Vibration Calculator

Input Parameters

Quantity type

Amplitude type

Value

Unit

Frequency (Hz)

ISO 10816 Machinery Group

Converted Results

Acceleration

—

m/s²

— g

Velocity

—

mm/s

— in/s

Displacement

—

mm

— mils

— µm

Crest Factor Peak ÷ RMS — enter both to calculate

Peak value

RMS value

CF

—

Pure sine CF = √2 ≈ 1.414. Values above 2.5 suggest impulsive content — check for bearing defects.

ISO 10816 Severity Awaiting input

Enter values to see the ISO 10816 severity assessment.

GoodSatisfactoryUnsatisfactoryUnacceptable

RMS Velocity (ISO basis) — mm/s

Frequency Response Chart

Start Hz

End Hz

Step Hz

Overlay

Good

Satisfactory

Unsatisfactory

Unacceptable

Overlay shown on velocity (metric) only

⚙ Bearing, Gear & Orders

Bearing fault frequencies, gear mesh frequency and running speed harmonics

Shaft speed

Shaft speed (RPM)

Running speed

— Hz (1×)

Bearing geometry

No. of balls (N)

Ball dia. (mm)

Pitch dia. (mm)

Contact angle α (°) — 0 for radial bearings

BPFO, BPFI, BSF and FTF show where bearing defect energy appears in the spectrum. Compare against your measured spectrum to identify fault modes.

Gear mesh frequency

Number of teeth

GMF

— Hz

GMF = teeth × shaft frequency. Sidebands at GMF ± running speed indicate gear wear or eccentricity.

Bearing fault frequencies

Code	Description	Hz	×RPM
BPFO	Ball Pass — Outer race	—	—
BPFI	Ball Pass — Inner race	—	—
BSF	Ball Spin Frequency	—	—
FTF	Fundamental Train (cage)	—	—

Running speed harmonics (orders)

Show up to order

Enter shaft RPM to see harmonics.

〜 Natural Frequency & Critical Speed

Calculate fn, check resonance separation margin, and convert RPM ↔ Hz

Natural frequency

Method

Stiffness k (N/m)

Mass m (kg)

Damping ratio ζ (typical 0.05–0.1)

Critical speed / resonance margin

Operating speed (RPM)

Required separation (%)

RPM ↔ Hz converter

Speed (RPM)

Frequency (Hz)

fn = (1/2π)√(k/m). Maintain ≥20% separation margin between operating speed and any natural frequency. ISO 10816-3 recommends avoiding operation within ±10% of critical speed.

—Hz

Enter values to calculate

Parameter	Value
Natural frequency fn	—
Critical speed	—
Damped frequency fd	—
Angular frequency ωn	—
Separation margin	—
Safe operating zone	—

⇄ Unit Converter

Instant vibration unit conversion — same quantity and cross-quantity

Quantity

Value

From unit

Amplitude type

Frequency Hz — for cross-quantity conversion

Add a frequency to also convert across quantities (velocity ↔ acceleration ↔ displacement).

Enter a value to see all conversions.

◈ Sensor Selection

Sensor guidance based on your application and measurement requirements

Maximum frequency of interest (Hz)

Expected vibration level

Application type

Guidance only. Always verify against manufacturer datasheets and your measurement system requirements.

⇡ 4–20 mA Sensor Calculator

Convert loop current to vibration level and verify loop supply requirements

Sensor configuration

Output quantity

Full-scale value (at 20 mA)

Full-scale unit

Zero offset (at 4 mA)

Measured loop current (mA)

Loop supply check

Supply voltage (V)

Burden resistance (Ω)

Cable resistance (Ω)

4 mA = zero / live-zero · 20 mA = full scale. Supply must exceed sensor minimum compliance voltage plus total loop resistance × 20 mA.

Measured vibration level

—mm/s

Enter loop current and sensor range above

Parameter	Value
Loop current	—
% of full scale	—
Vibration (full scale)	—
Scale factor	—

Loop supply check

Parameter	Value
Total loop resistance	—
Min. supply required	—
Voltage drop at 20 mA	—
Loop status	—

Typical 4–20 mA sensors require a minimum compliance voltage of 8–12 V at the sensor terminals. Always check the datasheet.

