# How Fast, in MPH, Does The Edge of a Router Bit Move?

Given a blade of diameter D inches, revolving at a rate of R rpm, a point on the perimeter of the blade will travel the length of the circumference C each revolution.

Speed = distance / time
C = pi x D
pi ~= 3.1416

So the speed is:

Distance/revolution x revolutions/time = C x R inches/minute
= pi x D x R inches/minute
= 3.1416 x D x R inches / minute.

But wait, you say, I asked for miles per hour! (forgive me for rounding, but…)

(3.1416 x D x R in/min) x (60 min/hr) = 3.1416 x 60 x D x R in/hr
= (188.5 x D x R in/hr) x (1 ft/ 12in) x (1 mi / 5280 ft) = 0.003 x D x R mi/hr.

So, for example, a 1 inch bit at 20,000 rpm is going:

(0.003 x 1 x 20,000) = 60 mph. at the perimeter.

Now, before you start thinking that’s too wimpy for words, try to envision crashing a metal object (say your car) into a solid piece of hardwood (say an oak tree) at 60 mph.

Or for you bikers, perhaps a better picture would be gravel hitting you at various speeds.

We’re not talking bullets, but safety glasses start making a lot of sense.

A 3 inch bit would be doing 180.

By the way, assuming you’re worried about a piece coming off at this speed and hitting you (say breaking a carbide edge loose), keep in mind that the kinetic energy of the moving object is:

1/2 mv ^ 2 (one half mass times velocity squared)

In an inelastic collision (such as the carbide embedding itself in your body), that energy is transferred to the struck object with rather ugly results.

The point of the last is that although going from a 1 to a 3 inch bit only gives 3x the speed, that imparts 9x the energy on your [insert target here].