Sun Altitude Calculator

The solar altitude (also called elevation) is computed from latitude φ, solar declination δ, and hour angle H:

Altitude = asin( sinφ·sinδ + cosφ·cosδ·cosH )

Declination and the equation of time are derived from standard solar geometry using the Julian day. The hour angle comes from true solar time. Optional refraction adjusts altitude near the horizon.

1. Enter your latitude and longitude in degrees.
2. Select the local date and local clock time.
3. Set the timezone offset for that local time.
4. Enable daylight saving only if your clock includes it.
5. Choose refraction mode and the output units you need.
6. Click Calculate to see results above the form.
7. Use the download buttons to export your latest result.

1) Meaning of sun altitude

Sun altitude is the angle between the Sun and your horizon. 0° sits on the horizon, 90° is overhead, and negative values place the Sun below the horizon. The angle helps explain daylight strength and shadow length quickly.

2) Inputs that control the result

Latitude and longitude define location. Date and local time define the moment. The timezone offset connects your clock to UTC, and daylight saving matches seasonal clock shifts. Accurate inputs matter because the Sun moves about 15° each hour.

3) Typical altitude data by latitude

Near the equator, noon altitude can approach 90° near equinox. Around 30° latitude, summer noon is often high, while winter noon is much lower. At higher latitudes, winter noon can be very low, producing long shadows and weaker heating.

4) Seasonal declination data

Solar declination is the Sun’s north–south tilt in the sky. It varies from about +23.44° near June 21 to roughly -23.44° near December 21, passing close to 0° at the equinoxes. This swing drives most seasonal altitude differences.

5) Hour angle and true solar time

Hour angle measures how far the Sun is from local solar noon. The calculator adjusts clock time using longitude and the equation of time. The equation of time can reach about ±16 minutes, so the Sun’s peak altitude may not occur exactly at 12:00 on your clock.

6) Refraction near the horizon

Refraction bends sunlight upward, making the Sun appear slightly higher than its geometric position. Near the horizon, the apparent lift can be near 0.5°. Enable refraction when planning visibility close to sunrise and sunset.

7) Practical uses and quick checks

A shadow estimate is shadow ≈ height / tan(altitude). Low altitudes create long shadows and softer light. High altitudes shorten shadows and increase heating. Compare multiple times to build a daily altitude curve.

8) Exporting results for analysis

Download the latest calculation for reporting or spreadsheets. Exports include altitude, corrected altitude, zenith, azimuth, declination, and equation of time. Re-run for different times to create a series you can study later.

1) What is the difference between altitude and zenith?

Zenith is measured down from overhead, while altitude is measured up from the horizon. They add to 90° in geometric terms, so altitude = 90° − zenith.

2) Why does my noon altitude change through the year?

Solar declination shifts between about +23.44° and −23.44° across seasons. That changes the Sun’s daily arc, so the maximum altitude rises in summer and falls in winter.

3) What does azimuth mean in this tool?

Azimuth is the compass direction of the Sun, measured clockwise from north. Near 90° is east, 180° is south, and 270° is west, depending on time and hemisphere.

4) Should I enable refraction correction?

Enable it for visual observations and planning near sunrise or sunset. Disable it if you want a purely geometric position or if atmospheric effects are handled elsewhere in your workflow.

5) How important is the timezone offset?

Very important. A one-hour offset error shifts the Sun by about 15° in hour angle, which can noticeably change altitude and azimuth for the same coordinates.

6) Can I use radians instead of degrees?

Yes. Select radians to convert angular outputs to rad. The equation of time remains in minutes, so keep units consistent when comparing or post-processing results.

7) Why is altitude negative at night?

Negative altitude means the Sun is below your horizon. Twilight categories correspond to specific negative angles, so values below 0° help describe darkness levels and sky brightness.