utility calculator

Solar Noon, Sunset, & Daylight Duration Calculator

Calculate NOAA solar noon, sunrise, sunset, and daylight duration based on latitude and longitude.

Formula Verified by Dr. Arthur Pendelton, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Quick Presets

Select Location Preset

Custom Geographic Coordinates

Observation Date

Latitude

Longitude

Timezone Offset (UTC hours)

Results

Solar Noon Time

12:02 PM

Sunrise Time04:40 AM

Sunset Time07:24 PM

Daylight Duration14 hours, 44 minutes

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Save this page to optimize solar panel angles, plan outdoor photography around solar noon, or track seasonal daylight variations.

Formula

Solar Angle Formulas

Hour Angle (ω) = arccos(-tan(φ) × tan(δ)) 
Solar Noon = 720 - 4 × LongitudeOffset - EquationOfTime

Integrates NOAA Equation of Time (EoT) models with geographic coordinates and atmospheric refraction constants.

Step by step

How the calculation works

1Select a city preset or manually input coordinates.
2Provide the local calendar date to model.
3Specify your timezone offset from UTC (e.g. -5 for EST, 0 for GMT, +9 for JST).
4Read the calculated sunrise, sunset, solar noon, and daylight duration values.

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How to understand and use this calculator

NOAA Solar Calculations: The Equation of Time and Declination

Astronomical solar calculations predict the position of the Sun relative to an observer on Earth. Because Earth has an elliptical orbit and is tilted on its axis by approximately 23.44°, the length of a solar day varies slightly throughout the year. This discrepancy is described by the Equation of Time (EoT), which measures the difference between apparent solar time (sundial time) and mean solar time (clock time).

Solar declination ($\delta$) is the angle between the Earth-Sun line and the Earth's equatorial plane. It varies from approximately -23.44° at the December solstice to +23.44° at the June solstice. Calculating declination and the Equation of Time is the first step in determining sunrise, sunset, and solar noon for any specific day of the year.

Daylight Duration: Astronomical Formulas for Day Length

The duration of daylight is determined by the latitude of the observer and the declination of the Sun. The hour angle ($\omega_s$) represents the angle of the Sun east or west of the local meridian at sunrise and sunset. It is calculated using the spherical trigonometry formula:

$$\omega_s = \arccos\left(\frac{\cos(\theta_0) - \sin(\phi)\sin(\delta)}{\cos(\phi)\cos(\delta)}\right)$$ where $\phi$ is the latitude of the observer, $\delta$ is the solar declination, and $\theta_0$ is the solar zenith angle at the horizon (standardized as 90.833° to account for atmospheric refraction and the Sun's angular radius). The total daylight duration in hours is then calculated as: $$D_{\text{hours}} = \frac{2 \times \omega_s}{15}$$.

Timezones, Longitude, and Solar Noon Offsets

Solar noon is the moment when the Sun reaches its highest point in the sky and crosses the observer's meridian. While clock time says noon is 12:00, solar noon rarely occurs exactly then. This offset is caused by the observer's longitude relative to their timezone's standard meridian.

For every degree of longitude east or west of the timezone meridian, solar noon shifts by 4 minutes. Apparent solar noon is calculated as: $$\text{Solar Noon} = 720 - 4 \times L_{\text{diff}} - EoT$$ minutes from midnight, where $L_{\text{diff}}$ is the difference between local longitude and the timezone meridian, and $EoT$ is the Equation of Time in minutes. Adjusting for this offset provides the exact clock time of solar noon.

Solar Altitude and Azimuth Angles for Energy Harvesters

Calculating solar noon and declination is crucial for optimizing solar energy harvesting systems. The maximum solar altitude angle at solar noon is: $$\beta = 90^\circ - \phi + \delta$$ (for northern hemisphere locations). To maximize annual energy capture, solar panels should be tilted at an angle equal to the local latitude, and adjusted seasonally by +15° in winter and -15° in summer.

To model the financial payback of solar configurations, you can use our solar panel payback calculator which integrates panel sizing with regional utility rates, or size charge controllers and inverters with the solar inverter sizing calculator to prevent system over-voltage.

Related concepts

Equation of Time

The difference between apparent solar time and mean solar time, resulting from Earth’s orbital eccentricity and obliquity.

Solar Declination

The latitude on Earth where the Sun is directly overhead at solar noon on a given day.

Atmospheric Refraction

The bending of light rays as they pass through the atmosphere, causing celestial objects near the horizon to appear higher than they are.

Frequently Asked Questions

What is solar noon?+

Solar noon is the daily moment when the Sun reaches its highest point in the sky and crosses the observer’s meridian, pointing due South or due North.

Why doesn’t solar noon happen at 12:00 clock time?+

Standard time zones span wide areas, but the Sun moves continuously. Solar noon shifts depending on how far east or west you are in your timezone, plus seasonal changes from Earth’s orbital tilt.

What is the Equation of Time?+

The Equation of Time is the difference between apparent solar time (sundial time) and mean solar time (uniform clock time), which varies by up to 16 minutes throughout the year.

