Convert radian / square minute to degree / square minute

Learn how to convert 1 radian / square minute to degree / square minute step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{r a d i a n}{s q u a r e m i n u t e}) = x (\frac{d e g r e e}{s q u a r e m i n u t e})

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

(\frac{r a d i a n}{s q u a r e s e c o n d})

Left side: 1.0 (\frac{r a d i a n}{s q u a r e m i n u t e}) = \frac{1.0}{3.6 \times 10^{3}} (\frac{r a d i a n}{s q u a r e s e c o n d}) = \frac{1.0}{3.6 \times 10^{3}} (\frac{r a d}{s^{2}})

Right side: 1.0 (\frac{d e g r e e}{s q u a r e m i n u t e}) = \frac{π}{6.48 \times 10^{5}} (\frac{r a d i a n}{s q u a r e s e c o n d}) = \frac{π}{6.48 \times 10^{5}} (\frac{r a d}{s^{2}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{r a d i a n}{s q u a r e m i n u t e}) = x (\frac{d e g r e e}{s q u a r e m i n u t e})

Insert known values =>

1.0 \times \frac{1.0}{3.6 \times 10^{3}} \times (\frac{r a d i a n}{s q u a r e s e c o n d}) = x \times \frac{π}{6.48 \times 10^{5}} \times (\frac{r a d i a n}{s q u a r e s e c o n d})

Or

1.0 \cdot \frac{1.0}{3.6 \times 10^{3}} \cdot (\frac{r a d}{s^{2}}) = x \cdot \frac{π}{6.48 \times 10^{5}} \cdot (\frac{r a d}{s^{2}})

Cancel SI units

1.0 \times \frac{1.0}{3.6 \times 10^{3}} \cdot (\frac{r a d}{s^{2}}) = x \times \frac{π}{6.48 \times 10^{5}} \times (\frac{r a d}{s^{2}})

Conversion Equation

\frac{1.0}{3.6 \times 10^{3}} = x \times \frac{π}{6.48 \times 10^{5}}

Cancel factors on both sides

Cancel factors

\frac{1.0}{3.6 \times 10^{3}} = x \times \frac{π}{6.48 \times {10^{5}}^{10^{2}}}

Simplify

\frac{1.0}{3.6} = x \times \frac{π}{6.48 \times 10^{2}}

Switch sides

x \times \frac{π}{6.48 \times 10^{2}} = \frac{1.0}{3.6}

Isolate

x

Multiply both sides by

(\frac{6.48 \times 10^{2}}{π})

x \times \frac{π}{6.48 \times 10^{2}} \times \frac{6.48 \times 10^{2}}{π} = \frac{1.0}{3.6} \times \frac{6.48 \times 10^{2}}{π}

Cancel

x \times \frac{π \times 6.48 \times 10^{2}}{6.48 \times 10^{2} \times π} = \frac{1.0 \times 6.48 \times 10^{2}}{3.6 \times π}

Simplify

x = \frac{6.48 \times 10^{2}}{3.6 \times π}

Solve

x

x \approx 57.295779513 \approx 57.2958

Conversion Equation

1.0 (\frac{r a d i a n}{s q u a r e m i n u t e}) \approx 57.2958 (\frac{d e g r e e}{s q u a r e m i n u t e})

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