Convert pound-force / square inch to gram / square inch
Learn how to convert
1
pound-force / square inch to
gram / square inch
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound-force}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{square \text{ } inch}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(pascal\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound-force}{square \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{4.4482216152605}{6.4516 \times 10^{-4}}\left(pascal\right)} = {\color{rgb(89,182,91)} \dfrac{4.4482216152605}{6.4516 \times 10^{-4}}\left(Pa\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gram}{square \text{ } inch}\right) = {\color{rgb(125,164,120)} \dfrac{9.80665}{6.4516 \times 10^{-1}}\left(pascal\right)} = {\color{rgb(125,164,120)} \dfrac{9.80665}{6.4516 \times 10^{-1}}\left(Pa\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound-force}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{square \text{ } inch}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{4.4482216152605}{6.4516 \times 10^{-4}}} \times {\color{rgb(89,182,91)} \left(pascal\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{9.80665}{6.4516 \times 10^{-1}}}} \times {\color{rgb(125,164,120)} \left(pascal\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{4.4482216152605}{6.4516 \times 10^{-4}}} \cdot {\color{rgb(89,182,91)} \left(Pa\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \cdot {\color{rgb(125,164,120)} \left(Pa\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{4.4482216152605}{6.4516 \times 10^{-4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Pa\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \times {\color{rgb(125,164,120)} \cancel{\left(Pa\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{4.4482216152605}{6.4516 \times 10^{-4}} = {\color{rgb(20,165,174)} x} \times \dfrac{9.80665}{6.4516 \times 10^{-1}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{4.4482216152605}{{\color{rgb(255,204,153)} \cancel{6.4516}} \times {\color{rgb(99,194,222)} \cancelto{10^{-3}}{10^{-4}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{9.80665}{{\color{rgb(255,204,153)} \cancel{6.4516}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}}}\)
\(\text{Simplify}\)
\(\dfrac{4.4482216152605}{10^{-3}} = {\color{rgb(20,165,174)} x} \times 9.80665\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 9.80665 = \dfrac{4.4482216152605}{10^{-3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{9.80665}\right)\)
\({\color{rgb(20,165,174)} x} \times 9.80665 \times \dfrac{1.0}{9.80665} = \dfrac{4.4482216152605}{10^{-3}} \times \dfrac{1.0}{9.80665}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{9.80665}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{9.80665}}} = \dfrac{4.4482216152605 \times 1.0}{10^{-3} \times 9.80665}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4.4482216152605}{10^{-3} \times 9.80665}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 4.4482216152605}{9.80665}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 453.59237\approx4.5359 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound-force}{square \text{ } inch}\right)\approx{\color{rgb(20,165,174)} 4.5359 \times 10^{2}}\left(\dfrac{gram}{square \text{ } inch}\right)\)
