Convert arc second to grade

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

Calculation Breakdown

Set up the equation

1.0 (a r c s e c o n d) = x (g r a d 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 (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 (g r a d e) = \frac{π}{2.0 \times 10^{2}} (r a d i a n) = \frac{π}{2.0 \times 10^{2}} (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 (g r a d e)

Insert known values =>

1.0 \times \frac{π}{6.48 \times 10^{5}} \times (r a d i a n) = x \times \frac{π}{2.0 \times 10^{2}} \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}{2.0 \times 10^{2}} \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}{2.0 \times 10^{2}} \times (r a d)

Conversion Equation

\frac{π}{6.48 \times 10^{5}} = x \times \frac{π}{2.0 \times 10^{2}}

Cancel factors on both sides

Cancel factors

\frac{π}{6.48 \times {10^{5}}^{10^{3}}} = x \times \frac{π}{2.0 \times 10^{2}}

Simplify

\frac{1.0}{6.48 \times 10^{3}} = x \times \frac{1.0}{2.0}

Switch sides

x \times \frac{1.0}{2.0} = \frac{1.0}{6.48 \times 10^{3}}

Isolate

x

Multiply both sides by

(\frac{2.0}{1.0})

x \times \frac{1.0}{2.0} \times \frac{2.0}{1.0} = \frac{1.0}{6.48 \times 10^{3}} \times \frac{2.0}{1.0}

Cancel

x \times \frac{1.0 \times 2.0}{2.0 \times 1.0} = \frac{1.0 \times 2.0}{6.48 \times 10^{3} \times 1.0}

Simplify

x = \frac{2.0}{6.48 \times 10^{3}}

Rewrite equation

\frac{1.0}{10^{3}} can be rewritten to 10^{- 3}

Rewrite

x = \frac{10^{- 3} \times 2.0}{6.48}

Solve

x

x \approx 0.000308642 \approx 3.0864 \times 10^{- 4}

Conversion Equation

1.0 (a r c s e c o n d) \approx 3.0864 \times 10^{- 4} (g r a d e)

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