Read the guide: Vibration frequency explained
How to convert vibration units
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Step 1: Type your value and pick its unit: g, m/s² or in/s² for acceleration, mm/s or in/s for velocity, µm or mils for displacement.
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Step 2: Set "Your value is" to RMS, peak or peak-to-peak, and choose how to see the answer under "Show results as". The tool applies the sine-wave factors below for you.
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Step 3: If you're converting between acceleration, velocity and displacement, enter the vibration frequency in Hz. The main peak from the vibration frequency analyzer works well.
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Step 4: Read the value in every other unit.
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Step 5: Compare the result with the vibration severity chart for machines, or the construction vibration limits for buildings.
This vibration unit converter handles the three ways vibration is described: acceleration (how hard it shakes), velocity (how fast it moves) and displacement (how far it moves). Changing units within one type is simple multiplication. Moving between types needs the frequency, because a fast vibration can have high acceleration and almost no movement at the same time.
Formulas behind the vibration unit converter
Same type, different unit
| From | To | Multiply by |
|---|---|---|
| g | m/s² | 9.80665 |
| g | in/s² | 386.09 |
| m/s² | g | 0.10197 |
| in/s | mm/s | 25.4 |
| mm/s | in/s | 0.03937 |
| mils | µm | 25.4 |
| µm | mils | 0.03937 |
A mil is one thousandth of an inch, not a millimeter.
Between acceleration, velocity and displacement
For a single sine vibration at frequency f, in Hz:
- Velocity v = a ÷ (2πf)
- Displacement d = v ÷ (2πf), which is the same as a ÷ (2πf)²
To go the other way, multiply: a = v × 2πf and v = d × 2πf. Use meters and seconds inside the formulas (m/s², m/s, m), then convert the answer.
Each step divides by 2πf. So at low frequencies, a small acceleration means a lot of movement. At high frequencies, a big acceleration can mean very little movement.
Real vibration is rarely one clean sine. For a mix of frequencies, a single-frequency conversion is an estimate. The sensor tools on this site convert each frequency band separately, which is more accurate.
Worked examples
- Acceleration to velocity. 0.0628 m/s² RMS at 10 Hz. v = 0.0628 ÷ (2π × 10) = 0.0628 ÷ 62.83 = 0.001 m/s, which is 1.0 mm/s RMS.
- Velocity to displacement. 4.5 mm/s RMS at 25 Hz. d = 4.5 ÷ (2π × 25) = 4.5 ÷ 157.1 = 0.0286 mm, which is 28.6 µm RMS. As peak-to-peak, that’s 28.6 × 2.828 = 81 µm, or about 3.2 mils.
- g to mm/s. 0.01 g peak at 5 Hz. That’s 0.0981 m/s². v = 0.0981 ÷ 31.42 = 0.0031 m/s, which is 3.1 mm/s peak.
RMS, peak and peak-to-peak
The same vibration can be described three ways:
- Peak: the largest value in one direction, measured from zero.
- Peak-to-peak: from the highest point to the lowest, so twice the peak.
- RMS (root mean square): an average of the size over time. It tracks the energy in the vibration.
For a clean sine wave:
| From | To | Multiply by |
|---|---|---|
| RMS | peak | 1.414 (√2) |
| peak | RMS | 0.707 |
| peak | peak-to-peak | 2 |
| RMS | peak-to-peak | 2.828 |
For real, messy vibration, the true peak is usually higher than RMS × 1.414. It can be much higher when there are knocks or impacts.
Different fields have different habits. Machine standards such as ISO 10816 use RMS velocity in mm/s. US machinery work often uses peak velocity in in/s, and displacement in mils peak-to-peak. Guidance for buildings uses peak particle velocity (PPV).
Common values, converted
These are the zone boundaries from the vibration severity chart:
| mm/s RMS | in/s RMS | in/s peak |
|---|---|---|
| 0.71 | 0.028 | 0.040 |
| 1.12 | 0.044 | 0.062 |
| 1.8 | 0.071 | 0.100 |
| 2.8 | 0.110 | 0.156 |
| 4.5 | 0.177 | 0.251 |
| 7.1 | 0.280 | 0.395 |
| 11.2 | 0.441 | 0.624 |
| 18 | 0.709 | 1.002 |
Where the numbers come from
The value of 1 g, 9.80665 m/s², is the internationally agreed standard gravity. The inch is defined as exactly 25.4 mm, which fixes the in/s and mil factors. The formulas between acceleration, velocity and displacement come from the math of a sine wave. The RMS and peak factors hold only for a single clean sine.
Frequently asked questions
How do I convert g to m/s²?
Multiply by 9.80665. So 0.1 g is 0.98 m/s², and 1 m/s² is about 0.102 g. The same factor works for RMS and peak values.
Can I convert mm/s to g without a frequency?
No. Velocity and acceleration are linked by frequency, so the same 1 mm/s is a tiny acceleration at 2 Hz and a much bigger one at 100 Hz. Enter the frequency of the main vibration to convert between them.
How do I convert in/s to mm/s?
Multiply by 25.4. So 0.1 in/s is 2.54 mm/s, and 1 mm/s is about 0.039 in/s. You don't need a frequency, because both are velocity.
Is RMS or peak velocity used for machines?
ISO machine vibration standards use RMS velocity in mm/s. Many US tools and reports use peak velocity in in/s instead. For a clean single-frequency vibration, peak is RMS × 1.414, so always check which one a limit uses.
Why do building limits use peak velocity?
Guidance for buildings, such as Caltrans and DIN 4150-3, is written in peak particle velocity (PPV). This site estimates PPV from a phone reading as RMS × 1.414.
Last updated .