01 · Inputs
Frequency & amplitude
Values update as you type. Conversions assume pure sinusoidal motion at a single frequency — for broadband or multi-tone signals the acceleration–velocity–displacement relationships do not hold.
02 · Results
Converted values
| Rect. | SIm/s² | Gravityg |
|---|---|---|
| RMS | — | — |
| 0-P | — | — |
| P-P | — | — |
| Rect. | Metricmm/s | Imperialips |
|---|---|---|
| RMS | — | — |
| 0-P | — | — |
| P-P | — | — |
| Rect. | Metricµm | Imperialmils |
|---|---|---|
| RMS | — | — |
| 0-P | — | — |
| P-P | — | — |
Displacement is reported peak-to-peak in most rotating-machinery standards, whereas velocity is normally reported RMS and acceleration 0-peak. Check the convention of the standard you are working to before comparing values.
03 · Reference
Formulas, rectifiers & units
Core vibration formulas (sinusoidal)
d = peak displacement, v = peak velocity, a = peak acceleration, f = frequency in Hz. Angular frequency ω is the rate of oscillation in radians per second.
| Angular frequency | ω = 2πf |
|---|---|
| Velocity from displacement | v = ω × d = 2πf × d |
| Acceleration from velocity | a = ω × v |
| Acceleration from displacement | a = ω² × d = (2πf)² × d |
| Displacement from velocity | d = v ÷ ω |
Rectifier type conversions
| Peak from RMS | Peak = RMS × √2 ≈ RMS × 1.414 |
|---|---|
| RMS from peak | RMS = Peak ÷ √2 ≈ Peak × 0.707 |
| Peak-to-peak from peak | Peak-to-Peak = 2 × Peak |
The √2 crest factor applies to a pure sine wave only. Broadband or impulsive signals have a higher crest factor, so RMS and peak must be measured, not derived.
Key unit conversions
Acceleration
| 1 g | 9.80665 m/s² |
|---|---|
| 1 g | 386.09 in/s² |
Velocity
| 1 in/s | 25.4 mm/s |
|---|---|
| 1 mm/s | 0.03937 in/s |
Displacement
| 1 mil | 25.4 µm |
|---|---|
| 1 µm | 0.03937 mils |
| 1 inch | 25.4 mm = 1000 mils |
| 1 mm | 1000 µm = 39.37 mils |
Frequency
| 1 Hz | 60 RPM |
|---|---|
| 1 RPM | 0.01667 Hz (1/60) |