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Daylight Hours Formula

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Daylight Hours is the duration of time when the sun is above the horizon and daylight is available at a particular location on Earth. Check FAQs

t d = 3600 \cdot a \cos (- \tan (Φ) \cdot \tan (δ))

t_d - Daylight Hours?Φ - Latitude Angle?δ - Declination Angle?

Daylight Hours Example

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With units

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Here is how the Daylight Hours equation looks like with Values.

Here is how the Daylight Hours equation looks like with Units.

Here is how the Daylight Hours equation looks like.

8012.3714 = 3600 \cdot a \cos (- \tan (55) \cdot \tan (23.0964))

8012.3714s = 3600 \cdot a \cos (- \tan (55°) \cdot \tan (23.0964°))

8012.3714 = 3600 \cdot a \cos (- \tan (55) \cdot \tan (23.0964))

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Daylight Hours Solution

Follow our step by step solution on how to calculate Daylight Hours?

FIRST Step Consider the formula

t d = 3600 \cdot a \cos (- \tan (Φ) \cdot \tan (δ))

Next Step Substitute values of Variables

∴

t d = 3600 \cdot a \cos (- \tan (55°) \cdot \tan (23.0964°))

Next Step Convert Units

∴

t d = 3600 \cdot a \cos (- \tan (0.9599rad) \cdot \tan (0.4031rad))

Next Step Prepare to Evaluate

∴

t d = 3600 \cdot a \cos (- \tan (0.9599) \cdot \tan (0.4031))

Next Step Evaluate

∴

t d = 8012.37136100474s

LAST Step Rounding Answer

∴

t d = 8012.3714s

Daylight Hours Formula Elements

Variables

Functions

Daylight Hours

Daylight Hours is the duration of time when the sun is above the horizon and daylight is available at a particular location on Earth.

Symbol: t_d

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Daylight Hours

Latitude Angle

Latitude Angle is the angle between a line to a point on the surface of the Earth and the equatorial plane.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Latitude Angle

Declination Angle

Declination Angle is the angle between the magnetic field lines and the horizontal plane at a particular location on the Earth's surface.

Symbol: δ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Declination Angle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: acos(Number)

Other formulas in Basics category

Go Tilt factor for reflected radiation

r r = \frac{ρ \cdot (1 - \cos (β))}{2}

Go Tilt factor for diffused radiation

r d = \frac{1 + \cos (β)}{2}

Go Hour Angle at Sunrise and Sunset

ω = a \cos (- \tan (Φ - β) \cdot \tan (δ))

Go Hour angle

ω = (\frac{ST}{3600} - 12) \cdot 15 \cdot 0.0175

How to Evaluate Daylight Hours?

Daylight Hours evaluator uses Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle)) to evaluate 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 evaluate Daylight Hours using this online evaluator? To use this online evaluator for Daylight Hours, enter Latitude Angle (Φ) & Declination Angle (δ) and hit the calculate button.

FAQs on Daylight Hours

What is the formula to find Daylight Hours?

The formula of Daylight Hours is expressed as Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle)). Here is an example- 8012.371 = 3600*acos(-tan(0.959931088596701)*tan(0.403107876291692)).

How to calculate Daylight Hours?

With Latitude Angle (Φ) & Declination Angle (δ) we can find Daylight Hours using the formula - Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle)). This formula also uses Cosine (cos)Tangent (tan), Inverse Cosine (acos) function(s).

Can the Daylight Hours be negative?

No, the Daylight Hours, measured in Time cannot be negative.

Which unit is used to measure Daylight Hours?

Daylight Hours is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Daylight Hours can be measured.

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