Convert arc second to second of arc

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

Calculation Breakdown

Set up the equation

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

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

(r a d i a n)

Left side: 1.0 (a r c s e c o n d) = \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 (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)

Insert known values into the conversion equation to determine

x

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

Insert known values =>

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

Or

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

Cancel SI units

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

Conversion Equation

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

Cancel factors on both sides

Cancel factors

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

Simplify

1.0 = x

Switch sides

x = 1.0

Solve

x

x = 1

Conversion Equation

1.0 (a r c s e c o n d) = 1 (s e c o n d o f a r c)

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