Turns to Milli-radians Converter

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Milli-radians





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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.

  1. Enter the input Turns value in the text field.
  2. 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.
  3. You may copy the resulting Milli-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 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

Calculation will be done after you enter a valid input.

Examples

1

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.

2

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 turn0 mrad
1 turn6283.1853 mrad
10 turn62831.8531 mrad
45 turn282743.3388 mrad
90 turn565486.6776 mrad
180 turn1130973.3553 mrad
360 turn2261946.7106 mrad
1000 turn6283185.3072 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?

2. Is this tool free or paid?

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