Convert peak and RMS velocity amplitudes for a zero-mean sinusoidal waveform over complete cycles, using the exact √2 relationship with m/s, km/h, mph or ft/s units.

For a zero-mean sinusoidal velocity over complete cycles. Enter a nonnegative amplitude. Peak alone cannot determine RMS for an arbitrary waveform.

Root Mean Square Velocity Formula

This calculator converts the peak and root mean square (RMS) amplitudes of a zero-mean sinusoidal velocity waveform, averaged over complete cycles. The relationship is not a general conversion for arbitrary motion.

VRMS = Vₚₑₐₖ / √(2)
Vₚₑₐₖ = VRMS√(2)

Vpeak is the nonnegative peak amplitude and VRMS is the nonnegative RMS amplitude, in consistent velocity units. The sine-wave factor 1/√2 is approximately 0.70710678; the calculator uses full floating-point precision.

How to Calculate RMS or Peak Velocity

Choose the amplitude to calculate, enter the known amplitude and its unit, then select the answer unit. For example, a 20m/s peak sine-wave amplitude gives 20/√2 =14.142136m/s RMS. Conversely, 14.1421356237m/s RMS corresponds to approximately 20m/s peak. A zero amplitude gives zero in either direction.

Why the Waveform Assumption Matters

RMS is the square root of the average of squared instantaneous values. For v(t) = Vpeaksin(ωt + φ), averaging sin² over complete cycles gives 1/2. Other waveforms, partial-cycle intervals or a nonzero mean can have a different RMS-to-peak ratio. A peak value by itself does not establish RMS in those cases. See Brüel & Kjær’s vibration handbook for the sinusoidal peak/RMS relationship.

Units

The calculator supports m/s, km/h, mph and ft/s. It converts using 1km/h =1/3.6m/s, 1mph =0.44704m/s and 1ft/s =0.3048m/s, then applies the sine-wave amplitude relationship. The expanded calculation details show the input conversion, formula and final-unit conversion.