Convert gram / square inch to gram / square foot

Learn how to convert 1 gram / square inch to gram / square foot step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(\dfrac{gram}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{square \text{ } foot}\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(pascal\right)\)

\(\text{Left side: 1.0 } \left(\dfrac{gram}{square \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}\left(pascal\right)} = {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}\left(Pa\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{gram}{square \text{ } foot}\right) = {\color{rgb(125,164,120)} \dfrac{9.80665 \times 10^{-1}}{9.290304}\left(pascal\right)} = {\color{rgb(125,164,120)} \dfrac{9.80665 \times 10^{-1}}{9.290304}\left(Pa\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(\dfrac{gram}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{square \text{ } foot}\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \times {\color{rgb(89,182,91)} \left(pascal\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{9.80665 \times 10^{-1}}{9.290304}}} \times {\color{rgb(125,164,120)} \left(pascal\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \cdot {\color{rgb(89,182,91)} \left(Pa\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{9.80665 \times 10^{-1}}{9.290304}} \cdot {\color{rgb(125,164,120)} \left(Pa\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Pa\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{9.80665 \times 10^{-1}}{9.290304}} \times {\color{rgb(125,164,120)} \cancel{\left(Pa\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{9.80665}{6.4516 \times 10^{-1}} = {\color{rgb(20,165,174)} x} \times \dfrac{9.80665 \times 10^{-1}}{9.290304}\)

Cancel factors on both sides

\(\text{Cancel factors}\)

\(\dfrac{{\color{rgb(255,204,153)} \cancel{9.80665}}}{6.4516 \times 10^{-1}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{9.80665}} \times 10^{-1}}{9.290304}\)

\(\text{Simplify}\)

\(\dfrac{1.0}{6.4516 \times 10^{-1}} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-1}}{9.290304}\)

Switch sides

\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-1}}{9.290304} = \dfrac{1.0}{6.4516 \times 10^{-1}}\)

Isolate \({\color{rgb(20,165,174)} x}\)

Multiply both sides by \(\left(\dfrac{9.290304}{10^{-1}}\right)\)

\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-1}}{9.290304} \times \dfrac{9.290304}{10^{-1}} = \dfrac{1.0}{6.4516 \times 10^{-1}} \times \dfrac{9.290304}{10^{-1}}\)

\(\text{Cancel}\)

\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-1}}} \times {\color{rgb(99,194,222)} \cancel{9.290304}}}{{\color{rgb(99,194,222)} \cancel{9.290304}} \times {\color{rgb(255,204,153)} \cancel{10^{-1}}}} = \dfrac{1.0 \times 9.290304}{6.4516 \times 10^{-1} \times 10^{-1}}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{9.290304}{6.4516 \times 10^{-1} \times 10^{-1}}\)

Rewrite equation

\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10.0 \times 10.0 \times 9.290304}{6.4516}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10.0^{2} \times 9.290304}{6.4516}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x} = 144 = 1.44 \times 10^{2}\)

\(\text{Conversion Equation}\)

\(1.0\left(\dfrac{gram}{square \text{ } inch}\right) = {\color{rgb(20,165,174)} 1.44 \times 10^{2}}\left(\dfrac{gram}{square \text{ } foot}\right)\)