⌇ Maximum Cable Length

Maximum cable length for IEPE / charge-mode accelerometers — single point and frequency sweep

Sensor & signal parameters

Sensor type

Max voltage swing (V peak)

Vibration frequency (Hz)

Constant current source (mA)

Cable capacitance (pF/m)

Result at entered frequency

—m

— ft

Parameter	Value
Max length	—
Max length (imperial)	—
Effective current (I − 1 mA)	—
Cable capacitance per metre	—

IEPE:L = (I − 1 mA) / (V_pk × 2πf × C)

Charge:L = 1 / (2πf × R_in × C × f_lo)

The 1 mA deduction accounts for sensor quiescent current. Default 100 pF/m is typical for low-noise coaxial — check your cable datasheet.

Max cable length vs frequency

From Hz

To Hz

Scale

Vertical marker shows result at entered frequency. Length inversely proportional to frequency — higher frequencies demand shorter cables.

Reference — typical cable capacitances

Cable type	Typical pF/m
Standard coaxial (RG-174)	101
Low-noise coaxial	85–100
Armoured coaxial	100–130
Twisted pair (unscreened)	50–80
High-capacitance coaxial	130–160

↗ Vibration Trend Logger

Track readings over time — chart trends with ISO severity zones

Machine / asset name

Date

RMS Velocity (mm/s)

ISO Group

Notes (optional)

Log repeat measurements to track trend. Chart points are colour-coded by severity zone.

Reading history

No readings logged yet.

Trend chart

◎ ISO 1940 Balance Quality

Calculate permissible residual unbalance per ISO 1940-1

Balance quality grade

Rotor mass (kg)

Max operating speed (RPM)

G = e · ω where e is the specific unbalance (mm) and ω is angular velocity (rad/s). Result is maximum permissible residual unbalance.

Grade reference

Result

—g·mm

Permissible residual unbalance

≡ ISO Reference

ISO 10816-3 velocity limits, key formulas and bearing fault equations

ISO 10816-3 — velocity limits (mm/s RMS)

Group	Good	Sat.	Unsat.	Unac.

Limits apply to RMS velocity at bearing housings, 10–1000 Hz. Always refer to the current published standard for formal assessments.

Key conversion formulas

v = a / (2πf)Acceleration → Velocity

d = v / (2πf)Velocity → Displacement

a = (2πf)² · dDisplacement → Acceleration

x_pk = √2 · x_rmsRMS → Peak

x_pkpk = 2√2 · x_rmsRMS → Peak-to-Peak

Bearing fault formulas

BPFO(N/2)·fr·(1 − (d/D)cosα)

BPFI(N/2)·fr·(1 + (d/D)cosα)

BSF(D/2d)·fr·(1 − ((d/D)cosα)²)

FTF(1/2)·fr·(1 − (d/D)cosα)

📋 Changelog

Version history for the Vibration Calculator

v1.9 Current

Fixed 4–20 mA loop supply check not calculating — default values now pre-filled including cable resistance. Corrected loop voltage drop calculation. Shortened table labels for improved layout. Polished print/PDF report.

v1.8

Added µm to displacement results card alongside mm and mils. Added dB level output (ISO 1683 reference) to Unit Converter for velocity, acceleration and displacement. Default example values pre-filled on load (1500 RPM Group 2a motor at Good severity).

v1.7

Added Gear Mesh Frequency (GMF) and running speed harmonics (orders) to the Bearing pane. Extended Natural Frequency pane with critical speed separation margin checker and RPM ↔ Hz converter. Added Crest Factor calculator to main results.

v1.6

Added 4–20 mA Sensor Calculator with loop supply verification. Added IEPE/Charge-mode Maximum Cable Length calculator with frequency sweep chart.

v1.5

Rebuilt as full single-screen app layout — persistent left sidebar navigation, header bar with export controls. All tools immediately accessible without scrolling.

v1.4

Added Unit Converter (same-quantity and cross-quantity), Vibration Trend Logger with Chart.js severity-zone chart, and ISO 1940 Balance Quality calculator.

v1.3

Added Bearing Fault Frequency calculator (BPFO, BPFI, BSF, FTF), Natural Frequency estimation, and Sensor Selection guidance. Extended ISO groups to full ISO 10816-3 set (Groups 1a, 1b, 2a, 2b, 3, 4).

v1.2

Added frequency response chart with ISO severity band overlay. Added RMS / Peak / Peak-to-Peak amplitude type selection. Metric and imperial display throughout.

v1.1

Initial release. Acceleration, velocity and displacement conversion at a given frequency. ISO 10816 severity assessment with zone classification.

Created by A.Webdell · KDP Electronic Systems Ltd
For engineering reference only. Always verify against current published standards for formal assessments.