Length of Day Calculator

Estimate daylight for any place and date. Include twilight, refraction, horizon dip, and equation details. Export results for clear physics reports and planning today.

Calculator Inputs

Meters.
Degrees. Use positive values for blocked horizons.
Degrees. Used only when custom mode is selected.
Degrees. Positive values make the Sun appear higher.

Example Data Table

Location Latitude Longitude Date UTC Offset Approximate Result
New York 40.7128 -74.0060 2026-06-21 -4 Long summer daylight
London 51.5072 -0.1276 2026-12-21 0 Short winter daylight
Quito -0.1807 -78.4678 2026-03-20 -5 Near twelve hours
Tromso 69.6492 18.9553 2026-06-21 2 Possible polar daylight

Formula Used

The calculator first estimates solar declination and equation of time from the day number. It then adjusts the chosen solar altitude for elevation, local horizon angle, and extra refraction.

Solar hour angle formula:

cos(H) = [sin(h) - sin(latitude) × sin(declination)] ÷ [cos(latitude) × cos(declination)]

Day length formula:

Day length = 2H ÷ 15

Here, H is the solar hour angle in degrees. Earth rotates about 15 degrees each hour. Sunrise and sunset are found by subtracting and adding the hour angle time from solar noon.

How to Use This Calculator

  1. Enter latitude in degrees. North is positive, and south is negative.
  2. Enter longitude in degrees. East is positive, and west is negative.
  3. Select the date for the daylight estimate.
  4. Enter your UTC offset for local clock time.
  5. Add elevation and horizon angle when local terrain matters.
  6. Choose standard sunrise, twilight, or a custom solar altitude.
  7. Press the calculate button.
  8. Download the CSV or PDF report when needed.

Understanding Day Length in Physics

Day length is the time between sunrise and sunset. It changes because Earth rotates with a tilted axis. The tilt makes the Sun follow different paths through the sky during the year. A higher path usually gives a longer day. A lower path gives a shorter day. Latitude controls the size of this change. Places near the equator change slowly. Places near the poles can reach full daylight or full darkness.

What The Calculator Measures

This calculator estimates daylight for a chosen location and date. It uses latitude, longitude, time zone, elevation, and horizon angle. It also allows different solar altitude limits. Standard sunrise uses the Sun center near minus 0.833 degrees. That value includes average refraction and the visible solar radius. Civil, nautical, and astronomical twilight use deeper Sun angles. These options help compare visible daylight with useful sky brightness.

Why Elevation And Horizon Matter

A person standing above sea level can see slightly beyond the flat horizon. This makes sunrise earlier and sunset later. Mountains, buildings, or trees can do the opposite. A positive horizon angle raises the required Sun altitude. The calculator combines these effects before solving the solar hour angle. The result is an adjusted daylight estimate, not just a calendar table value.

Interpreting The Results

The output shows solar declination, equation of time, solar noon, sunrise, sunset, and total day length. Solar declination describes the Sun position north or south of the equator. Equation of time corrects the difference between clock time and apparent solar time. Near polar regions, the formula may show continuous day or continuous night. That is a valid physical result for the selected altitude limit.

Accuracy Notes

The method is accurate enough for planning, study, and classroom physics. It uses common solar geometry formulas. Real observations can differ by weather, local terrain, pressure, temperature, and refraction. Use precise survey data when legal, navigation, or safety decisions depend on exact sunrise times. For normal learning, the calculator gives clear and repeatable results.

Best Uses

Use it for labs, travel checks, solar studies, garden planning, and astronomy practice. Change one input at a time. This shows how each physical factor changes the final daylight period with simple steps.

FAQs

What is length of day?

It is the time between sunrise and sunset for a selected location and date. In this calculator, it can also mean time above a selected twilight altitude.

Why does day length change?

Earth has a tilted rotation axis. Because of that tilt, the Sun appears higher or lower in the sky during different seasons.

What latitude should I enter?

Use decimal degrees. Northern latitudes are positive. Southern latitudes are negative. For example, 40.7 is north, and -33.9 is south.

What longitude format is used?

Use decimal degrees. Eastern longitudes are positive. Western longitudes are negative. This matches common solar calculation formulas.

What does UTC offset mean?

UTC offset converts solar time into local clock time. For example, Pakistan Standard Time uses 5, while Eastern Standard Time uses -5.

Why use minus 0.833 degrees?

Standard sunrise uses the Sun center below the horizon. This accounts for atmospheric refraction and the visible radius of the solar disk.

Can this calculator show polar day?

Yes. If the Sun stays above the selected altitude all day, the result shows continuous daylight for that altitude limit.

Is the result exact for every location?

No. Terrain, buildings, air pressure, temperature, and local refraction can shift observed sunrise or sunset. The result is a strong physics estimate.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.