You can't, not easily - look at the trouble MS have estimating file copy duration:
http://xkcd.com/612/[
^] sums it up well.
There are a huge number of variables: the read speed of the source, the write speed of the destination, any buffering the two of the do internally, any buffering Windows does, any networking between them, cache usage, memory available, and other tasks activities can all affect it one way of the other.
What you can do is do the copy yourself, and use a stopwatch to time how far it's got - that lets you make an estimate of when it will finish, but it will be very much a moving target!
This is the code I use to report progress in a background worker while moving a file:
private void MoveFile(string src, string dst, BackgroundWorker worker = null, ProgressReport prMain = null)
{
if (src != dst)
{
int iSrc = src.IndexOf(':');
int iDst = dst.IndexOf(':');
FileInfo fiSrc = new FileInfo(src);
if (fiSrc.Length < blockSize || (iSrc > 0 && iDst > 0 && iSrc == iDst && src.Substring(0, iSrc) == dst.Substring(0, iDst)))
{
File.Move(src, dst);
}
else
{
using (Stream sr = new FileStream(src, FileMode.Open))
{
using (Stream sw = new FileStream(dst, FileMode.Create))
{
long total = sr.Length;
long bytes = 0;
long cnt = total;
int progress = 0;
while (cnt > 0)
{
int n = sr.Read(transfer, 0, blockSize);
sw.Write(transfer, 0, n);
bytes += n;
cnt -= n;
int percent = (int)((bytes * 100) / total);
if (progress != percent)
{
progress = percent;
if (worker != null && prMain != null)
{
ProgressReport pr = new ProgressReport
{
FilesCount = prMain.FilesCount,
FileNumber = prMain.FileNumber,
Filename = prMain.Filename,
Action = prMain.Action,
FilePercentage = percent
};
worker.ReportProgress(-prMain.FileNumber, pr);
}
}
}
}
}
FileInfo fiDst = new FileInfo(dst);
fiDst.Attributes = fiSrc.Attributes;
fiDst.CreationTime = fiSrc.CreationTime;
fiDst.CreationTimeUtc = fiSrc.CreationTimeUtc;
fiDst.IsReadOnly = fiSrc.IsReadOnly;
fiDst.LastAccessTime = fiSrc.LastAccessTime;
fiDst.LastAccessTimeUtc = fiSrc.LastAccessTimeUtc;
fiDst.LastWriteTime = fiSrc.LastWriteTime;
fiDst.LastWriteTimeUtc = fiSrc.LastWriteTimeUtc;
File.Delete(src);
}
}
}
It would be relatively trivial to get a "completion" estimate from that.