# Convert gram / liter to pound / cubic foot

Learn how to convert 1 gram / liter to pound / cubic foot step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{gram}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{gram}{liter}\right) = {\color{rgb(89,182,91)} 1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 1.0\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{pound}{cubic \text{ } foot}\right) = {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{gram}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}$$
$$\text{Conversion Equation}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{0.28316846592}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{0.28316846592}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{5.0}{0.28316846592} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{0.28316846592}{5.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{5.0}{0.28316846592} \times \dfrac{0.28316846592}{5.0} = 1.0 \times \dfrac{0.28316846592}{5.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{5.0}} \times {\color{rgb(99,194,222)} \cancel{0.28316846592}}}{{\color{rgb(99,194,222)} \cancel{0.28316846592}} \times {\color{rgb(255,204,153)} \cancel{5.0}}} = 1.0 \times \dfrac{0.28316846592}{5.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{0.28316846592}{5.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0566336932\approx5.6634 \times 10^{-2}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{gram}{liter}\right)\approx{\color{rgb(20,165,174)} 5.6634 \times 10^{-2}}\left(\dfrac{pound}{cubic \text{ } foot}\right)$$