# Vibration Velocity to Acceleration and Displacement Converter

> Source: https://netray.co/tools/vibration-velocity-acceleration-displacement-converter
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Convert a single-frequency vibration reading between velocity, acceleration and displacement, with a frequency sweep chart.

## Category

maintenance

## Industry

Manufacturing

## Audience

- Reliability engineer
- Vibration analyst
- Maintenance technician

## Tool

**Kind:** calculator

**Inputs:**

#### Frequency

**Key:** freq

**Type:** number

**Default:** 50

**Min:** 0.5

**Step:** 1

**Unit:** Hz

**Help:** Running speed in rpm divided by 60 for 1x vibration.

#### Velocity, RMS

**Key:** vel_rms

**Type:** number

**Default:** 4.5

**Min:** 0

**Step:** 0.1

**Unit:** mm/s

**Outputs:**

#### Velocity, peak

**Key:** vel_pk

**Expr:** vel_rms * sqrt(2)

**Format:** decimal

**Description:** Peak equals RMS times 1.414 for a pure sine wave.

#### Displacement, peak to peak

**Key:** disp_pp

**Expr:** 2 * vel_pk / (2 * pi * freq) * 1000

**Format:** decimal

**Primary:** true

**Description:** In micrometres (um).

#### Acceleration, RMS

**Key:** acc_rms

**Expr:** 2 * pi * freq * vel_rms / 1000 / 9.80665

**Format:** decimal

**Description:** In g.

#### Acceleration, peak

**Key:** acc_pk_g

**Expr:** acc_rms * sqrt(2)

**Format:** decimal

**Primary:** true

**Description:** In g.

**Chart:**

#### Peak acceleration (g) at constant velocity vs frequency

**Type:** line

**X:** freq

**From:** 10

**To:** 1000

**Steps:** 40

**Series:**

- acc_pk_g

**Disclaimer:** Valid for a single sinusoidal component only. Broadband or multi-frequency signals cannot be converted this way.

## Content

**Intro:** Vibration is reported as displacement, velocity or acceleration depending on the frequency range and instrument. This converter changes between them for a single frequency so you can compare a handheld reading with an ISO limit or a sensor datasheet.

**Sections:**

#### How to use it

**Body:** Enter the frequency of the component you care about, for example 1x running speed, and the RMS velocity in mm/s. The tool returns peak velocity, peak-to-peak displacement in micrometres and acceleration in g. Use the chart to see why acceleration dominates at high frequency while displacement dominates at low frequency for the same velocity.

#### The relationships

**Body:** For a sine wave, velocity is the derivative of displacement and acceleration is the derivative of velocity. That gives v = 2 pi f d and a = 2 pi f v, where d and v are peak values. Peak-to-peak displacement is twice the peak value, and RMS is peak divided by the square root of two. Converting mm/s to m/s and dividing acceleration by 9.80665 gives g.

**Bullets:**

- Displacement is best for low frequency and slow machines
- Velocity is the usual choice for general machine condition (ISO 10816 / 20816 bands)
- Acceleration is best for high frequency and bearing defects

#### Common mistakes

**Body:** The most common error is mixing RMS, peak and peak-to-peak. A limit quoted as mm/s RMS is not the same number as the peak reading shown by some meters. Another is applying single-frequency conversion to a broadband overall value, which is not valid. Always record the unit and the detector type next to every reading in your route data.

**Bullets:**

- Comparing a peak reading with an RMS alarm limit
- Using rpm instead of Hz in the formula
- Converting an overall value that contains many frequencies

**Cta:** If your condition monitoring readings live in spreadsheets or a historian, Netray can bring them next to ERP asset and work order data for trend review.

**Faq:**

#### How do I convert mm/s to g?

**Answer:** For one frequency, acceleration in g equals 2 x pi x f x velocity in mm/s divided by 1000 and divided by 9.80665. Use the same detector type, RMS or peak, on both sides of the conversion.

#### Why does acceleration rise with frequency?

**Answer:** Acceleration is proportional to frequency times velocity. At the same velocity, a 1000 Hz component has twenty times the acceleration of a 50 Hz component.

#### What is the RMS to peak ratio?

**Answer:** For a pure sine wave the peak is 1.414 times the RMS value. Real machine signals with several components have a crest factor that differs, so do not apply this to overall values.

#### Can I use this for ISO 10816 limits?

**Answer:** Yes for comparing units at a single frequency, but ISO bands apply to broadband RMS velocity, typically 10 to 1000 Hz. Compare overall RMS velocity directly with the band for your machine class.

## Search terms

vibration velocity to acceleration converter, vibration displacement calculator, mm/s to g conversion, vibration unit conversion, velocity to displacement vibration formula, rms to peak vibration, vibration analysis calculator, g to mm/s

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