Skip to content
ENExplore Calculators

Solar Elevation Angle Calculator

Work out solar elevation angle instantly with clear inputs, formula shown and shareable results.

About Solar Elevation Angle Calculator

The solar elevation formula combines latitude, declination and hour angle: sin(altitude) = sin(lat)sin(dec) + cos(lat)cos(dec)cos(H). At 40 degrees latitude with 20 degrees declination and two hours past noon, the Sun stands 56.2 degrees up. Relative air mass, near 1.2 here, sets how much atmosphere the beam crosses and therefore the irradiance available.

Formulas

Solar elevation

sin(alt) = sin(lat) sin(dec) + cos(lat) cos(dec) cos(H)

Hour angle

H = 15 degrees per hour from solar noon

Worked example

With the default values below, Solar Elevation Angle Calculator returns Solar Elevation Angle of 57.49. Change any input above and every figure here is recalculated in your browser.

Inputs used

Latitudeaccepts -90–90 deg
40 deg
Solar declinationaccepts -23.5–23.5 deg
20 deg
Hour angle from solar noonaccepts -180–180 deg
30 deg

Results

Solar Elevation Angle
57.49 deg
Zenith Angle
32.51 deg
Relative Air Mass
1.185
Solar Azimuth From North
119.1 deg

Step by step

  1. 1Values used
  2. 2Solar elevation
  3. 3Hour angle
  4. 4Solar Elevation Angle= 57.49 deg
  5. 5Zenith Angle= 32.51 deg
  6. 6Relative Air Mass= 1.185
  7. 7Solar Azimuth From North= 119.1 deg

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is air mass 1?

The Sun directly overhead, one atmosphere thickness. AM1.5 is the standard test condition for solar panels, corresponding to about 48 degrees elevation.

Why does elevation matter for solar power?

Because both the cosine projection onto the panel and the atmospheric path length depend on it, so output falls steeply at low sun.

Related Calculators

Solar Elevation Angle Calculator | Calcrivo