Parseval's theorem - Average Power
It's possible to calculate average power (proportional to RMS amplitude) with the rfft, but it's more complicated because the DC and Nyquist bins are not doubled in the full fft (and the Nyquist bin doesn't exist if n is odd).

NumPy's rfft is preferred over SciPy's, because it outputs complex numbers, which are compatible with N-dimensional arrays, rather than SciPy's "packed" format.

def rms_rfft(spectrum, n=None):
    """
    Use Parseval's theorem to find the RMS value of an even-length signal
    from its rfft, without wasting time doing an inverse real FFT.

    spectrum is produced as spectrum = numpy.fft.rfft(signal)

    For a signal x with an even number of samples, these should produce the
    same result, to within numerical accuracy:

    rms_flat(x) ~= rms_rfft(rfft(x))

    If len(x) is odd, n must be included, or the result will only be
    approximate, due to the ambiguity of rfft for odd lengths.
    """
    if n is None:
        n = (len(spectrum) - 1) * 2
    sq = real(spectrum * conj(spectrum))
    if n % 2:  # odd
        mean = (sq[0] + 2*sum(sq[1:])           )/n
    else:
        mean = (sq[0] + 2*sum(sq[1:-1]) + sq[-1])/n
    root = sqrt(mean)
    return root/sqrt(n)


More details here: https://gist.github.com/endolith/1257010