# Solar Noon, Sunset, & Daylight Duration Calculator Calculate NOAA solar noon, sunrise, sunset, and total daylight duration based on latitude and longitude coordinates instantly. --- - **Canonical URL:** https://dothecalculation.com/calculators/solar-noon-daylight-calculator - **Category:** Everyday utilities - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology - **Reviewed by:** Sheharyar Shahid, Data Analyst & Advanced Excel Specialist (DAE) (https://dothecalculation.com/about/team/sheharyar-shahid) --- ## Solar Noon, Sunset & Daylight Duration Calculator Calculate NOAA astronomical solar noon, sunrise, sunset, solar declination, and daylight hours for any location on Earth. - NOAA-compliant Equation of Time and solar declination algorithms - Refraction-corrected sunrise and sunset calculations - Exact daylight duration and solar zenith angle outputs ## 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](/calculators/solar-payback-calculator) which integrates panel sizing with regional utility rates, or size charge controllers and inverters with the [solar inverter sizing calculator](/calculators/solar-inverter-sizing-calculator) to prevent system over-voltage. ## How to Use This Solar Noon & Daylight Calculator Select a city preset (New York, London, Tokyo, Sydney, or Cairo) for instant results, or enter custom latitude, longitude, and UTC timezone offset values for any location on Earth. Choose the observation date using the date picker. The results panel returns the exact clock time of solar noon, sunrise, and sunset for that date and location, along with the total daylight duration in hours and minutes. ## Worked Example: New York on the Summer Solstice For New York (latitude 40.7128°, longitude -74.006°, UTC-5) on June 21, 2026 — the summer solstice — the calculator returns sunrise at 04:24 AM, solar noon at 11:57 AM, sunset at 07:30 PM, and a daylight duration of 15 hours 6 minutes, the longest day of the year for that location. For comparison, the same coordinates on the March 20, 2026 equinox return sunrise at 06:01 AM, sunset at 06:06 PM, and almost exactly 12 hours 6 minutes of daylight — confirming the equinox principle that day and night are nearly equal in length everywhere on Earth except for the small refraction correction built into the formula. ## Related Calculators This calculator is part of a Date & Time Tools cluster. To calculate elapsed time or add days to a date, use the [Date Calculator](/calculators/date-calculator). To find a date's ordinal position in the year, see the [Day of the Year Calculator](/calculators/day-of-year-calculator), or convert the resulting times to another region with the [Time Zone Converter](/calculators/timezone-converter). ## 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. ## 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. ## Related guides - [How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide](https://dothecalculation.com/blog/site-guides/how-to-use-calculators) — Learn the fastest reliable workflow for using Do The Calculation calculators, reading results, checking formulas, and using save, print, share, and export actions correctly. - [Understanding Calculator Formulas: How DTC Turns Inputs into Results](https://dothecalculation.com/blog/site-guides/understanding-calculator-formulas) — Understand how Do The Calculation formulas are presented, what the explanation blocks mean, and how to verify calculator logic before using a result in a real decision. ## Related calculators - [Binary, Hexadecimal, & ASCII Multi-Base Converter](https://dothecalculation.com/calculators/binary-hex-ascii-calculator) — Convert integers and strings between binary, hexadecimal, ASCII, and decimal formats instantly with this free online conversion tool. - [Blood Donation Eligibility & Regeneration Tracker](https://dothecalculation.com/calculators/blood-donation-interval-calculator) — Track blood donation eligibility dates, countdowns, and iron and plasma regeneration phases instantly with this free tracker tool. - [Word Counter Calculator](https://dothecalculation.com/calculators/word-counter-calculator) — Count words, characters, sentences, and paragraphs in real-time, estimate reading times, and analyze word density/readability. - [Estate & Gift Tax Calculator](https://dothecalculation.com/calculators/estate-tax-planning-calculator) — Estimate federal and state estate and gift tax liabilities, applicable exemptions, and net inheritance passed on to heirs. - [Geocaching Waypoint Projection Calculator](https://dothecalculation.com/calculators/geocaching-projector-calculator) — Project new geocaching waypoint coordinates, exact latitude and longitude, from a starting point using bearing and distance. - [Business Days Difference & Working Day Calculator](https://dothecalculation.com/calculators/date-difference-business-calculator) — Calculate business days difference and total calendar days between two dates, excluding weekends and custom holidays instantly. --- _This calculator is for general educational and reference purposes only. Results are estimates and should not be used as the sole basis for critical decisions._ --- _Source: [Do The Calculation](https://dothecalculation.com/calculators/solar-noon-daylight-calculator). Quote freely with attribution and a link to this page._