RMS, peak, and peak-to-peak are three different ways of describing the amplitude of the same vibration signal, and confusing them is one of the most common sources of error in reading vibration numbers. They are related by simple factors, but the factors mean a value stated in the wrong convention can be off by a factor of two or more. Because casing and shaft measurements traditionally use different conventions and different units, an engineer setting an alarm must make sure the setpoint speaks the same language as the sensor.
RMS vs Peak vs Peak-to-Peak in one line: RMS is the root-mean-square amplitude representing the signal's energy, peak is the maximum excursion from zero, and peak-to-peak is the full swing from the lowest to the highest excursion. For a pure sine wave, peak equals RMS times 1.414 and peak-to-peak equals twice the peak. Casing velocity is usually stated as RMS in mm/s and shaft displacement as peak-to-peak in mils or microns, so a setpoint must match the sensor's convention.
RMS, the root-mean-square, is a statistical measure of the signal's energy content over time, and it is the convention most closely tied to the destructive potential of vibration. Peak is the maximum instantaneous amplitude the signal reaches away from its center, capturing the height of the largest excursion. Peak-to-peak is the total distance from the most negative to the most positive excursion, so it describes the full swing of the motion.
For a simple sinusoidal signal these three are linked by fixed ratios. The peak of a sine wave equals its RMS multiplied by 1.414, the square root of two, and its peak-to-peak equals twice its peak, which is 2.828 times the RMS. These relationships are exact only for a pure sine wave; for a complex real vibration signal the true peak can be higher relative to the RMS, and that ratio, the crest factor, is itself a useful indicator of impacting faults.
This distinction between a true peak and a derived peak matters. A true peak is measured directly from the time waveform and reflects the actual largest excursion, spikes and all. A derived peak is simply the RMS multiplied by 1.414, which assumes the signal is sinusoidal and therefore understates a signal full of sharp impacts. Knowing whether a stated peak is measured or derived is essential to interpreting it correctly.
Because the conventions differ by factors of roughly 1.4 and 2, quoting a value in the wrong one changes its magnitude substantially without any error message to warn you. A vibration reported as 4 mm/s peak is the same physical vibration as roughly 2.8 mm/s RMS, so treating a peak number as if it were RMS overstates it, while treating an RMS number as if it were peak understates it. Nothing about the bare number reveals which convention it was expressed in.
The confusion is compounded because different measurement types traditionally use different conventions and units. Casing vibration measured by a seismic sensor is commonly stated as RMS velocity in millimetres per second, whereas shaft vibration measured by a proximity probe is stated as peak-to-peak displacement in mils or microns. An engineer moving between casing and shaft data, or between vendors and standards that adopt different defaults, can easily carry a number into a context that assumes a different convention.
The result is real-world mistakes: an alarm that trips too early because an RMS limit was fed a peak reading, or a machine that runs into damage because a peak-to-peak limit was compared against a peak value that was half as large. Avoiding this means always carrying the convention and the units alongside the number, and converting explicitly when moving between them rather than assuming they match. A value without its convention is genuinely ambiguous.
When configuring a vibration alarm in a SCADA or monitoring system, the single most important check is that the setpoint's amplitude convention and units match those of the value the sensor and its conditioning actually deliver. If the channel reports RMS velocity in mm/s, the alarm threshold must be in RMS velocity in mm/s; if it reports peak-to-peak displacement in mils, the threshold must be peak-to-peak in mils. A mismatch produces an alarm that fires at the wrong level, and the error is invisible in the number itself.
This means confirming what the conditioning stage outputs before setting any limit. Many instruments can report RMS, derived peak, or true peak, and can express displacement, velocity, or acceleration, so the same physical vibration can appear as several different numbers depending on configuration. The setpoint should be derived in the same convention, converting a standard's or a vendor's stated limit into the channel's convention explicitly rather than pasting a raw number across.
Documenting the convention on the tag and in the alarm configuration protects against the mistake recurring when someone later reviews or adjusts the setpoint. In a cloud or SCADA environment where the same tag may be viewed by operators, analysts, and reliability engineers across sites, an unambiguous label of convention and units keeps everyone reading the number the same way. The discipline is simple but easy to skip, and skipping it is how alarm setpoints end up quietly off by a factor of two.
For a pure sine wave, peak equals RMS multiplied by 1.414 and peak-to-peak equals twice the peak, or 2.828 times the RMS. These factors are exact only for a sinusoid; a real signal with sharp impacts can have a higher true peak relative to its RMS. That is why a peak derived by multiplying RMS by 1.414 can understate the actual measured peak of a spiky signal.
Shaft vibration is measured as displacement by a proximity probe, and displacement is conventionally expressed as peak-to-peak in mils or microns because the full swing of the shaft within its clearance is what matters. Casing vibration is measured as velocity by a seismic sensor, and velocity severity is conventionally expressed as RMS in millimetres per second. Because the two use different conventions and units, care is needed when comparing them.
The alarm fires at the wrong level, and nothing in the number flags the error. If an RMS limit is compared against a peak reading, which is larger for the same vibration, the alarm trips too early. If a peak-to-peak limit is compared against a peak value, which is smaller, the machine can run into damage before the alarm trips. Matching the setpoint's convention and units to the channel's output prevents this.
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