# Convert pound-force • inch to gram-force • inch

Learn how to convert 1 pound-force • inch to gram-force • inch step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(pound-force \times inch\right)={\color{rgb(20,165,174)} x}\left(gram-force \times inch\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(newton \times meter\right)$$
$$\text{Left side: 1.0 } \left(pound-force \times inch\right) = {\color{rgb(89,182,91)} 0.112984829027617\left(newton \times meter\right)} = {\color{rgb(89,182,91)} 0.112984829027617\left(N \cdot m\right)}$$
$$\text{Right side: 1.0 } \left(gram-force \times inch\right) = {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}\left(newton \times meter\right)} = {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}\left(N \cdot m\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(pound-force \times inch\right)={\color{rgb(20,165,174)} x}\left(gram-force \times inch\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 0.112984829027617} \times {\color{rgb(89,182,91)} \left(newton \times meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left(newton \times meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 0.112984829027617} \cdot {\color{rgb(89,182,91)} \left(N \cdot m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left(N \cdot m\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 0.112984829027617} \cdot {\color{rgb(89,182,91)} \cancel{\left(N \cdot m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left(N \cdot m\right)}}$$
$$\text{Conversion Equation}$$
$$0.112984829027617 = {\color{rgb(20,165,174)} x} \times 2.4908891 \times 10^{-4}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 2.4908891 \times 10^{-4} = 0.112984829027617$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{2.4908891 \times 10^{-4}}\right)$$
$${\color{rgb(20,165,174)} x} \times 2.4908891 \times 10^{-4} \times \dfrac{1.0}{2.4908891 \times 10^{-4}} = 0.112984829027617 \times \dfrac{1.0}{2.4908891 \times 10^{-4}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.4908891}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.4908891}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}}} = 0.112984829027617 \times \dfrac{1.0}{2.4908891 \times 10^{-4}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{0.112984829027617}{2.4908891 \times 10^{-4}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-4}}\text{ can be rewritten to }10^{4}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{4} \times 0.112984829027617}{2.4908891}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx453.59237\approx4.5359 \times 10^{2}$$
$$\text{Conversion Equation}$$
$$1.0\left(pound-force \times inch\right)\approx{\color{rgb(20,165,174)} 4.5359 \times 10^{2}}\left(gram-force \times inch\right)$$