How does the Solar Angle Calculator determine the sun's position?

The Solar Angle Calculator uses your latitude, longitude, date, local time, and time zone to compute the solar declination from the day of year, apply the equation of time for an accurate local solar time, derive the hour angle, and then solve the standard spherical astronomy equations to find elevation and azimuth.

What is solar elevation angle and why does it matter?

Solar elevation angle is the angular height of the sun above the horizon, ranging from 0° (sunrise/sunset) to about 90° (sun directly overhead near the equator at noon). A higher elevation means more intense direct sunlight, which matters for solar panel efficiency, building shading, photography, and plant growth.

What is the difference between solar zenith angle and solar elevation angle?

They are complementary: solar zenith angle = 90° minus solar elevation angle. A zenith angle of 0° means the sun is directly overhead; 90° means the sun is on the horizon.

When should I enable the Daylight Saving Time toggle?

Enable DST if local clocks are currently set one hour ahead of standard time in your region. The Solar Angle Calculator will subtract that extra hour before computing solar time.

No. All calculations happen in your browser; nothing is sent to a server.

Solar Angle Calculator - CalculatorBox

How to Use Solar Angle Calculator

The Solar Angle Calculator tells you exactly where the sun sits in the sky for any location, date, and time. Enter a few values, and the calculator instantly shows solar elevation, zenith angle, azimuth, and more.

Latitude and Longitude — Type your coordinates or click one of the preset city buttons (New York, London, Tokyo, Sydney, Singapore) to fill them in automatically. Latitude ranges from −90° (South Pole) to +90° (North Pole); longitude ranges from −180° to +180°.
Date and Local Time — Select the date and time on your local clock. The Solar Angle Calculator uses these to compute the exact day of year and decimal hour needed for solar calculations.
Time Zone — Choose the UTC offset for your location. If local clocks are currently in Daylight Saving Time, also enable the DST toggle so the calculator adjusts correctly.
Optional Tilted Surface — If you want to know the angle of sunlight hitting a solar panel or inclined roof, enter the surface tilt (0° = flat, 90° = vertical) and surface azimuth (0° = facing north, 180° = facing south). The Solar Angle Calculator will add an incidence angle to the results.
Read the Results — The compass rose diagram shows the sun’s current direction at a glance. The result cards highlight solar elevation, zenith angle, azimuth, and solar noon time.

Formula & Theory - Solar Angle Calculator

The Solar Angle Calculator implements the widely used Spencer (1971) and standard spherical-trigonometry equations.

Day of Year and Solar Declination

The day of year n (1–365) feeds into the declination formula:

δ = 23.45° × sin( (360/365) × (n − 81) )

Solar declination δ represents how far the sun is north or south of the equator: +23.45° at the June solstice and −23.45° at the December solstice.

Equation of Time

A small correction accounts for Earth’s elliptical orbit and axial tilt:

EoT (minutes) = 9.87 sin(2B) − 7.53 cos(B) − 1.5 sin(B)
  where B = 2π(n − 81) / 364

Local Solar Time and Hour Angle

TC (minutes) = 4 × (longitude − LSTM) + EoT
  LSTM = 15° × UTC_offset
LST (hours) = local_clock_time + TC / 60
H (°) = 15 × (LST − 12)

Hour angle H is 0° at solar noon, negative in the morning, and positive in the afternoon.

Solar Elevation

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

Symbol	Meaning
α	Solar elevation angle
φ	Observer latitude
δ	Solar declination
H	Hour angle

Solar Azimuth

cos(Az) = [sin(δ) − sin(α) sin(φ)] / [cos(α) cos(φ)]

If the hour angle H > 0 (afternoon), azimuth = 360° − Az.

Incidence Angle on a Tilted Surface

cos(θ) = sin(α) cos(β) + cos(α) sin(β) cos(Az − γ)

Where β is the surface tilt and γ is the surface azimuth.

Assumptions and Limits

The Solar Angle Calculator uses a simplified declination equation that is accurate to within about ±0.3° for most of the year. It does not apply atmospheric refraction corrections (which lift the apparent sun roughly 0.5° near the horizon). Results are appropriate for everyday planning, solar panel orientation, architectural shading studies, and outdoor scheduling — not for precision navigation or scientific astronomy.

Use Cases for Solar Angle Calculator

The Solar Angle Calculator helps anyone who needs to understand where the sun will be at a specific time and place:

Solar panel installation — Find the optimal tilt and orientation angle for a rooftop or ground-mounted panel by checking the incidence angle at different times of day and seasons.
Architectural lighting design — Determine when direct sunlight enters a window, helping designers plan shading devices, overhangs, and glazing specifications.
Photography and videography — Plan golden-hour or blue-hour shoots by knowing exactly when the sun reaches a target elevation and direction.
Garden and greenhouse management — Identify which areas of a garden receive full sun or partial shade at different times of year to guide planting decisions.
Outdoor event planning — Check whether participants will be looking into the sun, and find the best seating orientation for comfort.
Construction and surveying — Estimate shadow lengths and directions for temporary structures, equipment placement, and site safety planning.

The Solar Angle Calculator produces results in real time as you adjust inputs, making it easy to sweep through different times of day or compare multiple dates without reloading the page.

Solar Angle Calculator