# Convert foot-candle to lumen / square inch

Learn how to convert 1 foot-candle to lumen / square inch step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(foot-candle\right)={\color{rgb(20,165,174)} x}\left(\dfrac{lumen}{square \text{ } inch}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(lux\right)$$
$$\text{Left side: 1.0 } \left(foot-candle\right) = {\color{rgb(89,182,91)} 10.746\left(lux\right)} = {\color{rgb(89,182,91)} 10.746\left(lx\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{lumen}{square \text{ } inch}\right) = {\color{rgb(125,164,120)} 1.55 \times 10^{3}\left(lux\right)} = {\color{rgb(125,164,120)} 1.55 \times 10^{3}\left(lx\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(foot-candle\right)={\color{rgb(20,165,174)} x}\left(\dfrac{lumen}{square \text{ } inch}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 10.746} \times {\color{rgb(89,182,91)} \left(lux\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.55 \times 10^{3}}} \times {\color{rgb(125,164,120)} \left(lux\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 10.746} \cdot {\color{rgb(89,182,91)} \left(lx\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.55 \times 10^{3}} \cdot {\color{rgb(125,164,120)} \left(lx\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 10.746} \cdot {\color{rgb(89,182,91)} \cancel{\left(lx\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.55 \times 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(lx\right)}}$$
$$\text{Conversion Equation}$$
$$10.746 = {\color{rgb(20,165,174)} x} \times 1.55 \times 10^{3}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 1.55 \times 10^{3} = 10.746$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{1.55 \times 10^{3}}\right)$$
$${\color{rgb(20,165,174)} x} \times 1.55 \times 10^{3} \times \dfrac{1.0}{1.55 \times 10^{3}} = 10.746 \times \dfrac{1.0}{1.55 \times 10^{3}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.55}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.55}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = 10.746 \times \dfrac{1.0}{1.55 \times 10^{3}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10.746}{1.55 \times 10^{3}}$$
Rewrite equation
$$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 10.746}{1.55}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0069329032\approx6.9329 \times 10^{-3}$$
$$\text{Conversion Equation}$$
$$1.0\left(foot-candle\right)\approx{\color{rgb(20,165,174)} 6.9329 \times 10^{-3}}\left(\dfrac{lumen}{square \text{ } inch}\right)$$