I used the below formula for Power Density or Irradiance. You have to convert the milliseconds to seconds.

That is part of your problem. You are assuming a continous pulse laser when you try to convert a pulse that lasts 3 milliseconds or 5 milliseconds into a pulse of 1 second. So for example on the Cynosure 9300, I can generate a pulse that does 20 joules at 40 ms and then change it to a pulse that generates 20 joules at 5 ms. The absolute power is the same, but the peak power is higher. This is like saying, I am going to drive 30 miles and drive it in one hour or drive it in 30 minutes. Your velocity is different but your absolute distance driven is the same.

So the question is what is the value of peak power? Or a better way of saying it is what is the value of longer or shorter pulsewidth and this is really one of the thermal relaxation time of the target. I am not going to get into that at this point, but the real value of the different pulse widths has to do with the size of the hair and the concurrent risk to the skin.

But the bottom line is that the total amount of power remains the same regardless of the pulse width, assuming that the pulse width is less than a second.

So your numbers make no real sense and have no real value as far as laser hair removal. They are just numbers and wrong numbers to begin with. Let me give you some real numbers that you can put into your equations.

For a 20 joule pulse on a Gentlelase at 18 mm spot size at 1.5 hz.

- The power is 20 joules/cm squared (it is calculated in joules fluence)
- The spot size is 2.54 cm squared (don’t know where you got 1 cm squared).

Doing the correct equations, the actual joules are 50.8 joules per pulse. This converts to 50.8 watts per pulse and at 1.5 pulses per second this converts to 76.2 watt seconds.

Now this is the amount of actual energy delivered to the skin. Now I could convert the watts per pulse to peak power and state that at 3 milliseconds this would be equal to a 16,933 watt seconds (50.8/.003 seconds) continuous pulse laser. But again that is meaningless because only 50.8 watts of actual power was delivered to the skin.

Where you are wrong in all your calculations and where your numbers become meaningless is that you are basing all your calculations on the pulse and not taking into account the target and what happens in the target. In fact by your calculations if I took a laser pulse of 20 joules in a 10 mm spot size and a .0001 second pulsewidth (called a q switched laser and used for tattoos) I would get a peak power of 150,000 watts. What the heck does that mean?

But what happens in the target with a q switched laser is that the laser pulse actually sets up a shock wave due to the very short 100 millionth of a second pulse that breaks up the tattoo ink. The point is that pulse width is important but that power density as you are calculating it is meaningless for pulsed lasers.