Convert quadrant to arc second

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

Calculation Breakdown

Set up the equation

1.0 (q u a d r a n t) = x (a r c s e c o n d)

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

(r a d i a n)

Left side: 1.0 (q u a d r a n t) = \frac{π}{2.0} (r a d i a n) = \frac{π}{2.0} (r a d)

Right 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)

Insert known values into the conversion equation to determine

x

1.0 (q u a d r a n t) = x (a r c s e c o n d)

Insert known values =>

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

Conversion Equation

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

Cancel factors on both sides

Cancel factors

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

Switch sides

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

Isolate

x

Multiply both sides by

(\frac{6.48 \times 10^{5}}{1.0})

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

Cancel

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

Simplify

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

Solve

x

x = 324000 = 3.24 \times 10^{5}

Conversion Equation

1.0 (q u a d r a n t) = 3.24 \times 10^{5} (a r c s e c o n d)

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