sunset, and how fast depends on latitude: on the equator the sun climbs almost vertically, about a degree every four minutes, while in Scandinavia it slants up at a shallow angle. That is why twilight and golden hour are short in the tropics and long in the north.
Through the year
How high the noon sun climbs
The highest elevation of a day, at solar noon, follows a simple rule: it is 90° minus the angle between your latitude and the sun’s declination, the latitude on Earth where the sun is overhead that day. The declination runs from +23.44° at the June solstice to −23.44° at the December one and passes 0° at the equinoxes, so the noon sun at any place rises and falls by 46.9° over a year.
| City | Latitude | 21 June | 20 March | 21 December |
|---|---|---|---|---|
| London | 51.5° N | 61.9° | 38.4° | 15.1° |
| Oslo | 59.9° N | 53.5° | 30.0° | 6.6° |
| New York | 40.7° N | 72.7° | 49.3° | 25.8° |
| Madrid | 40.4° N | 73.0° | 49.5° | 26.1° |
| Singapore | 1.4° N | 67.9° (to the north) | 88.5° | 65.2° |
| Sydney | 33.9° S | 32.7° (to the north) | 56.3° | 79.6° |
Two things stand out. In Oslo the December sun gets no higher than 6.6°, so even at midday a two-storey house throws a shadow about 50 metres long. And in Singapore the noon sun is north of the zenith in June and south of it in December; it passes almost straight overhead in late March and mid-September, as the article on the overhead sun explains.
In the field
Measuring the angles yourself
Azimuth with a compass. A magnetic compass points to magnetic north, not true north, and the difference, the magnetic declination, depends on where you are and drifts from year to year. In much of Europe it is within a few degrees, but in parts of North America it is more than ten, east or west. Look up the current value for your location before you trust a compass bearing, and keep the compass away from steel, cars and reinforced concrete. A phone compass suffers from all the same errors.
Azimuth from a shadow. The shadow of a vertical stick points directly away from the sun, so the sun’s azimuth is the shadow’s direction plus 180°. With a map or the sun position map on your phone you can work it the other way round and find north from the sun.
Elevation from a shadow. Measure a vertical stick and its shadow on level ground. The elevation is the arctangent of height divided by shadow length: a one-metre stick with a 1.9 m shadow gives arctan(1 / 1.9) = 27.8°. Never look at the sun to measure it, not even through sunglasses.
| Sun elevation | Shadow length | A 1.8 m person |
|---|---|---|
| 60° | 0.58 × height | 1.0 m |
| 45° | 1.00 × height | 1.8 m |
| 30° | 1.73 × height | 3.1 m |
| 20° | 2.75 × height | 4.9 m |
| 15° | 3.73 × height | 6.7 m |
| 10° | 5.67 × height | 10.2 m |
| 5° | 11.4 × height | 20.6 m |
A detail that matters at the horizon
True and apparent elevation
The atmosphere bends sunlight downwards, so the sun appears higher than it really is. The effect is about 0.57° on the horizon, more than the width of the sun itself, and falls to a few hundredths of a degree once the sun is 30° up. It is why the sun is still visible for a couple of minutes after it has geometrically set, and why sunrise and sunset are defined as the moment the top of the disc touches the horizon, with the centre 0.833° below it.
This site shows the true elevation for shadows and solar panels and the refracted, apparent elevation where it changes what you see. The method page lists every formula behind the numbers.
Putting them to use
Where the two angles matter
- Shadows: length from the elevation, direction from the azimuth. The shadow length calculator does both.
- Solar panels: the closer the sun is to the panel’s perpendicular, the more energy it collects. See how the best tilt changes with the seasons.
- Buildings: a low western sun on a summer evening shines straight through west-facing windows, which is why orientation matters for overheating.
- Photography: below about 6° of elevation the light turns warm and soft, the start of the golden hour.
Keep reading
Related articles
Where does the sun rise? Sunrise and sunset direction through the year
Due east only near the equinoxes: in London the sunrise point swings 80° along the horizon.
How to find north with the sun and a shadow
The shadow-tip and watch methods can be 20–70° out. The ones that work, and the real errors.