# Seconds to Radians Converter

⇅ Switch toRadians to Seconds Converter

## How to use this Seconds to Radians Converter 🤔

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

- Enter the input
**Seconds**value in the text field. - The calculator converts the given
**Seconds**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. - You may copy the resulting
**Radians**value using the Copy button. - To view a detailed step by step calculation of the conversion, click on the View Calculation button.
- You can also reset the input by clicking on button present below the input field.

## What is the Formula to convert Seconds to Radians?

The formula to convert given angle from Seconds to Radians is:

Angle_{(Radians)} = Angle_{(Seconds)} × π/ 648000

To convert any given angle from seconds to radians, substitute the given value of Angle_{(Seconds)} in the above formula, simplify the right-hand side value.

## Calculation

## Examples

### Consider that a microscope's fine adjustment is set to 30 arc seconds for detailed observation.

Convert this angle from seconds to Radians.

#### Answer:

**Given:**

The angle in seconds is:

Angle_{(Seconds)} = 30

**Formula:**

The formula to convert angle from seconds to radians is:

Angle_{(Radians)} = Angle_{(Seconds)} × π/ 648000

**Substitution:**

Substitute given weight **Angle _{(Seconds)} = 30** in the above formula.

Angle_{(Radians)} = 30 × 3.14159265359/ 648000

Angle_{(Radians)} = 0.0001454441

**Final Answer:**

Therefore, **30 "** is equal to **0.0001454441 rad**.

The angle is **0.0001454441 rad**, in radians.

### Consider that a telescope's alignment needs to be within 20 arc seconds for accurate tracking.

Convert this angle from seconds to Radians.

#### Answer:

**Given:**

The angle in seconds is:

Angle_{(Seconds)} = 20

**Formula:**

The formula to convert angle from seconds to radians is:

Angle_{(Radians)} = Angle_{(Seconds)} × π/ 648000

**Substitution:**

Substitute given weight **Angle _{(Seconds)} = 20** in the above formula.

Angle_{(Radians)} = 20 × 3.14159265359/ 648000

Angle_{(Radians)} = 0.00009696274

**Final Answer:**

Therefore, **20 "** is equal to **0.00009696274 rad**.

The angle is **0.00009696274 rad**, in radians.

## Seconds to Radians Conversion Table

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

Seconds (") | Radians (rad) |
---|---|

0 " | 0 rad |

1 " | 0.00000484814 rad |

10 " | 0.00004848137 rad |

45 " | 0.00021816616 rad |

90 " | 0.00043633231 rad |

180 " | 0.00087266463 rad |

360 " | 0.00174532925 rad |

1000 " | 0.00484813681 rad |

## Seconds

Seconds of arc, often simply called arcseconds, are a further subdivision of minutes of arc, with 60 seconds in one minute. This small unit is used for extremely precise angular measurements, such as those needed in astronomy, optics, and surveying, where even minute differences in angle can be significant.

## 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 Seconds to Radians in Angle?

The formula to convert Seconds to Radians in Angle is:

Seconds * π/ 648000

### 2. Is this tool free or paid?

This Angle conversion tool, which converts Seconds to Radians, is completely free to use.

### 3. How do I convert Angle from Seconds to Radians?

To convert Angle from Seconds to Radians, you can use the following formula:

Seconds * π/ 648000

For example, if you have a value in Seconds, you substitute that value in place of Seconds in the above formula, and solve the mathematical expression to get the equivalent value in Radians.