Vibration Calculator

This tool converts a known vibration amplitude (acceleration, velocity or displacement) into the equivalent values of the other two quantities at a given frequency. It uses the steady-state sinusoidal relationships v = ωx and a = ωv, and states every result with its RMS, peak or peak-to-peak convention.

It also supports frequency solving: if you know two different quantities from the same measurement (for example acceleration and velocity), the calculator recovers the frequency that links them.

Who should use it

• Condition-monitoring engineers reading vibration data in different units.
• Rotating-equipment specialists comparing accelerometer and velocity-probe readings.
• Field technicians converting a vibration pen reading into a displacement figure for a report.
• Engineering students learning how amplitude and frequency interact in vibration analysis.

Where engineers apply it

• ISO 20816-3 severity checks: converting an accelerometer reading to the RMS velocity the standard uses.
• Bearing-fault analysis: comparing a fault-frequency acceleration amplitude with its velocity equivalent.
• Field balancing: converting displacement (mil) readings to velocity (mm/s) for balance tolerances.
• Structural dynamics: checking whether a measured response is consistent with a single-frequency excitation.

Common mistake: entering a reading in mils when the calculator is expecting micrometres. 1 mil = 0.001 in = 25.4 µm — not 1 mm. The unit selector handles the conversion, but picking the wrong unit is the most frequent source of errors.

Common mistake: using RPM when the reading is a 2× or 3× harmonic. A 50 Hz vibration on a shaft running at 1,500 RPM is the 2× component, not the shaft speed. Enter the frequency of the vibration itself, not the shaft speed.

The results section shows the following for your inputs:

1. Each quantity in its canonical unit — acceleration in m/s² (with a g equivalent), velocity in mm/s (with an in/s equivalent), displacement in µm (with mm, mil and inch equivalents).
2. The amplitude basis — the “Entered” badge marks the value you supplied, and the “Calculated” badge marks the derived values.
3. Frequency and period — in Hz, CPM, RPM, seconds, and angular frequency ω in rad/s.
4. Velocity level L_v — in dB re 1 nm/s, useful for comparing readings across machines.
5. The all-conventions grid — each quantity listed in RMS, peak and peak-to-peak, so you can read off any convention without re-entering the inputs.
6. Warnings — shown when the frequency is below 2 Hz, above 20 kHz, when the two Solve-mode inputs are inconsistent by more than 2%, or when a non-RMS basis is used.

Export and share

• Copy all results — every line of the results in plain text.
• Copy summary — a compact report with inputs, results and assumptions.
• Copy share link — encodes the inputs in the URL query string so the same scenario can be reproduced.
• Print / Save as PDF — a clean printed report using the print stylesheet.
• Send velocity to Severity — copies the calculated RMS velocity into the ISO 20816-3 Severity tab.

This tab compares the broadband RMS velocity (in mm/s) against the zone boundaries of ISO 20816-3, the standard that replaced ISO 10816-3. The zone concept (A/B/C/D) and boundary values carry over.

Important: ISO 20816-3 applies to specific machine categories (pumps, fans, motors, compressors). Vertical pumps, cooling-tower fans and gear mesh have their own standards or conventions — the calculator shows the 20816-3 zone as a rough reference where relevant and flags the limitation in the preset note.

The Frequency Response tab plots all three quantities (displacement, velocity and acceleration) against frequency on logarithmic axes, at the constant RMS velocity from your Converter tab. The operating point is marked with a dashed vertical line.

The chart illustrates a key insight: at a constant velocity, displacement falls as 1/f and acceleration rises as f. A 5 mm/s RMS reading is 796 µm RMS at 1 Hz but only 8 µm RMS at 100 Hz — the same physical motion, very different displacement.

Scenario: a velocity probe reads 5 mm/s RMS on a pump bearing at 50 Hz. What are the equivalent acceleration and displacement, and does the reading satisfy ISO 20816-3 for a 45 kW pump on a rigid support?

Consistency check: if you enter both velocity and acceleration in Solve-frequency mode, the calculator verifies that 5 mm/s RMS and 1.571 m/s² RMS reproduce the same 50 Hz. If they don’t (because the actual reading is a mix of frequencies), the mismatch warning is your signal that a single-frequency assumption is not appropriate for that measurement.

Unit mistakes

• Mixing mil and mm: 1 mil = 0.001 in = 25.4 µm, not 1 mm. Entering 0.05 mm when the reading is 0.05 mil is a factor of 1000 error.
• Using mm/s when the instrument reports in/s: 1 in/s = 25.4 mm/s. The unit selector handles the conversion, but only if you pick the right one.
• Confusing g and m/s²: 1 g = 9.80665 m/s². A reading of 1.5 g is 14.71 m/s², not 1.5 m/s².

