Convert second of arc to rotation

Learn how to convert 1 second of arc to rotation step by step.

Calculation Breakdown

Set up the equation

1.0 (s e c o n d o f a r c) = x (r o t a t i o n)

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

(r a d i a n)

Left side: 1.0 (s e c o n d o f a r c) = \frac{π}{6.48 \times 10^{5}} (r a d i a n) = \frac{π}{6.48 \times 10^{5}} (r a d)

Right 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)

Insert known values into the conversion equation to determine

x

1.0 (s e c o n d o f a r c) = x (r o t a t i o n)

Insert known values =>

1.0 \times \frac{π}{6.48 \times 10^{5}} \times (r a d i a n) = x \times 2.0 \times π \times (r a d i a n)

Or

1.0 \cdot \frac{π}{6.48 \times 10^{5}} \cdot (r a d) = x \cdot 2.0 \times π \cdot (r a d)

Cancel SI units

1.0 \times \frac{π}{6.48 \times 10^{5}} \cdot (r a d) = x \times 2.0 \times π \times (r a d)

Conversion Equation

\frac{π}{6.48 \times 10^{5}} = x \times 2.0 \times π

Cancel factors on both sides

Cancel factors

\frac{π}{6.48 \times 10^{5}} = x \times π \times 2.0

Simplify

\frac{1.0}{6.48 \times 10^{5}} = x \times 2.0

Switch sides

x \times 2.0 = \frac{1.0}{6.48 \times 10^{5}}

Isolate

x

Multiply both sides by

(\frac{1.0}{2.0})

x \times 2.0 \times \frac{1.0}{2.0} = \frac{1.0}{6.48 \times 10^{5}} \times \frac{1.0}{2.0}

Cancel

x \times 2.0 \times \frac{1.0}{2.0} = \frac{1.0 \times 1.0}{6.48 \times 10^{5} \times 2.0}

Simplify

x = \frac{1.0}{6.48 \times 10^{5} \times 2.0}

Rewrite equation

\frac{1.0}{10^{5}} can be rewritten to 10^{- 5}

Rewrite

x = \frac{10^{- 5}}{6.48 \times 2.0}

Solve

x

x \approx 0.0000007716 \approx 7.716 \times 10^{- 7}

Conversion Equation

1.0 (s e c o n d o f a r c) \approx 7.716 \times 10^{- 7} (r o t a t i o n)

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