Convert cycle / square second to radian / square second

Learn how to convert 1 cycle / square second to radian / square second step by step.

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Calculation Breakdown

Set up the equation

\(1.0\left(\dfrac{cycle}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{square \text{ } second}\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{square \text{ } second}\right)\)

\(\text{Left side: 1.0 } \left(\dfrac{cycle}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{rad}{s^{2}}\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{radian}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 1.0\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 1.0\left(\dfrac{rad}{s^{2}}\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(\dfrac{cycle}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{square \text{ } second}\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}\)

\(\text{Conversion Equation}\)

\(2.0 \times π = {\color{rgb(20,165,174)} x} \times 1.0\)

\(\text{Simplify}\)

\(π \times 2.0 = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = π \times 2.0\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x}\approx6.2831853072\approx6.2832\)

\(\text{Conversion Equation}\)

\(1.0\left(\dfrac{cycle}{square \text{ } second}\right)\approx{\color{rgb(20,165,174)} 6.2832}\left(\dfrac{radian}{square \text{ } second}\right)\)