# Convert lumen / (square meter • steradian) to lumen / (square foot • steradian)

Learn how to convert 1 lumen / (square meter • steradian) to lumen / (square foot • steradian) step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{lumen}{square \text{ } meter \times steradian}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{lumen}{square \text{ } foot \times steradian}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{candela}{square \text{ } meter}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{lumen}{square \text{ } meter \times steradian}\right) = {\color{rgb(89,182,91)} 1.0\left(\dfrac{candela}{square \text{ } meter}\right)} = {\color{rgb(89,182,91)} 1.0\left(\dfrac{cd}{m^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{lumen}{square \text{ } foot \times steradian}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}\left(\dfrac{candela}{square \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}\left(\dfrac{cd}{m^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{lumen}{square \text{ } meter \times steradian}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{lumen}{square \text{ } foot \times steradian}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(\dfrac{candela}{square \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{candela}{square \text{ } meter}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(\dfrac{cd}{m^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{cd}{m^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{cd}{m^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{cd}{m^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$${\color{rgb(255,204,153)} \cancel{1.0}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}}}{9.290304 \times 10^{-2}}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{9.290304 \times 10^{-2}}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}} \times \dfrac{9.290304 \times 10^{-2}}{1.0} = \times \dfrac{9.290304 \times 10^{-2}}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{9.290304}} \times {\color{rgb(166,218,227)} \cancel{10^{-2}}}}{{\color{rgb(99,194,222)} \cancel{9.290304}} \times {\color{rgb(166,218,227)} \cancel{10^{-2}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{9.290304 \times 10^{-2}}{1.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = 9.290304 \times 10^{-2}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 0.09290304\approx9.2903 \times 10^{-2}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{lumen}{square \text{ } meter \times steradian}\right)\approx{\color{rgb(20,165,174)} 9.2903 \times 10^{-2}}\left(\dfrac{lumen}{square \text{ } foot \times steradian}\right)$$