RMS to Watts Converter (amplifier power from RMS voltage and speaker impedance)

Understanding the RMS to watts converter — concept and principle

This calculator converts an RMS, peak or peak-to-peak sine-wave voltage across a speaker or resistive load into average power ("RMS watts"), peak instantaneous power, current and dBW. Audio enthusiasts and engineers use it to check amplifier output and speaker matching.

RMS is chosen so V²/R gives true average power; the peaks reach twice that for an instant.

How it is calculated

P = V_rms² ÷ R

For a sine wave: V_rms = V_peak ÷ √2 = V_p-p ÷ (2√2)

Peak instantaneous power = V_peak² ÷ R = 2P

I_rms = V_rms ÷ R; dBW = 10 log₁₀(P ÷ 1 W)

The principle

The RMS value of an AC voltage is the steady DC voltage that would heat a resistor equally. That is why average power is simply V_rms² ÷ R. For a sine wave the instantaneous power swings between zero and twice the average. Amplifier specifications call the average power "RMS watts", although strictly it is the average power calculated from the RMS voltage.

Worked example

Default inputs: 28.28 V RMS into 8 Ω.

P = 28.28² ÷ 8 = 99.97 W (about 100 W), which is 20 dBW.
Peak voltage = 28.28 × √2 = 39.99 V; peak instantaneous power = 199.94 W.
RMS current = 28.28 ÷ 8 = 3.535 A.

Each point is the calculator re-run with only “Voltage (V)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Voltage (V)	Average power (W, “RMS watts”)
7.07	6.25
14.1	24.99
21.2	56.23
28.3	99.97
35.4	156.2
42.4	224.93
56.6	399.88

How to read the result

Doubling the power needs only √2 times the voltage, and gives about 3 dB more level. A speaker's nominal impedance is an approximation; its real impedance varies with frequency, so actual power differs. Music has a much lower average power than a continuous sine at the same peak.

Common mistakes

Using peak voltage in P = V² ÷ R without converting to RMS.
Treating "peak power" marketing figures as continuous power.
Assuming the speaker's impedance is constant across frequency.

Keep in mind: Driving speakers beyond their rating can damage them. Measure high voltages with appropriate equipment and care.

Frequently asked questions

What voltage gives 100 W into 8 Ω?

About 28.3 V RMS.

Why is peak power twice the average?

For a sine wave, instantaneous power swings from zero to twice the average.

Does a 4 Ω speaker draw more power?

At the same voltage, yes, twice as much.

How many dB is doubling power?

About 3 dB.

Sources: Standard AC power formulas P = V_rms²/R and V_rms = V_peak/√2 for a sine wave

Checked 9 Nov 2026. Average power in an AC circuit with a resistive load, P = V_rms²/R, and V_rms = V_peak/√2 for a sine wave — standard formulas.

Your numbers