Daylight Hours Calculator

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✖Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface.ⓘ Latitude Angle [Φ]			+10% -10%
✖The declination angle of the sun is the angle between the equator and a line drawn from the centre of the Earth to the centre of the sun.ⓘ Declination Angle [δ]			+10% -10%

✖Daylight hours is defined as the number of hours for which sunlight is available between sunrise and sunset.ⓘ Daylight Hours [t_d]

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Formula

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Daylight Hours

Formula

`"t"_{"d"} = 3600*acos(-tan("Φ")*tan("δ"))`

Example

`"2.222086h"=3600*acos(-tan("55°")*tan("23°"))`

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Daylight Hours Solution

STEP 0: Pre-Calculation Summary

Formula Used

Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle))
t_d = 3600*acos(-tan(Φ)*tan(δ))
This formula uses 3 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Daylight Hours - (Measured in Second) - Daylight hours is defined as the number of hours for which sunlight is available between sunrise and sunset.
Latitude Angle - (Measured in Radian) - Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface.
Declination Angle - (Measured in Radian) - The declination angle of the sun is the angle between the equator and a line drawn from the centre of the Earth to the centre of the sun.

STEP 1: Convert Input(s) to Base Unit

Latitude Angle: 55 Degree --> 0.959931088596701 Radian (Check conversion here)
Declination Angle: 23 Degree --> 0.40142572795862 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_d = 3600*acos(-tan(Φ)*tan(δ)) --> 3600*acos(-tan(0.959931088596701)*tan(0.40142572795862))

Evaluating ... ...

t_d = 7999.51083383851

STEP 3: Convert Result to Output's Unit

7999.51083383851 Second -->2.22208634273292 Hour (Check conversion here)

FINAL ANSWER

2.22208634273292 ≈ 2.222086 Hour <-- Daylight Hours

(Calculation completed in 00.004 seconds)

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Credits

Created by ADITYA RAWAT

DIT UNIVERSITY (DITU), Dehradun

ADITYA RAWAT has created this Calculator and 50+ more calculators!

Verified by Saurabh Patil

Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore

Saurabh Patil has verified this Calculator and 25+ more calculators!

< 8 Basics Calculators

Angle of incidence of sun rays

Go Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle))

Hour Angle at Sunrise and Sunset

Go Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle))

Daylight Hours

Go Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle))

Tilt factor for reflected radiation

Go Tilt factor for reflected radiation = (Reflectivity*(1-cos(Tilt Angle)))/2

Energy Conversion Efficiency of Solar Chimney

Go Max Efficiency of a Solar Chimney = 9.81*Height of Chimney/(1005*Ambient Air Temperature)

Tilt factor for diffused radiation

Go Tilt factor for diffused radiation = (1+cos(Tilt Angle))/2

Declination angle

Go Declination Angle = 23.45*sin(0.9863*(284+Number of days))

Hour angle

Go Hour angle = (Solar Time/3600-12)*15*0.0175

Daylight Hours Formula

Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle))
t_d = 3600*acos(-tan(Φ)*tan(δ))

Duration of sunshine hour

The sun traverses 15degrees in 1 hour. The sunshine is available between sunrise and sunset or in solar day length.

How to Calculate Daylight Hours?

Daylight Hours calculator uses Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle)) to calculate the Daylight Hours, The Daylight Hours formula is defined as the period of time during each Day that commences at sunrise on such Day and ends at the time of sunset on such Day. Daylight Hours is denoted by t_d symbol.

How to calculate Daylight Hours using this online calculator? To use this online calculator for Daylight Hours, enter Latitude Angle (Φ) & Declination Angle (δ) and hit the calculate button. Here is how the Daylight Hours calculation can be explained with given input values -> 0.000617 = 3600*acos(-tan(0.959931088596701)*tan(0.40142572795862)).

FAQ

What is Daylight Hours?

The Daylight Hours formula is defined as the period of time during each Day that commences at sunrise on such Day and ends at the time of sunset on such Day and is represented as t_d = 3600*acos(-tan(Φ)*tan(δ)) or Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle)). Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface & The declination angle of the sun is the angle between the equator and a line drawn from the centre of the Earth to the centre of the sun.

How to calculate Daylight Hours?

The Daylight Hours formula is defined as the period of time during each Day that commences at sunrise on such Day and ends at the time of sunset on such Day is calculated using Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle)). To calculate Daylight Hours, you need Latitude Angle (Φ) & Declination Angle (δ). With our tool, you need to enter the respective value for Latitude Angle & Declination Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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