The Sun’s position: understanding azimuth and altitude

Two angles describe a point in the sky

The horizontal coordinate system describes the sky as you experience it: a dome above you, the horizon around its base and the **zenith** directly overhead.

• **Azimuth** is measured along the horizon. In the convention used here, north is 0°, east 90°, south 180° and west 270°. Some older astronomical sources start from the south, so check the convention before comparing a table or chart.
• **Altitude** runs from 0° at the horizon to 90° at the zenith. Negative values place an object below the horizon. Some sources instead give zenith distance, the angular separation from the overhead point.

Both are local coordinates. At the same instant, an observer in New York and one at the Grand Canyon see the Sun in different directions and at different altitudes. A time alone is not enough to describe its position.

How the position changes through the day

Earth’s rotation makes the Sun appear to move along a daily arc. Its hour angle progresses at roughly fifteen degrees per hour, but that does not mean altitude or azimuth changes uniformly at that rate. At middle northern latitudes, the Sun rises in the eastern part of the horizon, reaches its highest point as it crosses the southern meridian and descends towards the west.

This **upper culmination** marks local apparent noon. It need not happen at 12:00 civil time, because your longitude within the time zone and the equation of time both shift the clock reading. Daylight-saving arrangements add another clock offset where they apply.

Latitude sets the broad pattern of the noon altitude, while solar declination changes it through the seasons. Outside the tropics, the difference between the June and December solstitial noon altitudes is close to 47°. In the tropics, the Sun can pass to either side of the zenith, so a blanket statement that it is always south at noon is wrong.

How the position changes through the year

Earth’s axial tilt makes the Sun’s declination range between about +23.4° and −23.4°. This changes both its maximum altitude and the horizon directions of sunrise and sunset.

At a middle Northern Hemisphere latitude, the June Sun follows a long, high arc from the northeast towards the northwest. In December its arc is shorter and lower, beginning towards the southeast and ending towards the southwest. Near the equinoxes it rises approximately east and sets approximately west. The scale of this seasonal sweep grows towards high latitudes, eventually leading to days without a sunset or sunrise.

The same calendar dates describe different seasons in the Southern Hemisphere. In a tropical destination, check the actual declination and latitude rather than borrowing a familiar northern compass rule. Refraction and the local horizon also affect the visible rise and set directions slightly.

Shadows, solar panels, gardens and photographs

Shadows lengthen as the Sun gets lower. On level ground, a vertical object casts a shadow equal to its height when the Sun is at 45° altitude. Near the horizon, the shadow becomes much longer. To understand whether a garden bed or terrace receives light, you need both the Sun’s altitude and the direction from which it shines, together with nearby obstructions.

Solar panels also depend on orientation and illumination geometry. A direction that is a sensible starting point at a middle northern latitude is not a worldwide prescription. Roof shape, local shading, latitude and the desired distribution of production through the day all matter. Apphemeride describes the Sun’s position; a site-specific energy assessment is a separate task.

Photography and architecture use the same two angles. To plan light along a Manhattan street or across a canyon wall, compare the solar direction with your subject and consider whether the altitude clears the buildings or terrain. A compass can help establish direction; a fist held at arm’s length gives only a rough visual angular scale, commonly around ten degrees.

Safety comes first. Determine the Sun’s position from shadows, a suitable projection or the app. Never establish its direction by looking directly at it without proper solar protection.

Details that matter for precise work

A geometric position and an apparent position are different. Refraction raises the apparent Sun, by roughly half a degree near the horizon but much less higher up; the effect tends to zero at the zenith. Solar parallax is only about nine arcseconds, yet it and observer elevation can matter in precise measurements even when they are negligible for a casual shadow estimate.

South of the tropics, the Sun’s upper culmination is towards the north rather than the south. Within the tropics it can occur north or south depending on date, and at suitable dates the Sun can pass overhead. These are geometric differences, not changes in the azimuth convention: north remains 0° and south remains 180°.