Skip to content
ENExplore Calculators

Daylight Duration Calculator

Calculate day length for a latitude and date.

About Daylight Duration Calculator

Day length depends on the interaction between latitude and solar declination. At the equator it barely varies, while above sixty degrees the swing exceeds twelve hours between solstices. This is why high-latitude summers have usable light until late evening while the same places lose most of the working day in winter.

Formula

Daylight Duration

Day length = 2 × arccos(−tan(latitude) × tan(declination)) ÷ 15

solar declination
The sun’s angle north or south of the equator, varying with the season
hour angle
Half the arc of daylight, converted at 15 degrees per hour

Worked example

With the default values below, Daylight Duration Calculator returns Daylight Duration of 16.404. Change any input above and every figure here is recalculated in your browser.

Inputs used

Latitudeaccepts -66–66 degrees
51.5 degrees
Day of the yearaccepts 1–366
172

Results

Daylight Duration
16.404 h
Solar Declination
23.440 degrees
Hours of Darkness
7.596 h
Daylight Duration
16h 24m
Season at This Latitude
Long summer days

Step by step

  1. 1Values used
  2. 2Daylight Duration
  3. 3Daylight Duration= 16.404 h
  4. 4Solar Declination= 23.440 degrees
  5. 5Hours of Darkness= 7.596 h
  6. 6Daylight Duration= 16h 24m
  7. 7Season at This Latitude= Long summer days

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Daylight Duration calculated?

Day length = 2 × arccos(−tan(latitude) × tan(declination)) ÷ 15 Day length depends on the interaction between latitude and solar declination. At the equator it barely varies, while above sixty degrees the swing exceeds twelve hours between solstices.

Why does Daylight Duration matter?

This is why high-latitude summers have usable light until late evening while the same places lose most of the working day in winter.

What values do I need to enter?

This calculator takes 2 inputs: Latitude, Day of the year. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

Related Calculators

Daylight Duration Calculator – Calculate Daylight Duration