Skip to main content

Rmsto Watts Converter

Convert rmsto watts between units instantly. Includes conversion tables, common equivalents, and calculation formulas.

Reviewed by Manoj Kumar, Mathematics Educator

Reviewed by Manoj Kumar, Mathematics Educator

Formula

Power (W) = Vrms^2 / Impedance | Vrms = sqrt(Power x Impedance)

Power in watts equals the RMS voltage squared divided by the load impedance in ohms. To find RMS voltage from power, take the square root of power times impedance. Peak voltage = Vrms x sqrt(2). Peak power = 2 x RMS power for a sine wave. dBW = 10 x log10(watts). dBm = 10 x log10(milliwatts).

Worked Examples

Example 1: Amplifier RMS Voltage to Power

Problem:An amplifier outputs 28.28 Vrms into an 8-ohm speaker. Calculate the power in watts.

Solution:Power = Vrms^2 / Impedance\nPower = 28.28^2 / 8\nPower = 799.76 / 8 = 99.97 W\nPeak voltage = 28.28 x 1.414 = 39.99 V\ndBW = 10 x log10(99.97) = 20.0 dBW

Result:28.28 Vrms at 8 ohms = 99.97 watts RMS = 20.0 dBW

Example 2: Watts to RMS Voltage

Problem:A 500-watt amplifier drives a 4-ohm subwoofer. What RMS voltage does it produce?

Solution:Vrms = sqrt(Power x Impedance)\nVrms = sqrt(500 x 4)\nVrms = sqrt(2000) = 44.72 V\nRMS current = 44.72 / 4 = 11.18 A\nPeak power = 500 x 2 = 1000 W

Result:500W at 4 ohms = 44.72 Vrms = 11.18 Arms = 1000W peak

Frequently Asked Questions

What is RMS voltage and how does it relate to watts?

RMS (Root Mean Square) voltage is the effective value of an alternating voltage that produces the same heating effect as an equivalent DC voltage. For a pure sine wave, the RMS voltage is the peak voltage divided by the square root of 2 (approximately 1.414). Power in watts is calculated as Vrms squared divided by impedance (P = Vrms^2 / Z). This relationship is fundamental in audio engineering for calculating the actual power delivered to speakers and amplifiers.

What is the difference between RMS watts and peak watts?

RMS watts (also called continuous power) represents the sustained power an amplifier can deliver or a speaker can handle over time. Peak watts represent the instantaneous maximum power during signal peaks, which is exactly double the RMS power for a sine wave. Many consumer audio products advertise peak watts because the numbers are larger and more impressive. However, RMS watts is the meaningful specification for comparing audio equipment performance, as it indicates the actual continuous power output.

References

Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy