Daylight Duration (Hours of Sunlight) by Latitude & Day of Year Calculator

Compute astronomical daylight length using the sunrise hour-angle equation.

Total Daylight Duration
14.92 hours
Nighttime Duration 9.08 hours
Solar Declination Angle (δ) 23.44 deg
Solar Noon Max Elevation Angle 72.74 deg
Inputs
deg
Observer latitude in degrees (+ North, − South).
day (1–365)
Day of the year (1 to 365; 80=Vernal Equinox, 172=Summer Solstice, 355=Winter Solstice).
Results & Graph
Total Daylight Duration
14.92 hours
Nighttime Duration
9.08 hours
Solar Declination Angle (δ)
23.44 deg
Solar Noon Max Elevation Angle
72.74 deg

Total Daylight Duration

Graph 1 • Latitude Degrees Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 hours 10.2 hours 20.4 hours 50%: 13.23 hours 13.2 50% 75%: 13.97 hours 14.0 75% 100%: 14.92 hours 14.9 100% 125%: 16.29 hours 16.3 125% 150%: 18.88 hours 18.9 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Total Daylight Duration 14.92 hours Nighttime Duration 9.08 hours Solar Declination Angle (δ) 23.44 deg Solar Noon Max Elevation Angle 72.74 deg
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Total Daylight Duration14.92 hoursNighttime Duration9.08 hoursSolar Declination Angle (δ)23.44 degSolar Noon Max Elevation Angle72.74 deg
Summary: At latitude 40.7° on day 172 (solar declination 23.44°), daylight lasts 14.92 hours (9.08 hours night).
Summary: At latitude 40.7° on day 172 (solar declination 23.44°), daylight lasts 14.92 hours (9.08 hours night).
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Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Daylight Hours by Latitude Formula

δ = 23.44° × sin(360°/365 × (DayOfYear − 81))
DaylightHours = (24 / π) × arccos(−tan(Lat) × tan(δ))
δ = 23.44° × sin(360°/365 × (DayOfYear − 81)); DaylightHours = (24 / π) × arccos(−tan(Lat) × tan(δ))
  • latitudeDegrees: Latitude Degrees (deg)
  • dayOfYear1to365: Day Of Year1to365 (day (1–365))

Rounding: Standardized test and time rules follow official scoring rubrics; continuous outputs round to 2 decimal places.

Worked Example: Benchmark Scenario: Daylight Hours by Latitude

Compute astronomical daylight length using the sunrise hour-angle equation.

  1. Enter your raw test counts, credit hours, or schedule parameters.
  2. Evaluate the formula: δ = 23.44° × sin(360°/365 × (DayOfYear − 81)); DaylightHours = (24 / π) × arccos(−tan(Lat) × tan(δ)).
  3. Inspect the primary score/duration, supporting metrics, and 3 SVG graphs.
Result: Computes Daylight Hours by Latitude via δ = 23.44° × sin(360°/365 × (DayOfYear − 81)); DaylightHours = (24 / π) × arccos(−tan(Lat) × tan(δ)).

Frequently Asked Questions

How does the Daylight Duration (Hours of Sunlight) by Latitude & Day of Year Calculator calculate results?

It evaluates δ = 23.44° × sin(360°/365 × (DayOfYear − 81)); DaylightHours = (24 / π) × arccos(−tan(Lat) × tan(δ)) directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to find the exact score or hours I need?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any input variable.

Are my academic or schedule inputs kept private?

Yes. All calculations run 100% locally in your browser.

Dates & Time · Calendar, Astronomical & Time

Daylight Duration (Hours of Sunlight) by Latitude & Day of Year Calculator: inputs, method, and how to read the result

Compute astronomical daylight length using the sunrise hour-angle equation.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Latitude Degrees: Observer latitude in degrees (+ North, − South).
  • Day Of Year1to365: Day of the year (1 to 365; 80=Vernal Equinox, 172=Summer Solstice, 355=Winter Solstice).

What the calculation includes

With the default values shown, Total Daylight Duration is 14.92 hours. The calculation follows Daylight Hours by Latitude Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Latitude Degrees from 40.7 deg to 44.77 deg changes Total Daylight Duration from 14.92 hours to 15.4 hours. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official published scoring scales, Carnegie unit conventions, and ISO calendar rules.
  • Official standardized test equating curves vary slightly by test form administration date.

Scope: Global Academic, Psychometric & ISO 8601 Time Standard Check the assumptions and limitations against your situation before relying on the estimate.

More in Dates & Time: GPA & Final Grade Calculator, Date Difference & Business Days Calculator, Time Duration, Shift Time Card, Overtime Pay & Time Zone Calculator.