Day Length Calculator

Day Length Calculator

Estimate daylight duration, sunrise, sunset, solar noon, twilight span, and polar day or night using latitude, date, zenith angle, elevation, and local clock offset.

Real Presets
📍Calculator Inputs
Uses the day of year for solar declination.
North positive, south negative.
East positive, west negative; affects clock times.
Use daylight time if your clock is currently shifted.
Default is 90.833°, which includes solar radius and refraction.
Use only when custom is selected.
Horizon dip adds about 1.76 arcminutes per square root meter.
Changes display only; calculation keeps full precision.
Day Length
--
official daylight
Sunrise
--
local clock time
Sunset
--
local clock time
Solar Noon
--
sun highest point
🧮Formula Breakdown

The calculator estimates solar declination for the selected day, converts latitude, declination, and zenith to radians, then evaluates the hour angle. The required day length formula is day length hours = 2*H/15, where H = acos((cosZ/(cosLat*cosDec))-tanLat*tanDec) in degrees. If the expression inside acos is below -1, the sun remains above the selected horizon all day; if it is above 1, the sun never reaches that horizon.

🗺Comparison Grid
12h
Equator near equinox
15h+
Mid-latitude summer
6h-
High-latitude winter
24h
Polar day condition
📊Zenith And Twilight Reference
Mode Zenith Angle Sun Position Typical Use
Geometric sunrise 90.000° Sun center on ideal horizon Pure geometry without refraction
Official sunrise 90.833° Upper limb visible with refraction Standard daylight length
Civil twilight 96.000° Sun center 6° below horizon Outdoor visibility transition
Nautical twilight 102.000° Sun center 12° below horizon Marine horizon visibility
Astronomical twilight 108.000° Sun center 18° below horizon Dark-sky astronomy planning
🌎Sample Day Lengths By Latitude
Latitude March Equinox June Solstice December Solstice
0° Equator About 12h 07m About 12h 07m About 12h 07m
30° North About 12h 07m About 14h 05m About 10h 09m
45° North About 12h 09m About 15h 26m About 8h 51m
60° North About 12h 13m About 18h 31m About 5h 52m
66.6° North About 12h 16m Near 24h Near 0h
75° North About 12h 25m 24h polar day 0h polar night
🏙Preset Location Comparison
Location Latitude Season Example Expected Pattern
New York City 40.7128° N June solstice Long summer day, sunrise early
London 51.5074° N December solstice Short winter day, low solar noon
Tromso 69.6492° N June and December Polar day or polar night
Quito 0.1807° S Equinox Nearly balanced day and night
Sydney 33.8688° S December solstice Southern Hemisphere long day
Reykjavik 64.1466° N June solstice Very long day, brief night
📐Calculation Terms
Term Symbol Units Role In Result
Solar zenith Z Degrees Defines the horizon or twilight threshold
Latitude Lat Degrees Sets seasonal daylight amplitude
Solar declination Dec Degrees Tracks Earth tilt through the year
Hour angle H Degrees Half the daylight arc of the sun
Equation of time EOT Minutes Shifts clock solar noon from 12:00
💡Day Length Tips
Horizon and elevation: The official 90.833° zenith already includes average refraction and the sun radius. Adding elevation accounts for a lower visible horizon, so high viewpoints can add several daylight minutes.
Longitude and time zone: Longitude does not change the total daylight for a latitude and date, but it moves sunrise, sunset, and solar noon on the clock. Match the offset to the clock you want to display.

Visit Tromso in mid-winter, and you’ll notice that there isn’t any sun. For weeks at a time it hovers just beneath horizon, bathing the place in constant twilight. Six months later, there’s a midnight sun over same town. That’s the geometry of things, not weather.

This calculator of day lengths can tell you how many hours of daylight you’ll get anywhere on earth. It makes complicated spherical trigonometry easy by just using multiplication. To make sense of its numbers, you have to grasp Earths tilt. Day and night is divided equally, most people believe. Technically that’s true at the equator. As you approach poles, it starts to get lopsided. How much so? That’s where calculator comes in (above).

How to Calculate Daylight Hours

All you have to do is input the date and your latitude. No need to worry about sun’s angle each day. Solar declination mean the sun’s position, expressed as an angle from equator. That swings back and forth through the year, from +twenty-three point five degrees up to the North Pole to -twenty-three point five down into the South Pole. When the tilt is matched by your own hemisphere, the sun trace out a longer arc across the sky. This results in long summer days.

For a scientist, or even more so a photographer, precision are key. The tool includes multiple settings called zenith modes, which refer to an angle off a perfect vertical (a straight line up from where you stand) above. If you’re looking at standard sunrise and sunset, this will be a peak of ninety point eight three three degrees, taking into account atmospheric refraction. That’s because the atmosphere refracts the light, bending it along the curve of the planet. And it appears to make sun higher than it actualy is. It also takes into account the disk size of the sun.

To find out when the sky has gotten dark enough for astrophotography, you need to set your watch to the astronomical twilight setting, which means that the sun must be eighteen degrees below horizon. In high latitudes, that can mean almost two hours’ difference between the civil and astronomical twilights, enough to change the nature of the ambient light entirely.

There’s another element that play a surprising role: your local horizon. If you’re standing atop a mountain, you’ll have a longer view over curvature of the Earth. That horizon dip results in the sun rising earlier (and setting later). To account for this, enter your altitude above sea level in meters into the calculator. It might be a tiny adjustment, but when planning down to the minute for a shoot, every second count.

If you’re in a steep valley, the sun will be obscured until it clear the nearest ridge. There’s no way for any calculator to know what’s around your location. You need to figure out the amount of time required for the sun to crest that next ridge.

There’s another wrinkle, time zones. Your real solar time is determined by your longitude. Standard time offsets are political boundaries. Twelve o’clock rarely match solar noon. That’s when the sun is overhead. In many places, it’s off by an hour or even more. How much it vary depends on how far east or west you are.

This calculator divides the total day into daylight time and then also separates out what the clock times will be. Date plus latitude determine the duration. Time zone offset and longitude changes the clock times. This is where most folks get it wrong. They think sunrise occur later in the summer. Actually, in a lot of locations, it begins moving earlier in late June. During this period, sunset keeps delaying. But it’s all spelled out clearly in the table of reference on the page.

Here, we see that as you move north, your daylight diminishes. At high latitudes, the sun hardly rise above horizon. This creates hours of a weak, scattered light. Near the equator, the sun rise steeply. So there are abrupt transitions from night to day.

And that brings us back to the hour angle, which is the angular distance the sun moves from noon until sunset. Double that angle and divide by fifteen and voila: hours of daylight. It is elegant in its simplicity.

It’s hard to appreciate what you don’t have, especially daylight. Whether you’re a photographer or a gardener, the dynamics remains identical. You should of checked the weather too. You are looking for that magic golden hour. Checking to see if there’s enough light.

The sun arcs. The Earth tilts. Light bends through atmosphere. These are exact numbers from the calculator. Understanding the geometry provides context. Your time doesn’t mean anything to the sun. It follows the rules of the sky.

Day Length Calculator