Convert lambert to lumen / (square foot • steradian)
Learn how to convert
1
lambert to
lumen / (square foot • steradian)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(lambert\right)={\color{rgb(20,165,174)} x}\left(\dfrac{lumen}{square \text{ } foot \times steradian}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{candela}{square \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(lambert\right) = {\color{rgb(89,182,91)} \dfrac{10^{4}}{3.14159265358979}\left(\dfrac{candela}{square \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{10^{4}}{3.14159265358979}\left(\dfrac{cd}{m^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{lumen}{square \text{ } foot \times steradian}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}\left(\dfrac{candela}{square \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}\left(\dfrac{cd}{m^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(lambert\right)={\color{rgb(20,165,174)} x}\left(\dfrac{lumen}{square \text{ } foot \times steradian}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{4}}{3.14159265358979}} \times {\color{rgb(89,182,91)} \left(\dfrac{candela}{square \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{candela}{square \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{4}}{3.14159265358979}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{cd}{m^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{cd}{m^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{4}}{3.14159265358979}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{cd}{m^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{9.290304 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{cd}{m^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{4}}{3.14159265358979} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}} = \dfrac{10^{4}}{3.14159265358979}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{9.290304 \times 10^{-2}}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{9.290304 \times 10^{-2}} \times \dfrac{9.290304 \times 10^{-2}}{1.0} = \dfrac{10^{4}}{3.14159265358979} \times \dfrac{9.290304 \times 10^{-2}}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{9.290304}} \times {\color{rgb(166,218,227)} \cancel{10^{-2}}}}{{\color{rgb(99,194,222)} \cancel{9.290304}} \times {\color{rgb(166,218,227)} \cancel{10^{-2}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{4}}} \times 9.290304 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}}{3.14159265358979 \times 1.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 9.290304}{3.14159265358979}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx295.71956089\approx2.9572 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(lambert\right)\approx{\color{rgb(20,165,174)} 2.9572 \times 10^{2}}\left(\dfrac{lumen}{square \text{ } foot \times steradian}\right)\)
