Sun Angle Calculator

About the Sun Angle Calculator

The position of the sun in the sky is determined by three factors: your latitude, the time of day, and the day of the year. The solar altitude (elevation angle) measures how high the sun sits above the horizon, while the azimuth indicates its compass direction. Together, these angles define shadows, solar panel tilt, building orientation, and daylight quality.

At solar noon, the sun reaches its highest altitude, which equals 90° minus the latitude plus or minus the solar declination (±23.45° over the year). In summer at 40°N latitude, the sun reaches about 73°; in winter, only 27°. This dramatic difference drives seasonal heating patterns and is the reason buildings need different shading strategies for summer vs. winter.

The equation of time — a correction up to ±16 minutes — accounts for Earth's elliptical orbit and axial tilt, which cause solar noon to differ from clock noon. This calculator computes precise solar angles at any location and time, useful for architects, solar engineers, photographers, and anyone who works with natural light.

When This Page Helps

Architects use sun angles for shading design and natural lighting. Solar installers optimize panel tilt and orientation. Photographers plan golden-hour shoots. Gardeners determine sunny vs. shaded areas. This calculator serves all these needs with precise solar geometry.

How to Use the Inputs

1. Enter your latitude and longitude (or select a preset city).
2. Enter the day of year (1 = Jan 1, 172 = June 21, 355 = Dec 21).
3. Enter the local hour as a decimal (12.5 = 12:30 PM).
4. Enter your UTC time zone offset.
5. Review altitude, azimuth, shadow length, and the hourly sun path.

Example Calculation

Tips & Best Practices

• Solar noon is rarely at 12:00 clock time — it depends on longitude within your time zone and the equation of time.
• Shadow length = height / tan(altitude). At altitude 45°, shadow equals the height of the object.
• Air mass of 1.5 (AM1.5) is the standard reference for solar panel testing.
• For solar panel tilt, a common rule is tilt = latitude for year-round, latitude − 15° for summer, latitude + 15° for winter.

When To Use This Calculator

Calculate solar altitude, azimuth, zenith angle, and shadow length for any location, date, and time. Includes hourly sun path table. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Frequently Asked Questions

• What is the equation of time?

  A correction factor (±16 minutes) that accounts for Earth's elliptical orbit and 23.45° axial tilt. It's why a sundial doesn't match a clock exactly.

• Why does the sun altitude matter for solar panels?

  Panels produce maximum power when perpendicular to sunlight. The optimal tilt angle approximately equals your latitude so panels face the sun at noon in equinoxes.

• How do I convert day of year?

  Jan 1 = 1, Feb 1 = 32, Mar 21 (equinox) ≈ 80, Jun 21 (solstice) ≈ 172, Sep 22 (equinox) ≈ 265, Dec 21 (solstice) ≈ 355.

• What is azimuth?

  The horizontal compass direction of the sun, measured clockwise from true North. 0° = North, 90° = East, 180° = South, 270° = West.

• Can the sun be directly overhead?

  Only between the tropics (23.45°N to 23.45°S). At these latitudes, the sun passes through zenith (altitude = 90°) twice per year.

• What is air mass?

  Air mass describes how much atmosphere sunlight passes through. AM1 = sun at zenith, AM1.5 = altitude 42° (standard for solar testing), AM2 = altitude 30°.