# Turns to Milli-radians Converter

⇅ Switch toMilli-radians to Turns Converter

## How to use this Turns to Milli-radians Converter 🤔

Follow these steps to convert given angle from the units of Turns to the units of Milli-radians.

- Enter the input
**Turns**value in the text field. - The calculator converts the given
**Turns**into**Milli-radians**in realtime ⌚ using the conversion formula, and displays under the**Milli-radians**label. You do not need to click any button. If the input changes,**Milli-radians**value is re-calculated, just like that. - You may copy the resulting
**Milli-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 Turns to Milli-radians?

The formula to convert given angle from Turns to Milli-radians is:

Angle_{(Milli-radians)} = Angle_{(Turns)} × 2000 × π

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

## Calculation

## Examples

### Consider that a turntable rotates by 0.25 turns to play a vinyl record.

Convert this rotation from turns to Milli-radians.

#### Answer:

**Given:**

The angle in turns is:

Angle_{(Turns)} = 0.25

**Formula:**

The formula to convert angle from turns to milli-radians is:

Angle_{(Milli-radians)} = Angle_{(Turns)} × 2000 × π

**Substitution:**

Substitute given weight **Angle _{(Turns)} = 0.25** in the above formula.

Angle_{(Milli-radians)} = 0.25 × 2000 × 3.14159265359

Angle_{(Milli-radians)} = 1570.7963

**Final Answer:**

Therefore, **0.25 turn** is equal to **1570.7963 mrad**.

The angle is **1570.7963 mrad**, in milli-radians.

### Consider that a wind turbine completes 2 turns in a light breeze.

Convert this rotation from turns to Milli-radians.

#### Answer:

**Given:**

The angle in turns is:

Angle_{(Turns)} = 2

**Formula:**

The formula to convert angle from turns to milli-radians is:

Angle_{(Milli-radians)} = Angle_{(Turns)} × 2000 × π

**Substitution:**

Substitute given weight **Angle _{(Turns)} = 2** in the above formula.

Angle_{(Milli-radians)} = 2 × 2000 × 3.14159265359

Angle_{(Milli-radians)} = 12566.3706

**Final Answer:**

Therefore, **2 turn** is equal to **12566.3706 mrad**.

The angle is **12566.3706 mrad**, in milli-radians.

## Turns to Milli-radians Conversion Table

The following table gives some of the most used conversions from Turns to Milli-radians.

Turns (turn) | Milli-radians (mrad) |
---|---|

0 turn | 0 mrad |

1 turn | 6283.1853 mrad |

10 turn | 62831.8531 mrad |

45 turn | 282743.3388 mrad |

90 turn | 565486.6776 mrad |

180 turn | 1130973.3553 mrad |

360 turn | 2261946.7106 mrad |

1000 turn | 6283185.3072 mrad |

## Turns

A turn, also known as a revolution or full circle, represents a complete rotation around a central point and is equal to 360 degrees or 2π radians. Turns are used in various disciplines, including engineering, navigation, and geometry, to describe full rotations. The concept of turns is deeply rooted in both mathematical theory and practical applications, such as in the design of gears and wheels.

## Milli-radians

Milli-radians (mrad) are a unit of angular measurement equal to one-thousandth of a radian. This small unit is used in fields such as ballistics, gunnery, and optics, where precise angular measurements are critical. Milli-radians allow for the calculation of minute angular displacements, distances, and target adjustments.

## Frequently Asked Questions (FAQs)

### 1. What is the formula for converting Turns to Milli-radians in Angle?

The formula to convert Turns to Milli-radians in Angle is:

Turns * 2000 * π

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

This Angle conversion tool, which converts Turns to Milli-radians, is completely free to use.

### 3. How do I convert Angle from Turns to Milli-radians?

To convert Angle from Turns to Milli-radians, you can use the following formula:

Turns * 2000 * π

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