How long is 1Gigabyte of video using a 6megapixels digital camera?

It depends on your camera - for example, here's the capacity chart from the Olympus website:
http://olympusamerica.com/cpg_section/xd...
click on the tab for 1gb xD card.

the manual or website tells you exactly how long

As mentioned, it depends on the camera and what format it records the video in.

My Canon Powershot S3 IS 6 mp camera records in .AVI format, and 1 gb memory card (high speed) will record around 8 minutes of video on 30 fps at 640x480.

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The file size depends on what video format your camera uses (NTSC, PAL, etc. -- i.e.: the general resolution and number of frames/second), the compression employed by the file format (mpeg-1, m-jpeg, etc.), the bit depth of each pixel (sometimes called the color depth), and the ACTUAL resolution (a resolution of 2048脳1536 = 3,145,728 pixels, but is listed as 3.1 megapixels).

Keep in mind that your camera may be rated as 6Mp, but the video will be reduced to the standard format used for encoding. For example NTSC (the U.S. standard video format) is based on 525 lines of resolution (much less than the stills from your 6Mp camera), so much of the data is discarded during formatting. This is called 鈥榣ossy鈥?(because data is 鈥榣ost鈥?.

In addition, with video compression algorithms (which are also lossy in nature), the amount of compression achieved depends greatly on the actual data contained in the formatted video. This means two six-minute movies made with the same camera and settings will generally differ in file size, so even if all the variables are known, there is no way to EXACTLY calculate an answer.

However鈥?br>
Here are some general formulas to calculate the amount of raw data (without formatting or compression):

1). # Pixels = Horizontal Resolution * Vertical Resolution

2a). Raw Data (in bytes) = (# Pixels * (Bit Depth / 8)) * Frame Rate

Or鈥?br>
2b). Seconds of Video = Raw Data (in bytes) / ((# Pixels * (Bit Depth / 8)) * Frame Rate)

For example, the following variables:

Video standard = 29.97 frames/second
Bit depth of each pixel = 32bits
# Pixels = 3,145,728 pixels (2048脳1536)
File Size (in bytes) = 1,073,741,824 bytes (1GB )

Would yield the following equations and answer:

Seconds of Video = 1,073,741,824 / ((3,145,728 * (32 / 8)) * 29.97)
Seconds of Video = 1,073,741,824 / ((3,145,728 * 4) * 29.97)
Seconds of Video = 1,073,741,824 / (12,582,912 * 29.97)
Seconds of Video = 1,073,741,824 / 377,109,872.64
Seconds of Video = 2.85 seconds

Again, this is RAW DATA without formatting or compression, so it seems WAY too few seconds (demanding greater appreciation for video format standards and compression algorithms).

Bottom line鈥?br>
Your best bet (if you already own the camera) is to shoot a continuous video which fills your 1GB memory and see how long it is, time-wise. As mentioned above, the play time will not always be the same, but it should be close, so you only have to do this once.

If you do not own the camera (i.e.: you are contemplating buying a specific camera), this information is usually estimated in the documentation or sometimes even given on the box.

Good luck; hope this helps!