Sun Angle Calculator

How to Use the Sun Angle Calculator

1. 1. Choose the place. Pick a city to fill in its latitude, longitude and time zone, or type your own coordinates in decimal degrees: north and east are positive, south and west negative. Use my location asks your browser for your position; it is used on this page only.
2. 2. Set the date and time. The time is the clock time in the zone you chose, so a daylight-saving date is handled for you. Set to now jumps to the current moment in that zone.
3. 3. Read the angles. Elevation is how high the Sun stands above the horizon; azimuth is its compass bearing, clockwise from true north (0° north, 90° east, 180° south, 270° west). The zenith angle is simply 90° minus the elevation.
4. 4. Check the day. Below the result are that date's sunrise, solar noon, sunset, daylight and the elevation at solar noon, with a chart of the elevation through the day and the working in numbers.

How the Sun's Position Is Calculated

The calculator uses the algorithm behind NOAA's Solar Calculator, which is built on Jean Meeus's Astronomical Algorithms. For the instant you give, it finds the Sun's declination δ, the latitude on Earth where the Sun is directly overhead, and the equation of time, the gap between a sundial and a clock. It converts your clock time to true solar time, which gives the hour angle H: 0° at solar noon, negative in the morning, positive in the afternoon, and 15° for every hour.

sin(elevation) = sin φ sin δ + cos φ cos δ cos H

H = (true solar time ÷ 4) − 180°

90° − |φ − δ|

Here φ is your latitude. The last line is the shortcut for the highest point of the day: at solar noon the Sun is as high as it will get, and its elevation depends only on how far your latitude is from the declination. A small refraction correction is then added, because air bends low sunlight upward; it is about 0.5° at the horizon and negligible above 45°. Both values are shown, so you can use the geometric one for geometry and the refracted one for what you would see.

Worked Examples

At 12:00 clock time on 21 June 2026 in New York, the Sun is 68.89° above the horizon at an azimuth of 140.48°, south-east, and a 1 m pole casts a 0.39 m shadow. That is not the day's maximum: solar noon there is 12:58, because New York keeps daylight-saving time and sits west of the middle of its zone. In Quito at the March equinox the noon Sun is 89.77° up, almost directly overhead.

Why Solar Noon Is Rarely 12:00

Clocks follow time zones; the Sun follows longitude. Solar noon is the moment the Sun crosses your meridian, so it arrives about four minutes later for every degree you live west of your zone's central meridian. Daylight saving moves clock noon an hour later again. On top of that the equation of time swings between roughly −14 and +16 minutes through the year, because Earth's orbit is elliptical and its axis is tilted. This is why the London figure above is 1:02 PM in summer and the New York one is 11:54 AM in December.

Polar Day and Polar Night

North of the Arctic Circle in summer, and south of the Antarctic Circle in the southern summer, the Sun can stay up all day. The calculator reports polar day when the sunrise equation has no solution because the Sun never drops to −0.833°, and polar night when it never climbs to that height. At Tromsø, Norway, on 21 June 2026 the Sun is up all day and peaks at 43.81°; on 21 December it never rises, and its highest point is 2.98° below the horizon, which is bright enough for civil twilight.

Accuracy and Limits

• Sunrise and sunset use the standard convention: the Sun's centre at −0.833°, which covers the Sun's radius plus average refraction. NOAA states the results are accurate to within a minute between 72° north and south, and to within ten minutes beyond.
• Refraction assumes standard air. Real refraction changes with pressure and temperature, so elevations below about 5° are approximate.
• Terrain is ignored. Hills, buildings and your altitude above sea level move the observed sunrise and sunset; this is the sea-level horizon.
• Dates far from today work, but the algorithm is tuned for the years around 2000 and drifts slowly over centuries.

Frequently Asked Questions

What is the solar elevation angle?

It is the angle between the horizon and the Sun's centre, measured upward from 0° at the horizon to 90° directly overhead. It is negative when the Sun is below the horizon. The zenith angle is its complement: elevation plus zenith equals 90°.

How do I find the sun's angle at my location right now?

Press Use my location, then Set to now. The calculator reads your latitude and longitude from the browser and the current date and time in your time zone, then shows the elevation and azimuth. If you would rather not share your position, pick the nearest city or type coordinates.

What is the difference between azimuth and elevation?

Azimuth is the Sun's direction along the horizon, measured clockwise from true north, so 90° is east and 180° is south. Elevation is how high it is above the horizon. Together they pin down the Sun's place in the sky, which is why surveyors and solar designers always quote both.

How do I calculate the sun's angle at noon?

Use 90° − |latitude − declination|. At New York's latitude of 40.71° on the June solstice, when the declination is +23.44°, that is 90° − 17.27° = 72.73°. In December the declination is −23.44°, so the noon Sun is only 25.88° high. The calculator shows the declination for any date.

What tilt angle is best for solar panels?

A common rule of thumb for a fixed panel facing the equator is a tilt close to your latitude, which suits year-round output. Add about 10 to 15 degrees to favour winter, subtract them to favour summer. Use the noon elevation here to see how the Sun's height changes across the year, and a dedicated tool such as NREL's PVWatts for real yield.

Why does the sun angle differ from other sun calculators?

Small differences come from the refraction model, whether the answer includes refraction at all, and whether coordinates and time zones were entered the same way. The calculator shows elevation with and without refraction so you can compare like with like. Differences of a few hundredths of a degree are normal; a gap of an hour usually means a daylight-saving or time zone mismatch.