# Sun Angle Calculator

Calculate solar elevation, zenith, and azimuth angles from latitude, day of year, and time. Plan solar panels, photography, and architecture.

## What this calculates

The sun's position in the sky changes throughout the day and across seasons. The solar elevation angle tells you how high the sun is above the horizon, while the azimuth tells you its compass direction. These two angles together define exactly where the sun is at any moment, which matters for solar panel placement, building design, photography golden hours, and agricultural planning.

## Inputs

- **Latitude** (°) — min -90, max 90 — Positive for North, negative for South.
- **Day of Year** — min 1, max 365 — Jan 1 = 1, Jun 21 = 172, Dec 21 = 355.
- **Solar Time (hour)** (h) — min 0, max 24 — Solar time in hours (12 = solar noon, not clock noon).

## Outputs

- **Solar Elevation Angle** (°) — Angle of the sun above the horizon (negative = below)
- **Solar Zenith Angle** (°) — Angle from directly overhead to the sun
- **Solar Azimuth** (°) — Compass bearing of the sun (0° = North, 180° = South)
- **Solar Declination** (°) — Tilt of Earth's axis toward the sun on this day

## Details

This calculator uses the standard astronomical formulas for solar position based on three inputs:

  - Latitude: Your north-south position on Earth (-90° to +90°)

  - Day of year: Determines the solar declination (Earth's axial tilt toward the sun)

  - Solar time: Hour of the day in solar time (12 = solar noon, when the sun crosses your meridian)

The solar declination swings between +23.45° (summer solstice, June 21) and -23.45° (winter solstice, December 21). At the equinoxes (March 20, September 22), declination is near 0°.

The hour angle is 15° per hour from solar noon. At 10 AM solar time, the hour angle is -30°. At 2 PM solar time, it is +30°.

At solar noon, the elevation angle simplifies to: Elevation = 90° - |latitude - declination|. For example, at 40°N on the summer solstice (declination = 23.45°), the noon elevation is 90° - (40 - 23.45) = 73.45°.

Note: this uses a simplified model. For precise applications like solar tracking systems, you would also account for atmospheric refraction, the equation of time, and longitude correction from your time zone meridian.

## Frequently Asked Questions

**Q: What is solar elevation vs solar azimuth?**

A: Solar elevation is the angle of the sun above the horizon (0° at the horizon, 90° directly overhead). Solar azimuth is the compass direction toward the sun, measured clockwise from north (0° = north, 90° = east, 180° = south, 270° = west). Together they pinpoint the sun's exact position in the sky.

**Q: What is solar noon?**

A: Solar noon is the moment when the sun crosses your local meridian and reaches its highest point for the day. It is not always 12:00 PM on your clock because clock time depends on your time zone and daylight saving time. Solar noon can differ from clock noon by up to an hour or more depending on your position within your time zone.

**Q: How does this help with solar panel placement?**

A: For fixed solar panels, you want them tilted at an angle equal to your latitude for best year-round performance. The azimuth tells you which direction to face them (due south in the Northern Hemisphere, due north in the Southern Hemisphere). Knowing the sun's seasonal arc also helps you plan for shading from nearby structures or trees.

**Q: Why does the sun never reach directly overhead at my location?**

A: The sun can only be directly overhead (90° elevation) at latitudes between 23.45°N and 23.45°S, the region between the Tropics of Cancer and Capricorn. Outside the tropics, the sun's maximum elevation is always less than 90° because Earth's axial tilt limits how far north or south the sub-solar point can reach.

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Source: https://vastcalc.com/calculators/physics/sun-angle
Category: Physics
Last updated: 2026-04-08