I would suggest you have a look at BackgroundWorker. If you have a loop that large in your WinForm it will block and your app will look like it has hanged.

Look at BackgroundWorker.ReportProgress() to see how to report progress back to the UI thread.

For example:

private void Calculate(int i)
{
    double pow = Math.Pow(i, i);
}

private void button1_Click(object sender, EventArgs e)
{
    progressBar1.Maximum = 100;
    progressBar1.Step = 1;
    progressBar1.Value = 0;
    backgroundWorker.RunWorkerAsync();
}

private void backgroundWorker_DoWork(object sender, DoWorkEventArgs e)
{
    var backgroundWorker = sender as BackgroundWorker;
    for (int j = 0; j < 100000; j++)
    {
        Calculate(j);
        backgroundWorker.ReportProgress((j * 100) / 100000);
    }
}

private void backgroundWorker_ProgressChanged(object sender, ProgressChangedEventArgs e)
{
    progressBar1.Value = e.ProgressPercentage;
}

private void backgroundWorker_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e)
{
    // TODO: do something with final calculation.
}