Convert lumen / square inch to watt / square meter
Learn how to convert
1
lumen / square inch to
watt / square meter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{lumen}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{watt}{square \text{ } meter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(lux\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{lumen}{square \text{ } inch}\right) = {\color{rgb(89,182,91)} 1.55 \times 10^{3}\left(lux\right)} = {\color{rgb(89,182,91)} 1.55 \times 10^{3}\left(lx\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{watt}{square \text{ } meter}\right) = {\color{rgb(125,164,120)} 683.0\left(lux\right)} = {\color{rgb(125,164,120)} 683.0\left(lx\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{lumen}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{watt}{square \text{ } meter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.55 \times 10^{3}} \times {\color{rgb(89,182,91)} \left(lux\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 683.0}} \times {\color{rgb(125,164,120)} \left(lux\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.55 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \left(lx\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 683.0} \cdot {\color{rgb(125,164,120)} \left(lx\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.55 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(lx\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 683.0} \times {\color{rgb(125,164,120)} \cancel{\left(lx\right)}}\)
\(\text{Conversion Equation}\)
\(1.55 \times 10^{3} = {\color{rgb(20,165,174)} x} \times 683.0\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 683.0 = 1.55 \times 10^{3}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{683.0}\right)\)
\({\color{rgb(20,165,174)} x} \times 683.0 \times \dfrac{1.0}{683.0} = 1.55 \times 10^{3} \times \dfrac{1.0}{683.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{683.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{683.0}}} = 1.55 \times 10^{3} \times \dfrac{1.0}{683.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.55 \times 10^{3}}{683.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx2.2693997072\approx2.2694\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{lumen}{square \text{ } inch}\right)\approx{\color{rgb(20,165,174)} 2.2694}\left(\dfrac{watt}{square \text{ } meter}\right)\)
