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Solar Position Calculator

Reviewed by Calculator Editorial Team

The Solar Position Calculator determines the sun's position in the sky (azimuth and altitude) for any given date, time, and location on Earth. This information is essential for solar energy applications, astronomy, and engineering projects.

What is Solar Position?

Solar position refers to the angular measurements that describe where the sun is located in the sky relative to a specific location on Earth. These measurements are typically expressed in terms of azimuth and altitude:

  • Azimuth: The angle between the sun's position and true north, measured clockwise from 0° to 360°.
  • Altitude: The angle between the sun's position and the horizon, ranging from -90° (below the horizon) to +90° (directly overhead).

Knowing the solar position helps in optimizing solar panel installations, predicting solar energy output, and understanding daylight patterns for various applications.

How to Use This Calculator

To calculate the solar position, follow these steps:

  1. Enter the date and time for which you want to calculate the solar position.
  2. Input your location's latitude and longitude coordinates.
  3. Click the "Calculate" button to generate the results.
  4. Review the azimuth and altitude values in the results section.

Note: This calculator uses the standard solar position algorithm based on the SOLPOS model developed by the National Renewable Energy Laboratory (NREL).

Formula Used

The solar position is calculated using the following formulas:

Julian Day (JD)

JD = 367 × year - floor(7 × (year + floor((month + 9) / 12)) / 4) + floor(275 × month / 9) + day + 1721028.5

Julian Century (JC)

JC = (JD - 2451545) / 36525

Geometric Mean Longitude (L)

L = 280.46646 + JC × (36000.76983 + JC × 0.0003032)

Geometric Mean Anomaly (G)

G = 357.52911 + JC × (35999.05029 - 0.0001537 × JC)

Eccentricity of Earth's Orbit (e)

e = 0.016708634 - JC × (0.000042037 + 0.0000001267 × JC)

Sun's Equation of Center (C)

C = sin(G) × (1.914602 - JC × (0.004817 + 0.000014 × JC)) + sin(2 × G) × (0.019993 - 0.000101 × JC) + sin(3 × G) × 0.000289

Sun's True Longitude (λ)

λ = L + C

Sun's True Anomaly (v)

v = G + C

Sun's Radius Vector (R)

R = (1.000001018 × (1 - e²)) / (1 + e × cos(v))

Sun's Apparent Longitude (λ')

λ' = λ - 0.00569 - 0.00478 × sin(125.04 - 1934.136 × JC)

Mean Obliquity of the Ecliptic (ε)

ε = 23 + (26 + (21.448 - JC × (46.815 + JC × (0.00059 - JC × 0.001813))) / 60) / 60

Sun's Right Ascension (α)

α = atan2(cos(ε) × sin(λ'), cos(λ'))

Sun's Declination (δ)

δ = asin(sin(ε) × sin(λ'))

Equation of Time (E)

E = 4 × (tan(ε / 2)² × sin(2 × L) - 2 × e × sin(G) + 4 × e × sin(G) × cos(2 × L) - 0.5 × e³ × sin(3 × G) + 2 × C)

True Solar Time (TST)

TST = (hour + minute / 60 + second / 3600) × 15 + E

Hour Angle (H)

H = TST - 180

Solar Zenith Angle (θ)

θ = acos(sin(φ) × sin(δ) + cos(φ) × cos(δ) × cos(H))

Solar Azimuth Angle (A)

A = atan2(sin(H), cos(H) × sin(φ) - tan(δ) × cos(φ))

Solar Altitude Angle (h)

h = 90° - θ

Where:

  • φ = latitude
  • λ = longitude
  • year, month, day = date components
  • hour, minute, second = time components

Example Calculation

Let's calculate the solar position for June 21, 2023 at 12:00 PM (noon) at 40.7128° N, 74.0060° W (New York City):

  1. Date: June 21, 2023
  2. Time: 12:00 PM
  3. Latitude: 40.7128° N
  4. Longitude: 74.0060° W

Using the calculator:

Results

Azimuth: 180.2°

Altitude: 68.4°

This means the sun is directly overhead (altitude of 68.4°) and positioned at 180.2° azimuth, which is due south in this location.

Frequently Asked Questions

What is the difference between solar azimuth and altitude?

Solar azimuth measures the sun's position east or west of true north, while solar altitude measures how high the sun appears in the sky above the horizon.

How accurate is this solar position calculator?

This calculator uses the standard SOLPOS algorithm with an accuracy of about ±0.1° for most locations and times of year.

Can I use this calculator for any location on Earth?

Yes, you can enter any valid latitude and longitude coordinates to calculate the solar position for that location.

What factors affect solar position calculations?

Solar position depends on date, time, location, and atmospheric conditions. This calculator assumes a standard atmosphere and ignores local terrain effects.