How do I convert vibration velocity to displacement?

Displacement = Velocity / (2πf), where f is the frequency in Hz. For example, 1 mm/s RMS at 50 Hz gives displacement = 1/(2π×50) = 0.00318 mm = 3.18 μm 0-pk. Peak-to-peak is double the 0-pk value.

What is the dB reference for vibration velocity?

The standard reference for vibration velocity in dB is 10⁻⁹ m/s (1 nm/s or 10⁻⁶ mm/s). The formula is dB = 20 × log₁₀(v / v_ref), where v is the RMS velocity in m/s and v_ref = 10⁻⁹ m/s (ISO 1683 preferred reference).

What is the relationship between RMS and peak vibration values?

For a sinusoidal signal, Peak = RMS × √2 (≈ 1.414). Peak-to-peak = 2 × Peak. This relationship only holds exactly for pure sinusoidal vibration.

How do I convert mm/s to g (acceleration)?

First convert velocity to acceleration: a = v × 2πf. If velocity is in mm/s, divide by 1000 to get m/s, then a = (v/1000) × 2πf gives m/s². Divide by 9.80665 to get g.

Why does vibration conversion require frequency?

Velocity, displacement, and acceleration are related through derivatives in time. Since d/dt of a sinusoid at frequency f multiplies the amplitude by 2πf, you need the frequency to convert between these quantities.

Free Engineering Tool · #006

Vibration Unit Converter

Convert between vibration velocity, displacement, acceleration, and dB at any frequency. All results shown simultaneously.

mm/s ↔ μm g ↔ m/s² dB ref 10⁻⁹ m/s

Value

Input Unit

Frequency

Frequency Unit

Hz RPM

Quick presets

Results

Velocity

Velocity RMS

—

Velocity Peak

—

Velocity dB

—

Displacement

Displacement 0-Peak

—

Displacement Peak-to-Peak

—

Acceleration

Acceleration RMS

—

Acceleration Peak

—

Acceleration RMS (g)

—

Acceleration Peak (g)

—

Vibration Relationships

For a sinusoidal vibration signal at angular frequency ω = 2πf, the three vibration quantities — displacement (d), velocity (v), and acceleration (a) — are related by differentiation:

RMS vs Peak vs Peak-to-Peak

For a pure sinusoidal signal:

Peak = RMS × √2 (≈ 1.414)
Peak-to-Peak = 2 × Peak
RMS = Peak / √2 (≈ 0.7071)

Decibel Scale (dB)

Vibration velocity is often expressed in dB with a reference of 10⁻⁹ m/s (= 10⁻⁶ mm/s), the ISO 1683 preferred reference:

For example, 1 mm/s RMS = 10⁻³ m/s → dB = 20 × log₁₀(10⁻³ / 10⁻⁹) = 20 × 6 = 120 dB.

Quick Reference Table

Velocity (mm/s RMS)	dB ref 10⁻⁹ m/s	Typical Assessment
0.28	109	Very good (new machines)
0.71	117	Good
1.12	121	Satisfactory (Group 1)
1.8	125	Satisfactory (Group 2)
2.8	129	Acceptable (Group 2)
4.5	133	Unacceptable for most
7.1	137	Danger zone

⚠️ Note: These conversions assume pure sinusoidal (single-frequency) vibration. Real-world signals are complex and may contain many harmonics; broadband RMS values do not convert directly with these formulas.