Convert gradian to second of arc

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

Calculation Breakdown

Set up the equation

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

Insert known values =>

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

Conversion Equation

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

Cancel factors on both sides

Cancel factors

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

Simplify

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

Switch sides

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

Isolate

x

Multiply both sides by

(\frac{6.48 \times 10^{3}}{1.0})

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

Cancel

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

Simplify

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

Solve

x

x = 3240 = 3.24 \times 10^{3}

Conversion Equation

1.0 (g r a d i a n) = 3.24 \times 10^{3} (s e c o n d o f a r c)

View All Examples