Convert rotation to degree

Learn how to convert 1 rotation to degree step by step.

Calculation Breakdown

Set up the equation

1.0 (r o t a t i o n) = x (d e g r e e)

Define the base values of the selected units in relation to the SI unit

(r a d i a n)

Left side: 1.0 (r o t a t i o n) = 2.0 \times π (r a d i a n) = 2.0 \times π (r a d)

Right side: 1.0 (d e g r e e) = \frac{π}{180.0} (r a d i a n) = \frac{π}{180.0} (r a d)

Insert known values into the conversion equation to determine

x

1.0 (r o t a t i o n) = x (d e g r e e)

Insert known values =>

1.0 \times 2.0 \times π \times (r a d i a n) = x \times \frac{π}{180.0} \times (r a d i a n)

Or

1.0 \cdot 2.0 \times π \cdot (r a d) = x \cdot \frac{π}{180.0} \cdot (r a d)

Cancel SI units

1.0 \times 2.0 \times π \cdot (r a d) = x \times \frac{π}{180.0} \times (r a d)

Conversion Equation

2.0 \times π = x \times \frac{π}{180.0}

Cancel factors on both sides

Cancel factors

π \times 2.0 = x \times \frac{π}{180.0}

Simplify

2.0 = x \times \frac{1.0}{180.0}

Switch sides

x \times \frac{1.0}{180.0} = 2.0

Isolate

x

Multiply both sides by

(\frac{180.0}{1.0})

x \times \frac{1.0}{180.0} \times \frac{180.0}{1.0} = 2.0 \times \frac{180.0}{1.0}

Cancel

x \times \frac{1.0 \times 180.0}{180.0 \times 1.0} = 2.0 \times \frac{180.0}{1.0}

Simplify

x = 2.0 \times 180.0

Solve

x

x = 360 = 3.6 \times 10^{2}

Conversion Equation

1.0 (r o t a t i o n) = 3.6 \times 10^{2} (d e g r e e)

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