Solar Noon & Day Length Calculator

°N
(1–365)
Everyday Life Updated 16 Jun 2026

Solar Noon & Day Length Calculator is a everyday life calculator that helps you calculate solar noon & day length values from your input data. The formula used is: Declination = 23.45° × sin(π × (284 + DOY) / 182)\nHour Angle = arccos(−tan(lat) × tan(decl))\nDay Length = 2 × HA / 15\nSunrise = 12 − HA/15; Sunset = 12 + HA/15. Enter values using the units shown next to each input. Common units such as litres, kg, and minutes are labelled.

Formula

Declination = 23.45° × sin(π × (284 + DOY) / 182) Hour Angle = arccos(−tan(lat) × tan(decl)) Day Length = 2 × HA / 15 Sunrise = 12 − HA/15; Sunset = 12 + HA/15

Example Calculation

Inputs
  • Latitude: 33.7 °N
  • Day of Year: 172 (1–365)

Suppose you enter: Latitude = 33.7, Day of Year = 172. The calculator applies the formula (Declination = 23.45° × sin(π × (284 + DOY) / 182)\nHour Angle = arccos(−tan(lat) × tan(decl))\nDay Length = 2 × HA / 15\nSunrise = 12 − HA/15; Sunset = 12 + HA/15) and shows all output values below. Change any input field to immediately see how the result changes.

Frequently asked questions

What is the Solar Noon & Day Length?
The Solar Noon & Day Length Calculator is a everyday life calculator that helps you calculate solar noon & day length values from your input data. Enter values using the units shown next to each input. Common units such as litres, kg, and minutes are labelled.
When should I use this calculator?
Use this calculator whenever you need a quick, accurate result for solar noon & day length values from your input data without working through the arithmetic manually.
What units should I enter?
Enter values using the units shown next to each input. Common units such as litres, kg, and minutes are labelled.
How accurate are the results?
Based on widely accepted formulas for everyday use. Actual results may vary with individual circumstances.
How do I interpret the result?
Use the result as a practical estimate. Adjust inputs to explore different scenarios.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.