Sun Angle Calculator for Solar Position

What Are Solar Elevation and Azimuth?

Solar elevation is the angle of the sun above the horizon. Solar azimuth is the compass direction to the sun, measured clockwise from north. Together they describe the sun's position for a given latitude, date, and local solar time.

Solar Position Formulas

Solar declination $\delta$ depends on day of year $n$:

$$\delta = 23.45^\circ \cdot \sin\left(\frac{360^\circ}{365}(284 + n)\right)$$

Hour angle $\omega$ is $(\text{hour} - 12) \times 15^\circ$. Solar elevation $\alpha$ is:

$$\alpha = \arcsin(\sin\phi\sin\delta + \cos\phi\cos\delta\cos\omega)$$

where $\phi$ is latitude. Azimuth follows from standard spherical astronomy relations using the same inputs.

Frequently Asked Questions

What is local solar time?

Local solar time assumes the sun crosses the meridian at 12:00. It ignores longitude offset and equation of time unless you adjust the hour input.

What is solar declination?

Declination is the sun's north-south position relative to the celestial equator. It varies from about +23.45° at June solstice to -23.45° at December solstice.

How is azimuth measured?

This tool reports azimuth clockwise from north: 0° is north, 90° is east, 180° is south, and 270° is west.

Why is elevation highest near solar noon?

At solar noon the hour angle is zero, so the sun is closest to the local meridian and reaches its maximum elevation for that day.

Can elevation be negative?

Yes. Negative elevation means the sun is below the horizon, which occurs at night or at high latitudes during polar conditions.

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Sun Angle Calculator

What Are Solar Elevation and Azimuth?

Solar Position Formulas

Frequently Asked Questions

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