# Why does 9.7Vrms == 27 Vpp? I thought it was 9.7/0.707 == 13.72!

At first, I thought this calculator was wrong, because I have always used an RMS to peak-to-peak conversion as $$\ V_{RMS} = \frac{V_{pp}\sqrt{2}}{2}\$$:

And then I saw a respected SE user report the same value on this post answer, stating that "22dBu (9.7V RMS) is 27 Vpp"!

I feel a little silly for asking, but what am I misunderstanding about peak-to-peak vs RMS conversion for audio?

• @jsotola, ok, updated, but 27 >> 13.71, which is the point of the question. Commented Jul 13 at 0:36
• because 13.71 x 2 = ~27. PP mean from minus to plus. Commented Jul 13 at 1:10

## 2 Answers

For one thing, the formula you posted is wrong. Vrms of a sine wave cannot be higher than the amplitude.

Here are some formulas:

Vpp = 2 × sqrt(2) × Vrms.

Vp = sqrt(2) × Vrms.

Vpp = 2 × Vp.

An example.

We know mains voltage is sine wave with 230 VRMS. We know the peak voltage is 1.414 times that or 325 V, which is the amplitude of sine wave.

Sine wave has both positive and negative peaks, so it goes between -325 V and +325 V. Which means the voltage between negative and positive peak is 650 V.

(Divide voltages by two if you live in 115VAC mains land.)

So for audio, it is just the same. A modern audio DAC IC has 2 VRMS ouput, it means 2.828 peak voltage or amplitude, and 5.656 peak-to-peak.

For a sine wave $$\V_{RMS} = \frac{V_P}{\sqrt{2}}\$$

Vpp = Vp*2

Audio that isn't a sine wave will be a bit different.

• Thanks! I was thinking Vp not Vpp. Commented Jul 13 at 1:21