Calculate depth-of-field on BMPC 4K using a 50mm/1.8 I stand up the back of a room on a riser and capture a speaker at podium + their presentation on the screen using a blackmagic production 4K. I estimate I am 8 metres from the subject.

Currently I'm using an f2.8 lens and adjusting it in davinci as the room is poorly lit.

Is there a way to gauge the depth of field that will be in focus if I use an f1.8 lens?

Thanks in advance
You will need an app or chart for the calculation. There are apps on both iOS and Android for this. Just search depth of field calculator. 

With a 50mm lens shooting at f/1.8 you're depth of field will be very shallow; more so the closer your subject is to the camera, with your DOF becoming deeper if your subject moves away. 

Some lenses have a built in Hyper-Focal chart on the top of the lens; showing what your "Reasonably considered in Focus area is at" which changes as you change your aperture. 

If you need a less shallow depth of field, you can always stop down the lens. Also keep in mind; the 50mm 1.8 is not incredibly sharp at 1.8 to begin with. Most lenses have sweet spots in terms of tack sharp; typically about 1/3 into the f-stop range. 

The only lenses that will give you pristine tack sharp focus at apertures like 1.8, are for example the Master Primes by Arri; running $30k per prime. 

Hope this helps.