# Convert ton / cubic foot to pound / cubic foot

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

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{ton}{cubic \text{ } foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{ton}{cubic \text{ } foot}\right) = {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{pound}{cubic \text{ } foot}\right) = {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{ton}{cubic \text{ } foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{10^{5}}{2.8316846592} = {\color{rgb(20,165,174)} x} \times \dfrac{45.359237}{2.8316846592}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{10^{5}}{{\color{rgb(255,204,153)} \cancel{2.8316846592}}} = {\color{rgb(20,165,174)} x} \times \dfrac{45.359237}{{\color{rgb(255,204,153)} \cancel{2.8316846592}}}$$
$$\text{Simplify}$$
$$10^{5} = {\color{rgb(20,165,174)} x} \times 45.359237$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 45.359237 = 10^{5}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{45.359237}\right)$$
$${\color{rgb(20,165,174)} x} \times 45.359237 \times \dfrac{1.0}{45.359237} = 10^{5} \times \dfrac{1.0}{45.359237}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{45.359237}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{45.359237}}} = 10^{5} \times \dfrac{1.0}{45.359237}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{5}}{45.359237}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx2204.6226218\approx2.2046 \times 10^{3}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{ton}{cubic \text{ } foot}\right)\approx{\color{rgb(20,165,174)} 2.2046 \times 10^{3}}\left(\dfrac{pound}{cubic \text{ } foot}\right)$$