Amplitude basis mistakes

• Assuming RMS when the instrument reports peak: a peak reading of 5 mm/s is only 3.54 mm/s RMS. The ISO severity zone will be wrong if the basis is not corrected.
• Mixing bases across inputs: if quantity 1 is RMS and quantity 2 is peak, the calculator converts them correctly — but the consistency check uses the converted SI peak values, so a wrong basis shows up as a mismatch warning.

Frequency mistakes

• Using RPM when the vibration is a harmonic: 50 Hz on a 1,500 RPM shaft is 2× running speed. Enter the frequency of the vibration, not the shaft speed.
• Forgetting to convert CPM to Hz: 3,000 CPM is 50 Hz. The frequency unit selector handles the conversion if you pick CPM.
• Zero or negative frequency: the calculator rejects frequencies at or below zero, because the sinusoidal relationships are undefined there.

Model mistakes

• Applying the sine ratios to random vibration: the RMS/peak/peak-to-peak ratios are valid only for sinusoidal signals. Random vibration needs a PSD analysis.
• Treating the ISO zone as applicable to any machine: ISO 20816-3 covers specific machine categories. Vertical pumps, cooling-tower fans and gear mesh have separate standards — the calculator flags this in the preset notes.

Results are an estimate computed with IEEE-754 double precision and standard engineering formulas. The calculator assumes:

• The vibration is steady-state and single-frequency sinusoidal — one dominant frequency.
• The amplitude basis is correctly stated for every input.
• The unit conversions use exact factors (1 in = 25.4 mm, 1 g = 9.80665 m/s², 1 mil = 25.4 µm).

Not evaluated here: broadband or random vibration, impact signals, non-sinusoidal waveforms, multiple simultaneous frequencies, and phase relationships between quantities. Real vibration data usually needs a spectrum or PSD analysis to be interpreted correctly.

The calculator round-trip tests its own conversions (acceleration → velocity → displacement → acceleration) to within 1×10⁻⁹ relative error. Displayed values are rounded for readability only.

What does a vibration calculator calculate?

It converts a known vibration amplitude (acceleration, velocity or displacement) into the equivalent values of the other two quantities at a given frequency, using the sinusoidal relationships v = ωx and a = ωv, and states every result with its RMS, peak or peak-to-peak convention.

How do you convert vibration velocity to displacement?

For a sine wave, displacement peak = velocity peak / (2πf). In consistent units: x_pk [µm] ≈ 159.15 × v_pk [mm/s] / f [Hz]. The frequency must be known — velocity alone cannot give displacement.

How do you convert acceleration to velocity?

Velocity peak = acceleration peak / (2πf). Again the frequency is required: the same acceleration means very different velocity at 10 Hz versus 1,000 Hz.

What is the difference between RMS, peak, and peak-to-peak?

For a pure sine: peak = √2 × RMS, peak-to-peak = 2 × peak. These ratios are valid only for sinusoidal signals; for random or impact signals the relationship depends on the actual waveform (crest factor), so the conversions here would not apply.

How does frequency affect vibration displacement?

At constant velocity, displacement falls as 1/f and acceleration rises as f. A 5 mm/s reading is 796 µm RMS at 1 Hz but only 8 µm RMS at 100 Hz — see the Frequency Response tab.

How do you convert Hz to RPM?

RPM = Hz × 60 for a 1× (once-per-revolution) component. A 2× component at 50 Hz corresponds to a shaft running at 1,500 RPM (2 × 50 Hz = 100 Hz = 6,000 CPM → 3,000 RPM shaft speed; more precisely: shaft speed = component frequency × 60 / order).

Can velocity be converted to displacement without frequency?

No. Velocity and displacement are linked only through frequency. If you have two independent measurements (e.g. velocity and acceleration of the same component), use the Solve frequency mode to recover the frequency first.

Can these formulas be applied to random vibration?

Not directly. Random vibration is described by a power spectral density and RMS levels; RMS/peak conversions and the ω-based relationships here assume a single-frequency sinusoid. Use a dedicated PSD/random-vibration analysis for that case.

What does the ISO 20816-3 Severity tab rate?

The tab compares the broadband RMS velocity against the zone boundaries of ISO 20816-3 for the machine group (above or below 300 kW) and support type (rigid or flexible) you select. The zones are A (good), B (satisfactory), C (unsatisfactory) and D (unacceptable).

Is the ISO zone applicable to every machine?

No. ISO 20816-3 covers specific machine categories (pumps, fans, motors, compressors). Vertical pumps, cooling-tower fans and gear mesh have their own standards or conventions. The calculator flags this in the preset notes where relevant.

What do the warnings in the Results section mean?

They flag frequency below 2 Hz or above 20 kHz, inconsistent inputs in Solve mode (more than 2% mismatch), non-RMS amplitude bases, and other situations where the sine-wave assumption may not hold. Read them before using the results in a report.