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For a Gaussian beam with a given beam waist in mm,  multiply this formula by two to obtain the formula given above (The multiplication factor is due to the fact that for a Gaussian beam, the peak power in the center is twice the average power density of the beam. The value is actually closer to 255, not 250, but this difference is trivial, introducing only ~2% error.  We use 250 simply because it’s easier to remember and perform mental calculations than 255! )

power densityw/m2

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If you always wanted to learn an easy way to calculate power density –without even using our calculator, even in your head, this is the perfect blog post for you.

Here is how this equation is derived: We can write an expression for the power density of a 1 mm diameter beam, which is simply:

Dividing the expression of power density of a 1 mm beam — Power / π(0.5mm)^2 — by an expression of power density as a function of diameter — Power / π(0.5d)^2 — we find that the ratio is d^2. Thus, power density as a function of diameter can be expressed as the power density of a 1 mm beam divided by d^2:

Since beam size is usually given with the beam diameter in terms of millimeters, to calculate power density in W/cm^2 you will also have to:

Power densityvs energydensity

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If you don’t want to damage any of your instruments, make sure you know your laser’s power density.  If you aren’t sure what it is, you can use this power density calculator.

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This calculation can be a bit tedious and time consuming, especially for technicians and field engineers who want to make as quick and easy a calculation as possible.

Using the following formula you can directly find power density of a laser beam using the diameter of the beam in millimeters: