How much gigabytes of sd card do I need for recording overnight with a Nikon D5100 camera?

I need to record the activities going around my house. Some weird stuff is going on and I want to record it, maybe I can understand what's going on.

You will have to do some math.

Bytes per second X 60 seconds X 60 minutes
will tell you how many bytes will be filled per hour.

[Don't forget that you Never get the full number of GB on a card that it can hold
because some of its capacity has to be used for file management.]

Lower resolution will consume less space,
so cut it down as far as you can stand
to maximize the available time.

Another way would be with a cheap DVR-equipped CCTV system.
Its capacity would be much greater than any SD card can provide.

Step 1: Read the manual.

It sounds like you want to put the camera somewhere, press record, walk away, later, get the camera, press stop and everything in-between will be recorded to video.

Link to the manual:
http://download.nikonimglib.com/archive2/bFpVn006cKZa029I4QC02Vipsb29/D5100RM_EU(En)02.pdf

Title page: The D5100 is a digital camera… Not a camcorder.

Recording movies starts on page 107.

Page 108: The camera can overheat and automatically shut down - or not begin recording if already hot and not yet cool enough. Typically, this takes about 20 minutes of video capture. Page 109 says the display will provide a 30 second countdown before auto shut down.

Typically, the single video file duration with these sorts of still image dSLRs is 29 minutes, 59 seconds. Did not find that reference in this manual. There's also not much in the way of video capacity and card size.

I used to shoot with a Sony NEX-EA50UH. At medium quality HD video, a 32 gig Class 10 card could store up to about 6 hours of HD video. I suggest using 2 32 gig cards… That way if one card breaks, you have the other available. Of course, we assume the camera has not overheated and you are not waiting for it to coll down enough to capture more video.

And we also assume you have a plan for power - or you will need 2-12 batteries… If you are recharging, then probably three… One in use while the other two are recharging. If you are not recharging, then all 12 charged and ready to go.

We also assume all the lights will be on - dSLR video under poor lighting conditions is notorious for being really "noisy" (speckled)… Even when a fast lens is used. Open the aperture as wide as possible and the shutter as fast as it will allow for decent photos (too fast and the images will be dark; to slow and there will be trails or "ghosting".) And be sure not to use the camera handheld to limit the blurring - under poor lighting conditions, the auto-focus won't know what to focus on resulting in blurry images…

Good luck trying to figure out what's going on your house.

What you need to know

* the largest video file a digital SLR camera can produce is 4 gb.
* after about 20 minuted, the sensor in a digital SLR gets hot and shuts off the camera
* If you are shooting time lapse video, then the maximum number of shots the camera can take is 9999.
* if you use a smaller file size when shooting time lapse (2464 x 1632 pixels), the memory cards limitation of 4 gb will fill slower and you may be able to get a full nights time lapse recording on your camera and memory card. Since the cameras sensor is shut off during each of the time intervals while using the interval timer to create a time lapse video, there's little chance that the sensor will overheat
* and of course, your camera is stills camera with a video "feature"

The size of your sd card is not the limiting factor. For all sorts of reasons the maximum time for a single shoot is 20-30 minutes.
That is when you hit the maximum file size of 4Gb.
Another consideration is the camera shutting down after an hour or so of video shooting due to the sensor overheating.
Your battery is ulikely to last much more than an hour or 2.
DSLRs are stlls cameras adapted for video. To do what you want a web cam connected to a laptop or a camcorder would be more suitable.

Simple bottom line:

You can't do what you want to do with that camera.

How much you can record depends on how much storage you have available & camera settings.

Usually this sort of question is asked like how much time I could record with xxGB.

In most cases the camera would state how much time you have based on the settings you have & storage available to you.