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The Hour angle is the measure of time since solar noon, expressed in degrees, indicating the position of the sun in the sky relative to an observer. Check FAQs
ω=acos(-tan(Φ-β)tan(δ))
ω - Hour angle?Φ - Latitude Angle?β - Tilt Angle?δ - Declination Angle?

Hour Angle at Sunrise and Sunset Example

With values
With units
Only example

Here is how the Hour Angle at Sunrise and Sunset equation looks like with Values.

Here is how the Hour Angle at Sunrise and Sunset equation looks like with Units.

Here is how the Hour Angle at Sunrise and Sunset equation looks like.

119.9552Edit=acos(-tan(55Edit-5.5Edit)tan(23.0964Edit))
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Hour Angle at Sunrise and Sunset Solution

Follow our step by step solution on how to calculate Hour Angle at Sunrise and Sunset?

FIRST Step Consider the formula
ω=acos(-tan(Φ-β)tan(δ))
Next Step Substitute values of Variables
ω=acos(-tan(55°-5.5°)tan(23.0964°))
Next Step Convert Units
ω=acos(-tan(0.9599rad-0.096rad)tan(0.4031rad))
Next Step Prepare to Evaluate
ω=acos(-tan(0.9599-0.096)tan(0.4031))
Next Step Evaluate
ω=2.09361265775303rad
Next Step Convert to Output's Unit
ω=119.955169224438°
LAST Step Rounding Answer
ω=119.9552°

Hour Angle at Sunrise and Sunset Formula Elements

Variables
Functions
Hour angle
The Hour angle is the measure of time since solar noon, expressed in degrees, indicating the position of the sun in the sky relative to an observer.
Symbol: ω
Measurement: AngleUnit: °
Note: Value should be greater than 0.
Latitude Angle
The Latitude Angle is the angular measurement that indicates a location's distance north or south of the equator, influencing solar energy exposure and system performance.
Symbol: Φ
Measurement: AngleUnit: °
Note: Value can be positive or negative.
Tilt Angle
The Tilt Angle is the angle at which solar panels are positioned relative to the ground, optimizing sunlight exposure for increased energy efficiency.
Symbol: β
Measurement: AngleUnit: °
Note: Value should be greater than 0.
Declination Angle
The Declination Angle is the angle between the rays of the sun and the plane of the Earth's equator, affecting solar energy collection throughout the year.
Symbol: δ
Measurement: AngleUnit: °
Note: Value can be positive or negative.
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 to find Hour angle

​Go Hour angle
ω=(ST3600-12)150.0175

Other formulas in Basics category

​Go Tilt factor for reflected radiation
rr=ρ(1-cos(β))2
​Go Tilt factor for diffused radiation
rd=1+cos(β)2
​Go Energy Conversion Efficiency of Solar Chimney
ηmax=9.81H1005Ta
​Go Declination angle
δ=23.45sin(0.9863(284+N))

How to Evaluate Hour Angle at Sunrise and Sunset?

Hour Angle at Sunrise and Sunset evaluator uses Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)) to evaluate the Hour angle, The Hour Angle at Sunrise and Sunset formula is defined as a measure of the angular distance between the sun at the local solar time and the sun at solar noon. Hour angle is denoted by ω symbol.

How to evaluate Hour Angle at Sunrise and Sunset using this online evaluator? To use this online evaluator for Hour Angle at Sunrise and Sunset, enter Latitude Angle (Φ), Tilt Angle (β) & Declination Angle (δ) and hit the calculate button.

FAQs on Hour Angle at Sunrise and Sunset

What is the formula to find Hour Angle at Sunrise and Sunset?
The formula of Hour Angle at Sunrise and Sunset is expressed as Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)). Here is an example- 6864.118 = acos(-tan(0.959931088596701-0.0959931088596701)*tan(0.403107876291692)).
How to calculate Hour Angle at Sunrise and Sunset?
With Latitude Angle (Φ), Tilt Angle (β) & Declination Angle (δ) we can find Hour Angle at Sunrise and Sunset using the formula - Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)). This formula also uses Cosine (cos)Tangent (tan), Inverse Cosine (acos) function(s).
What are the other ways to Calculate Hour angle?
Here are the different ways to Calculate Hour angle-
  • Hour angle=(Solar Time/3600-12)*15*0.0175OpenImg
Can the Hour Angle at Sunrise and Sunset be negative?
Yes, the Hour Angle at Sunrise and Sunset, measured in Angle can be negative.
Which unit is used to measure Hour Angle at Sunrise and Sunset?
Hour Angle at Sunrise and Sunset is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Hour Angle at Sunrise and Sunset can be measured.
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