How is sunrise and sunset defined in astronomy?+

Sunrise and sunset are defined as the moments when the upper edge of the Sun’s disk touches the astronomical horizon, corrected by 34 arcminutes for atmospheric refraction.

What is solar declination?+

Solar declination is the angle between the Earth-Sun line and the Earth’s equator, which varies seasonally from -23.44° in December to +23.44° in June.

Why is day length longer at the equator?+

At the equator, day length remains close to 12 hours year-round because the Earth’s tilt does not significantly alter the circle of illumination relative to the equator.

How does atmospheric refraction affect sunrise and sunset?+

Refraction bends sunlight around the curvature of the Earth, making the Sun visible in the sky before it has physically risen above the horizon, extending daylight by several minutes.

What is the hour angle in solar mathematics?+

The hour angle is the angular distance of the Sun from the observer’s meridian, measured in degrees (15 degrees equals 1 hour of Earth’s rotation).

How do I calculate solar altitude at noon?+

Altitude = 90° - Latitude + Solar Declination (where northern latitudes are positive and southern declination in winter is negative).

Can solar noon be used to find true North?+

Yes, at solar noon in the Northern Hemisphere (outside the tropics), the shadow cast by a vertical stick points exactly due North.

How to understand and use this calculator

NOAA Solar Calculations: The Equation of Time and Declination

Daylight Duration: Astronomical Formulas for Day Length

Timezones, Longitude, and Solar Noon Offsets

Solar Altitude and Azimuth Angles for Energy Harvesters

Related concepts

Equation of Time

The difference between apparent solar time and mean solar time, resulting from Earth’s orbital eccentricity and obliquity.

Solar Declination

The latitude on Earth where the Sun is directly overhead at solar noon on a given day.

Atmospheric Refraction

The bending of light rays as they pass through the atmosphere, causing celestial objects near the horizon to appear higher than they are.

Frequently Asked Questions

What is solar noon?+

Solar noon is the daily moment when the Sun reaches its highest point in the sky and crosses the observer’s meridian, pointing due South or due North.

Why doesn’t solar noon happen at 12:00 clock time?+

Standard time zones span wide areas, but the Sun moves continuously. Solar noon shifts depending on how far east or west you are in your timezone, plus seasonal changes from Earth’s orbital tilt.

What is the Equation of Time?+

The Equation of Time is the difference between apparent solar time (sundial time) and mean solar time (uniform clock time), which varies by up to 16 minutes throughout the year.

How is sunrise and sunset defined in astronomy?+

Sunrise and sunset are defined as the moments when the upper edge of the Sun’s disk touches the astronomical horizon, corrected by 34 arcminutes for atmospheric refraction.

What is solar declination?+

Solar declination is the angle between the Earth-Sun line and the Earth’s equator, which varies seasonally from -23.44° in December to +23.44° in June.

Why is day length longer at the equator?+

At the equator, day length remains close to 12 hours year-round because the Earth’s tilt does not significantly alter the circle of illumination relative to the equator.

How does atmospheric refraction affect sunrise and sunset?+

Refraction bends sunlight around the curvature of the Earth, making the Sun visible in the sky before it has physically risen above the horizon, extending daylight by several minutes.

What is the hour angle in solar mathematics?+

The hour angle is the angular distance of the Sun from the observer’s meridian, measured in degrees (15 degrees equals 1 hour of Earth’s rotation).

How do I calculate solar altitude at noon?+

Altitude = 90° - Latitude + Solar Declination (where northern latitudes are positive and southern declination in winter is negative).

Can solar noon be used to find true North?+

Yes, at solar noon in the Northern Hemisphere (outside the tropics), the shadow cast by a vertical stick points exactly due North.

Solar Noon, Sunset, & Daylight Duration Calculator

Inputs

Quick Presets

Custom Geographic Coordinates

Results

Bookmark this solar noon calculator

Solar Angle Formulas

How the calculation works

Learn more about this calculation

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Understanding Calculator Formulas: How DTC Turns Inputs into Results

Solar Noon, Sunset, & Daylight Duration Calculator

Inputs

Quick Presets

Custom Geographic Coordinates

Results

Bookmark this solar noon calculator

Key output metrics

Day vs Night Split

How to understand and use this calculator

NOAA Solar Calculations: The Equation of Time and Declination

Daylight Duration: Astronomical Formulas for Day Length

Timezones, Longitude, and Solar Noon Offsets

Solar Altitude and Azimuth Angles for Energy Harvesters

Related concepts

Frequently Asked Questions

Solar Angle Formulas

How the calculation works

Learn more about this calculation

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Understanding Calculator Formulas: How DTC Turns Inputs into Results

Key output metrics

Day vs Night Split

How to understand and use this calculator

NOAA Solar Calculations: The Equation of Time and Declination

Daylight Duration: Astronomical Formulas for Day Length

Timezones, Longitude, and Solar Noon Offsets

Solar Altitude and Azimuth Angles for Energy Harvesters

Related concepts

Frequently Asked Questions