# How does an infrared thermometer actually calculate temperature?

I am slightly confused about infrared radiation and the equations related to it.

$P = A \epsilon \sigma T^4$ (1)

and

$B_{\lambda}(\lambda,T) = \frac{2hc^2}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda k_B T}}-1}$ (2)

I understand that equation one is just integral form of equation two. Are P and B just the power output of the black body radiation?

Perhaps I should explain. I am working with an infrared thermometer (MLX90614) and I am wondering exactly what this picks up. Does it pick up the power of the infrared radiation through a lens and convert it to an electric signal so we can get the temperature of the object? Or does it measure the wavelength of the infrared radiation that is coming in and get temperature that way? THANKS!

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I'm not sure abt the equation but the intensity of infrared received by yr "thermometer" will affect its resistance and your sys will then measure this varying current or voltage. I'm sure there is a preset values of range of wavelength on your sys. –  user6760 Apr 9 at 7:29

Normally, such a probe should also measure the ambient temperature and it should know the emissivity $\epsilon$ value of the material you point at, to properly calculate the temperature. E.g. shiny metals are more difficult to measure, because the large part is reflected from other objects. Also consult the manual, page 45.
The distance problem fortunately compensates: the farther you are, the lower intensity per area you see with $\frac{1}{R^2}$. However, the larger area you see, because your optics has a defined viewing angle - it goes with $R^2$. –  jaromrax Apr 15 at 20:23