Solar Elevation Angle Calculator

The solar elevation angle α is the Sun’s height above the horizon. This calculator uses:

sin(α) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H)

• φ = latitude
• δ = solar declination
• H = hour angle (0° at solar noon, ±15° per hour)

In Date-Time mode, declination and the equation of time are approximated using common engineering formulas, then solar time and hour angle are derived from longitude and time zone.

1. Select Date-Time mode for automated declination and hour angle.
2. Enter your latitude and longitude in degrees.
3. Provide date, local clock time, and time zone offset.
4. Keep standard meridian on Auto, or set it manually.
5. Press Calculate to see elevation, zenith, azimuth, and times.
6. Use Download CSV or Download PDF for reporting.

Sample inputs and outputs for quick verification (approximate).

1) What the solar elevation angle represents

Solar elevation (α) is the angle between the Sun and your local horizon. A value of 0° places the Sun on the horizon, while 90° places it overhead. Elevation is a fast way to anticipate shadow behavior during the day. When α is negative, the Sun is below the horizon, which helps with twilight checks and sunrise validation.

2) Inputs that control elevation

Elevation depends on latitude (φ), solar declination (δ), and hour angle (H). Latitude ranges from −90° to 90° and limits how high the Sun can climb. Hour angle tracks time from solar noon and changes by 15° per hour.

3) Declination data through the year

Declination varies roughly from −23.45° near the December solstice to +23.45° near the June solstice. Around the equinoxes, δ is close to 0°. In Date-Time mode, δ is estimated from the day of year (n) for seasonal realism.

4) Hour angle and local solar time

Clock time is not identical to solar time. Local solar time shifts with longitude relative to the standard meridian and with the equation of time (EoT). EoT often stays within about ±16 minutes over a year, creating a time correction before H is computed. This is why nearby cities can have different solar noon times.

5) Zenith and azimuth outputs

Zenith angle (θz) is the complement of elevation: θz = 90° − α. The azimuth here is clockwise from true North: 0° North, 90° East, 180° South, and 270° West. Near sunrise or sunset, azimuth can shift rapidly with time.

6) Sunrise, sunset, and day length

Sunrise and sunset come from the sunrise hour angle H0 using cos(H0) = −tan(φ)·tan(δ). When this has a real solution, day length is 2·H0/15 hours. If there is no real solution, the location may experience polar day or polar night on that date.

7) Practical uses for energy and shading

Solar designers use elevation to estimate incident angles and obstruction risk for panels. Building teams use it to plan shading devices, daylighting, and glare control. Outdoor work, photography, and events benefit from predicting lighting direction when combined with azimuth.

8) Accuracy notes and best practices

Best results come from accurate coordinates and the correct UTC offset. For precision work near the horizon, atmospheric refraction matters and can raise apparent elevation slightly. For planning and comparison, the trigonometric core used here remains dependable.

1) What is the difference between elevation and zenith?

Elevation is measured up from the horizon. Zenith is measured down from overhead. They are complementary: zenith equals 90° minus elevation.

2) Why can local solar time differ from my clock time?

Clock time follows time zones, but solar time follows the Sun. Longitude offset from the standard meridian and the equation of time shift solar noon, creating a time correction of several minutes.

3) What does a negative elevation angle mean?

Negative elevation means the Sun is below the horizon. It is useful for twilight planning and for confirming when sunrise will occur.

4) How should I enter longitude signs?

Use positive longitude for locations east of Greenwich and negative for locations west of Greenwich. This sign convention keeps the time correction and hour angle consistent.

5) Why does the calculator sometimes report no sunrise or sunset?

At high latitudes, the Sun can stay above the horizon all day or remain below it all day during certain seasons. In those cases, sunrise and sunset do not happen on that date.

6) Are the declination and equation-of-time formulas precise?

They are standard approximations intended for estimates, education, and planning. For navigation or astronomy-grade precision, use full ephemeris models and include atmospheric refraction near the horizon.

7) How is azimuth defined in this calculator?

Azimuth is measured clockwise from true North: 0° North, 90° East, 180° South, and 270° West. This matches common mapping and surveying conventions.