First of all, practically speaking, a 100 film in a contact printing frame for 180 seconds in sunny 16 light ends up black when developed, and you don't need to know by how many stops, because it will be by a very healthy amount.
You can't apply an f stop in this case, because you need a focal length and a hole for an f stop to exist. When you are exposing something to raw light with nothing in place to reduce that light (like a lens or aperture), the concepts of aperture or f stop cease to apply, since the aperture is effectively infinite; as large as it can get, at any rate.
So, what you are really asking is how many times more light. If you prefer to think of that in terms of "stops", that is fine (almost all of us do it, I think), but realize that it is simply a choice of terminology that refers to doublings and halvings of amounts of light, and not a true measurement of f stops. First, you have to figure out how many times more light, then you can figure out how many "stops" to call it.
Regardless of whether or not you are taking a photograph, or what lens, shutter, aperture, ISO, etc. that you are using, a certain amount of light falls in a certain lighting condition. This light exists in the world, regardless of photography, and can be referred to using various systems of units. This amount is usually given to you by a light meter as an exposure value (EV); a term that takes a measurement of light that is falling, and puts it into photographic terms. Each EV represents a shutter speed/aperture/EI combination (and equivalent exposures) that theoretically will make the metered surface a mid tone grey.
So, to know how much light hits a piece of film in a contact frame versus how much hits a piece of film in a camera, you basically have to figure out just how much light the lens and aperture are cutting from the amount of light that exists at the scene; what percentage of the light that actually exists at the scene actually strikes the film when you take a picture with a camera. Once you know how much light is cut from the light at the scene just by using a lens or aperture, you can compare it to the amount that falls on the film without a lens or aperture (100% of the light that exists), then figure out how many "stops" difference there is at a given exposure time.
So, what you really want to do to compare is to pick a constant shutter speed for both the in-camera film and the film in the contact frame. If your in-camera exposure is '125 at f/16, and this causes to the film to achieve a certain amount of density, then how much less light does the film in the contact frame need in order to get the film to that same density with a '125 exposure?
It's impossible to test without either a giant shutter for the contact frame, or much slower exposure times (ND filters for the camera and ND gel sheets for the contact frame). Try to get a film that does not suffer from bad reciprocity failure. I might choose Fuji T64. It is nice and slow, and it is listed as being good out to four minutes with no exposure adjustments (though IMO it can go much longer). It has to be filtered with orange (Wratten #85) to use in daylight, which reduces its effective EI by 2/3 stop to EI 40. So, in sunny 16 conditions, you get '30 at f/16-1/3. Say you want a four second exposure time. To get this, you need to add 7 stops (see!) of ND; both to the camera and to the printing frame. If you want longer exposures than four seconds, you can add more ND. I would sandwich the film with a homemade film strip that is a series of bracketed grey card exposures of known density, or a premade step wedge.