# Convert newton to (gram • meter) / square second

Learn how to convert 1 newton to (gram • meter) / square second step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(newton\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram \times meter}{square \text{ } second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(newton\right)$$
$$\text{Left side: 1.0 } \left(newton\right) = {\color{rgb(89,182,91)} 1.0\left(newton\right)} = {\color{rgb(89,182,91)} 1.0\left(N\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{gram \times meter}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 10^{-3}\left(newton\right)} = {\color{rgb(125,164,120)} 10^{-3}\left(N\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(newton\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram \times meter}{square \text{ } second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(newton\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-3}}} \times {\color{rgb(125,164,120)} \left(newton\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(N\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(N\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(N\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(N\right)}}$$
$$\text{Conversion Equation}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times 10^{-3}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times 10^{-3}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 10^{-3} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{10^{-3}}\right)$$
$${\color{rgb(20,165,174)} x} \times 10^{-3} \times \dfrac{1.0}{10^{-3}} = 1.0 \times \dfrac{1.0}{10^{-3}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-3}}}} = 1.0 \times \dfrac{1.0}{10^{-3}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{10^{-3}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = 10^{3}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 1000 = 1 \times 10^{3}$$
$$\text{Conversion Equation}$$
$$1.0\left(newton\right) = {\color{rgb(20,165,174)} 1 \times 10^{3}}\left(\dfrac{gram \times meter}{square \text{ } second}\right)$$