Convert atomic unit of force to newton

Learn how to convert 1 atomic unit of force to newton step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(atomic \text{ } unit \text{ } of \text{ } force\right)={\color{rgb(20,165,174)} x}\left(newton\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton\right)\)
\(\text{Left side: 1.0 } \left(atomic \text{ } unit \text{ } of \text{ } force\right) = {\color{rgb(89,182,91)} 8.23872206 \times 10^{-8}\left(newton\right)} = {\color{rgb(89,182,91)} 8.23872206 \times 10^{-8}\left(N\right)}\)
\(\text{Right side: 1.0 } \left(newton\right) = {\color{rgb(125,164,120)} 1.0\left(newton\right)} = {\color{rgb(125,164,120)} 1.0\left(N\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(atomic \text{ } unit \text{ } of \text{ } force\right)={\color{rgb(20,165,174)} x}\left(newton\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 8.23872206 \times 10^{-8}} \times {\color{rgb(89,182,91)} \left(newton\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(newton\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 8.23872206 \times 10^{-8}} \cdot {\color{rgb(89,182,91)} \left(N\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(N\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 8.23872206 \times 10^{-8}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(N\right)}}\)
\(\text{Conversion Equation}\)
\(8.23872206 \times 10^{-8} = {\color{rgb(20,165,174)} x} \times 1.0\)
\(\text{Simplify}\)
\(8.23872206 \times 10^{-8} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = 8.23872206 \times 10^{-8}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000000824\approx8.2387 \times 10^{-8}\)
\(\text{Conversion Equation}\)
\(1.0\left(atomic \text{ } unit \text{ } of \text{ } force\right)\approx{\color{rgb(20,165,174)} 8.2387 \times 10^{-8}}\left(newton\right)\)

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