Solar elevation angle

The solar elevation angle is the height of the sun above the horizon, in degrees. At sunrise and sunset it is about 0°, and it peaks at solar noon at a value set by your latitude and the time of year.

Free, no sign-up. Sundial shows it as "Sun height" for any address and minute.

Definition

Stand on flat ground and imagine a line from your eye to the sun. The solar elevation angle is the angle between that line and the horizon. You'll also see it called the solar altitude angle or just sun height. All three mean the same.

Its partner is the solar zenith angle, measured down from straight overhead instead of up from the horizon. The two always add up to 90°:

zenith angle = 90° − elevation

So a sun 15° above the horizon has a zenith angle of 75°. Solar engineers tend to use zenith, surveyors and photographers tend to use elevation. Direction is a separate angle, the azimuth or bearing, covered in the sun angle calculator.

The noon formula

At solar noon, when the sun is highest, there is a short approximation:

elevation at noon ≈ 90° − latitude + declination

Declination is the sun's position north or south of the equator. It is about +23.44° at the June solstice, about −23.44° at the December solstice, and close to 0° at the two equinoxes. Use your latitude as a positive number in the northern hemisphere.

Here are worked examples, checked against SunCalc, the astronomical library Sundial uses:

The March row is a little out because the 2026 March equinox falls in the afternoon of the 20th, so at London's noon the sun is still just south of the equator. A gap of a few tenths of a degree makes no visible difference to a shadow. Away from the solstices, declination isn't a round number, so the formula needs the day's value or a calculator.

Southern hemisphere and the tropics

A form that works everywhere is 90° − |latitude − declination|, with southern latitudes and declinations written as negative. For Sydney (−33.87°) on 21 December that gives 90 − |−33.87 + 23.44| = 79.6°, which matches SunCalc. In the southern hemisphere the noon sun is in the north, so north-facing walls and gardens are the sunny ones. Between the tropics the noon sun can pass overhead and then sit on the "wrong" side of the sky for part of the year.

Elevation at other times of day

Away from noon the angle depends on the hour as well, through a longer formula (sin elevation = sin latitude × sin declination + cos latitude × cos declination × cos hour angle). In practice it's easier to read it off. On 21 June London's sun is 36.3° up at 9 am and 54.0° at 3 pm. On 21 December the same hours give 5.4° and 5.2°, barely clear of the rooftops.

On the sun path map you can drag the clock and watch the Sun height figure change minute by minute, while the shadows lengthen to match.

From elevation to shadow length

Elevation is the number that controls shadow length:

shadow length = height ÷ tan(elevation)

At 45° a shadow is as long as the object is tall. At Manchester's December noon, 13.1°, every metre of height casts 4.30 m of shadow, so a two-storey house about 8 m to the ridge throws a shadow over 34 m long at the brightest point of the day. The shadow calculator has a full table.