Convert dyne • meter to gram-force • meter

Learn how to convert 1 dyne • meter to gram-force • meter step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(dyne \times meter\right)={\color{rgb(20,165,174)} x}\left(gram-force \times meter\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton \times meter\right)\)
\(\text{Left side: 1.0 } \left(dyne \times meter\right) = {\color{rgb(89,182,91)} 10^{-5}\left(newton \times meter\right)} = {\color{rgb(89,182,91)} 10^{-5}\left(N \cdot m\right)}\)
\(\text{Right side: 1.0 } \left(gram-force \times meter\right) = {\color{rgb(125,164,120)} 9.80665 \times 10^{-3}\left(newton \times meter\right)} = {\color{rgb(125,164,120)} 9.80665 \times 10^{-3}\left(N \cdot m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(dyne \times meter\right)={\color{rgb(20,165,174)} x}\left(gram-force \times meter\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \times {\color{rgb(89,182,91)} \left(newton \times meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 9.80665 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left(newton \times meter\right)}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(N \cdot m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 9.80665 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(N \cdot m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N \cdot m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 9.80665 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(N \cdot m\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-5} = {\color{rgb(20,165,174)} x} \times 9.80665 \times 10^{-3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-5}}} = {\color{rgb(20,165,174)} x} \times 9.80665 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)
\(10^{-2} = {\color{rgb(20,165,174)} x} \times 9.80665\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 9.80665 = 10^{-2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{9.80665}\right)\)
\({\color{rgb(20,165,174)} x} \times 9.80665 \times \dfrac{1.0}{9.80665} = 10^{-2} \times \dfrac{1.0}{9.80665}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{9.80665}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{9.80665}}} = 10^{-2} \times \dfrac{1.0}{9.80665}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2}}{9.80665}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0010197162\approx1.0197 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(dyne \times meter\right)\approx{\color{rgb(20,165,174)} 1.0197 \times 10^{-3}}\left(gram-force \times meter\right)\)

Cookie Policy