Does the Sun Always Rise Due East? Read Sunrise Azimuth

Does the Sun rise exactly east every day?

Azimuth gives the direction around the horizon. It answers a different question from sunrise time, which tells you when a defined event occurs. A clock reading alone does not tell you which landmark the Sun will rise behind.

Read the bearing before comparing the direction

With this convention, 60° is 30° north of east; 120° is 30° south of east. A setting direction of 300° is 30° north of west. Angles wrap around at north, so 359° and 1° differ by just 2°, not by 358° along the shorter turn.

Altitude or elevation is the angle above the horizon. An object can have azimuth 90° and altitude 20°: it is eastward and twenty degrees up. Do not interpret an azimuth as a height, an ecliptic longitude, or a sidereal sign position. They use different reference directions and planes.

Why the direction changes through the year

Solar declination describes the Sun's angular position north or south of the celestial equator. Earth's axial tilt and its motion around the Sun make this quantity change through the year. In the usual sunrise geometry, positive declination shifts the rising point north of east, while negative declination shifts it south of east, wherever that horizon crossing exists.

The same declination does not give the same bearing at every latitude. The two latitude groups below demonstrate this without assigning dates or cities. Their values of −23.44°, 0° and +23.44° are selected model inputs, close to the familiar seasonal extremes and the equatorial crossing; they are not an ephemeris for a particular year.

“East” in the everyday statement that the Sun rises in the east names a broad side of the sky. “Due east” is the specific bearing 90°. Much confusion disappears once those two levels of precision are distinguished.

A small geometric model you can check

Let φ be latitude and δ be solar declination, both positive northward. Put the Sun's center at geometric altitude 0°, ignore refraction, and assume an unobstructed level horizon. For a normal rising crossing, the azimuth A satisfies:

cos A = sin δ / cos φ, with A selected between 0° and 180° for the eastern horizon. For the corresponding evening crossing at unchanged declination, the bearing is 360° − A.

This is the zero-altitude specialization of the standard solar-position relation in NOAA's equations. It is a teaching model, not a replacement for the full sunrise calculation. Use degrees consistently on a calculator, or convert to radians before using a programming language's sine and cosine functions.

Six morning and evening comparisons

At latitude 28° north and declination +23.44°, the model gives a morning azimuth of about 63.22°. That is about 26.78° north of east, because 90° − 63.22° = 26.78°. Its evening counterpart is about 296.78°, north of west.

At zero declination, both shown latitudes give 90° and 270°. At the equator with positive declination, the morning bearing is 66.56°, not the 63.22° of the second latitude group. The location changes the result even though the Sun's declination is the same.

The extra decimals support checking the example arithmetic. They do not express the accuracy of a view over buildings, hills or a hazy horizon. The table describes no particular sunrise date, weather condition or camera position.

Why a real sunrise need not match the zero-altitude table

Standard sunrise calculations commonly refer to the upper edge appearing at the horizon, with an allowance for refraction. NOAA's example equations use a solar-center zenith angle of 90.833° for this purpose, rather than the 90° used in our model. That changes the geometric condition and can change the resulting bearing.

A mountain ridge or a building adds another local condition: the Sun may become visible to you only after reaching a higher altitude. A location's published sunrise and your first unobstructed sight are therefore not necessarily the same event. Check the horizon assumptions before treating a difference as an error.

The sunrise and twilight guide explains why first light is a different event again. The equinox guide discusses why the same sunrise conventions also matter when comparing daylight lengths.

What if the formula has no real answer?

At latitude 70° north with declination +23.44°, sin δ / cos φ is greater than 1. A real cosine cannot take that value, so this model has no horizon crossing. The Sun stays above the geometric horizon. With declination −23.44°, it stays below instead.

Do not clamp a clearly out-of-range value to 1 and print a northward “sunrise.” That would invent an event. At the poles the formula's denominator vanishes, so this particular expression is unsuitable there. Borderline grazing events also require more care than this simplified exercise provides.

Compare maps, compasses and reports consistently

1. Record the location, date, time zone and which event or instant the bearing describes.
2. Check whether north means true north or magnetic north.
3. Match solar center versus upper edge, and the treatment of refraction and terrain.
4. Keep altitude separate from azimuth and compare bearings across the 0°/360° boundary correctly.

USNO's data notes specify true-north azimuth. A compass or phone may be set to magnetic north or may apply a correction; check its setting rather than assuming agreement. Magnetic declination and solar declination are different quantities despite sharing a word.

Use local sunrise and sunset times for the time portion of a plan, and a solar-position source for a bearing with clearly stated conventions. Astrogyana's timing tool should not be read as an azimuth result when it only displays event times. For the clock-related question, continue with solar noon versus clock noon.

Frequently asked questions