Calculate vibration g-force from frequency and displacement, solve for amplitude or frequency from peak g, or convert an acceleration in m/s² to g.

Single-frequency sinusoidal motion. Results are peak values, not RMS or instantaneous values.

Changing this choice reinterprets a displacement input. Unit changes convert the number.

Optional settings

Vibration G Force Formula

Vibration g-force expresses sinusoidal acceleration as a multiple of standard gravity. For a vibrating system with displacement amplitude D, frequency f, and time t, the motion can be modeled from displacement to acceleration and then converted into g’s.

x(t) = Dsin(2π f t)
a(t) = - (2π f)²Dsin(2π f t)

GF(t) = |a(t)| / g₀

GF(t) = GFpeak × |sin(2πft)|

Where:

  • GF(t) = instantaneous vibration g-force
  • D = displacement amplitude in meters
  • f = frequency in hertz
  • t = time in seconds
  • 9.80665 = standard gravity in m/s2

The calculator reports peak acceleration magnitude for sinusoidal motion. Time and phase are background theory here and are not calculator inputs. It also reverse-solves positive displacement or frequency.

Peak Vibration G Force

If you want the maximum acceleration reached during one full cycle, use the peak form. This occurs when the sine term reaches its maximum magnitude.

GFpeak = (2πf)² × D / 9.80665

This version is especially useful for shaker testing, machinery vibration checks, design limits, and quick comparisons between different amplitudes and frequencies.

Useful Rearrangements

If you know the peak g-force and need to solve for displacement amplitude or frequency, these forms are helpful:

D = (GFpeak × 9.80665) / (2πf)²

f = √(GFpeak × 9.80665 / D) / (2π)

D = (Xₚₚ) / (2)

Use the last relation when your measurement is peak-to-peak displacement rather than amplitude. Entering peak-to-peak travel as amplitude will overstate the calculated g-force.

How to Calculate Vibration G Force

  1. Convert frequency to hertz and displacement to meters.
  2. If your motion is given as peak-to-peak displacement, divide by 2 to get amplitude.
  3. Use single-sided amplitude in the peak relation; peak-to-peak travel is twice this amplitude.
  4. Compute the peak acceleration from the squared angular frequency and amplitude.
  5. Divide acceleration by standard gravity to express the result in g.
θ = 2π f t

At the start of a cycle, the instantaneous g-force is zero. At one-quarter of a cycle, the instantaneous g-force reaches its peak magnitude.

Example

Suppose a vibration has a frequency of 400 Hz, a displacement amplitude of 1.25 mm, and a time equal to one-quarter of a cycle. At that instant, the sine term equals 1, so the instantaneous g-force is also the peak g-force.

D = 1.25 mm = 0.00125 m

t = 1 / (4 × 400)

t = 0.000625 s

GFpeak = (2π × 400)² × 0.00125 / 9.80665

At one-quarter cycle, GF(t) = GFpeak ≈ 805.14 g.

The vibration acceleration is approximately 805.14 g.

Quick Interpretation

Change Effect on Vibration G Force
Double the displacement amplitude The g-force doubles
Double the frequency The g-force increases by four times
Measure at the start of a cycle The instantaneous g-force is zero
Measure at one-quarter of a cycle The instantaneous g-force reaches peak magnitude

Input Notes That Prevent Errors

  • Amplitude is not total travel. If a system moves 2 mm peak-to-peak, the amplitude is 1 mm.
  • Frequency has the strongest influence. Because acceleration scales with the square of frequency, even modest frequency increases can produce much larger g values.
  • Time only matters for instantaneous results. If you only need the highest acceleration in a cycle, use the peak formula.
  • Magnitude removes direction. The positive and negative halves of the cycle have opposite acceleration directions but the same magnitude.
  • Unit consistency matters. Most unrealistic outputs come from mixing inches, millimeters, hertz, or time units without converting properly.

Where This Calculation Is Used

  • Rotating machinery and imbalance analysis
  • Shaker table and sinusoidal vibration testing
  • Electronics, sensors, and PCB durability checks
  • Automotive and aerospace vibration environments
  • Mount, isolator, and fixture design reviews
  • Comparing allowable vibration limits against test conditions

Assumptions and Limits

This calculator is intended for sinusoidal vibration. It is most accurate when the motion can be represented by a single frequency and a single displacement amplitude.

  • It does not model random vibration spectra.
  • It does not replace shock or impact calculations.
  • It assumes the reported displacement is the amplitude for the same axis being evaluated.
  • The inverse modes solve positive displacement or frequency from peak g; they do not solve for time or phase.

Frequently Asked Questions

What is the difference between acceleration in m/s2 and acceleration in g?

They describe the same physical acceleration on different scales. Expressing acceleration in g simply normalizes it by standard gravity.

GF = (a) / (9.80665)

Why can a very small displacement create a very large g-force?

Because vibration acceleration grows with the square of frequency. High-frequency motion can create large acceleration even when the actual displacement is tiny.

When should I use peak g-force instead of instantaneous g-force?

Use peak g-force when you want the maximum acceleration reached during a cycle. Use instantaneous g-force when the exact time or phase of motion matters.

Is vibration g-force the same as shock g-force?

No. Vibration g-force is typically tied to continuous periodic motion, while shock g-force describes a short-duration impact or pulse. The analysis methods and assumptions are different.

What is the most common input mistake?

The most common mistake is entering peak-to-peak displacement as amplitude. For the formula, halve peak-to-peak displacement to obtain amplitude. In the calculator, select Peak-to-peak travel and enter the full travel; it halves the value internally.