Vibration unit converter
For single-frequency sine vibration enter a value and the frequency; see the peak, RMS and peak-to-peak equivalents of acceleration, velocity and displacement in all common units, and the dB level. Frequency can be entered in Hz or rpm (CPM).
The calculation runs in your browser; the values you enter are not sent anywhere.
Frequency: 50 Hz = 3,000 CPM · Angular frequency ω = 314.2 rad/s
Conversion results
| Unit | Peak | RMS | Peak-to-peak |
|---|---|---|---|
| Acceleration | |||
| m/s² | 2.221 | 1.571 | 4.443 |
| g | 0.2265 | 0.1602 | 0.453 |
| mm/s² | 2,221 | 1,571 | 4,443 |
| in/s² | 87.46 | 61.84 | 174.9 |
| Velocity | |||
| mm/s | 7.071 | 5 | 14.14 |
| in/s | 0.2784 | 0.1969 | 0.5568 |
| Displacement | |||
| µm | 22.51 | 15.92 | 45.02 |
| mil | 0.8861 | 0.6266 | 1.772 |
| mm | 0.02251 | 0.01592 | 0.04502 |
| in | 0.0008861 | 0.0006266 | 0.001772 |
Level (dB, from the RMS value)
The reference varies with the instrument, the standard edition and the manufacturer; common values are listed. Choose the reference of the instrument you use or enter your own.
Level: 123.9 dB
Level: 134 dB
Level: 144 dB
Assumptions
- The conversion is valid only for single-frequency sine vibration (a = ω·v = ω²·d). For a signal with several components or a broadband one, each component must be converted separately at its own frequency; converting a broadband RMS value with a single frequency is misleading.
- The √2 ratio between RMS and peak applies only to a sine; for impulsive or noisy signals the peak/RMS ratio (crest factor) is different.
- g = 9.80665 m/s², 1 in = 25.4 mm, 1 mil = 0.001 in are used.
- dB references vary with instrument and standard edition; verify the reference of your own instrument or standard before publishing.
ω = 2π f · v = a / ω = ω d · a = ω v = ω² d · RMS = peak / √2 · peak-to-peak = 2 × peak · dB = 20 log₁₀(RMS / reference)
A helper calculation; verify against the standard and the instrument manual before publishing. The conversion is for single-frequency sine; real machine signals have many components. When comparing with limit values, use the measurement definition of the relevant standard (band, unit, RMS/peak).
Let's decide together which unit and which band you should monitor for your machine.
Request a conversation01
How to use it
A
Enter the value and choose its unit and type (peak, RMS, peak-to-peak).
B
Enter the frequency in Hz or CPM; for the 1× component the running speed is enough.
C
Read the acceleration, velocity and displacement table; if needed choose a dB reference to see the level.
02
Why is a frequency needed?
In sine vibration acceleration, velocity and displacement are three views of the same motion, linked by frequency: velocity = acceleration / (2π f), displacement = velocity / (2π f). Without frequency you cannot move from one unit to another; for example 1 g of acceleration means a large displacement at 10 Hz and a sub-micron motion at 1000 Hz.
That is why displacement is preferred at low frequency, velocity at medium and acceleration at high frequency: each makes the relevant quantity easier to read in that range.
03
Peak, RMS and peak-to-peak
Peak is the distance of the sine from zero to its highest point; peak-to-peak is from the lowest to the highest point (2 × peak); RMS is the effective value representing energy content (peak / √2 ≈ 0.707 × peak). Limits for velocity are usually given as RMS and for displacement as peak-to-peak, so check the type of a value before comparing it with a limit.
The conversion is valid only for a sine. A real machine signal has several components and impacts; the peak/RMS ratio is then different from √2.
04
Units and dB
Acceleration is given in m/s² or g (9.80665 m/s²), velocity in mm/s or in/s, displacement in µm or mil (a thousandth of an inch). Instruments of US origin tend to use in/s and mil, those of European origin mm/s and µm.
The decibel level is the logarithm of a ratio to a reference, and the reference varies with instrument and standard edition. The same vibration can therefore show a different dB value on different instruments; keep the reference the same when comparing.
FAQ
- Why is frequency needed to go from velocity to acceleration?
- In sine vibration acceleration = 2π f × velocity, so the same velocity value means a different acceleration at different frequencies. Without the frequency the conversion cannot be made.
- What does entering the frequency in CPM mean?
- CPM is cycles per minute; Hz = CPM / 60. If the running speed is known in rpm, the frequency of the 1× component is the same number in CPM.
- Is converting RMS to peak always × 1.414?
- No, only for a pure sine. For a broadband or impulsive signal the peak/RMS ratio (crest factor) is higher and depends on the signal. For this reason the tool should be used only for single-frequency sine.
- Which dB reference should I choose?
- The reference of the instrument or standard you use. References differ; common values are listed, but verify from the instrument manual which one applies. You can also enter your own reference.
- How many m/s² is 1 g?
- 9.80665 m/s² (standard gravity). The tool uses this value for all g conversions.
Measure in the right unit and the right band
Let's decide together which quantity and which frequency band your machine's monitoring plan should use.