Hour Angles to Radians Converter

Enter Hour Angles


Radians





⇅ Switch toRadians to Hour Angles Converter

How to use this Hour Angles to Radians Converter 🤔

Follow these steps to convert given angle from the units of Hour Angles to the units of Radians.

  1. Enter the input Hour Angles value in the text field.
  2. The calculator converts the given Hour Angles into Radians in realtime ⌚ using the conversion formula, and displays under the Radians label. You do not need to click any button. If the input changes, Radians value is re-calculated, just like that.
  3. You may copy the resulting Radians value using the Copy button.
  4. To view a detailed step by step calculation of the conversion, click on the View Calculation button.
  5. You can also reset the input by clicking on Reset button present below the input field.

What is the Formula to convert Hour Angles to Radians?

The formula to convert given angle from Hour Angles to Radians is:

Angle(Radians) = Angle(Hour Angles) × π / 12

Substitute the given value of angle in hour angles, i.e., Angle(Hour Angles) in the above formula and simplify the right-hand side value. The resulting value is the angle in radians, i.e., Angle(Radians).

Calculation

Calculation will be done after you enter a valid input.

Examples

1

Consider that the position of a celestial body is tracked at 6 hour angles.
Convert this angle from hour angles to Radians.

Answer:

Given:

The angle in hour angles is:

Angle(Hour Angles) = 6

Formula:

The formula to convert angle from hour angles to radians is:

Angle(Radians) = Angle(Hour Angles) × π / 12

Substitution:

Substitute given weight Angle(Hour Angles) = 6 in the above formula.

Angle(Radians) = 6 × 3.14159265359 / 12

Angle(Radians) = 1.5708

Final Answer:

Therefore, 6 hour angle is equal to 1.5708 rad.

The angle is 1.5708 rad, in radians.

2

Consider that a sundial shows a time difference of 4 hour angles.
Convert this angle from hour angles to Radians.

Answer:

Given:

The angle in hour angles is:

Angle(Hour Angles) = 4

Formula:

The formula to convert angle from hour angles to radians is:

Angle(Radians) = Angle(Hour Angles) × π / 12

Substitution:

Substitute given weight Angle(Hour Angles) = 4 in the above formula.

Angle(Radians) = 4 × 3.14159265359 / 12

Angle(Radians) = 1.0472

Final Answer:

Therefore, 4 hour angle is equal to 1.0472 rad.

The angle is 1.0472 rad, in radians.

Hour Angles to Radians Conversion Table

The following table gives some of the most used conversions from Hour Angles to Radians.

Hour Angles (hour angle)Radians (rad)
0 hour angle0 rad
1 hour angle0.2618 rad
10 hour angle2.618 rad
45 hour angle11.781 rad
90 hour angle23.5619 rad
180 hour angle47.1239 rad
360 hour angle94.2478 rad
1000 hour angle261.7994 rad

Hour Angles

Hour angles are a unit of angular measurement used in astronomy to describe the position of celestial objects relative to an observer's local meridian. One hour angle corresponds to 15 degrees, reflecting the Earth's rotation rate of 15 degrees per hour. Hour angles are crucial in celestial navigation and the tracking of astronomical objects.

Radians

Radians are a fundamental unit of angular measurement in the International System of Units (SI). One radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. Radians are essential in mathematics and physics, particularly in calculus and trigonometry, where they simplify equations and allow for the natural expression of rotational and periodic phenomena.

Frequently Asked Questions (FAQs)

1. What is the formula for converting Hour Angles to Radians in Angle?

2. Is this tool free or paid?

3. How do I convert Angle from Hour Angles to Radians?