# Convert foot / (minute • second) to mile / square minute

Learn how to convert 1 foot / (minute • second) to mile / square minute step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{foot}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } minute}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{meter}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{foot}{minute \times second}\right) = {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}\left(\dfrac{m}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{mile}{square \text{ } minute}\right) = {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{foot}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } minute}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{0.3048}{2.16 \times 10^{5}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6 \times 10^{3}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{0.3048}{2.16 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}$$
$$\text{Simplify}$$
$$\dfrac{0.3048}{2.16 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6} = \dfrac{0.3048}{2.16 \times 10^{2}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{3.6}{1609.344}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6} \times \dfrac{3.6}{1609.344} = \dfrac{0.3048}{2.16 \times 10^{2}} \times \dfrac{3.6}{1609.344}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1609.344}} \times {\color{rgb(99,194,222)} \cancel{3.6}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(255,204,153)} \cancel{1609.344}}} = \dfrac{0.3048 \times 3.6}{2.16 \times 10^{2} \times 1609.344}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{0.3048 \times 3.6}{2.16 \times 10^{2} \times 1609.344}$$
Rewrite equation
$$\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 0.3048 \times 3.6}{2.16 \times 1609.344}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0000031566\approx3.1566 \times 10^{-6}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{foot}{minute \times second}\right)\approx{\color{rgb(20,165,174)} 3.1566 \times 10^{-6}}\left(\dfrac{mile}{square \text{ } minute}\right)$$