DOF Calculator


Want an easy-to-use tool to assess the probability of your random vibration test being in-tolerance?

Our DOF (degrees-of-freedom) calculator will answer the following questions:

  • Is it statistically possible to satisfy the tolerances of your random vibration test?
  • How much time will it take to average enough data to meet your specifications?

Download Calculator (Excel)

What is the DOF value?

Random vibration test standards often specify a degrees-of-freedom (DOF) value. DOF is an averaging specification derived from the FFT computation of the power spectral density (PSD). The average PSD of a Gaussian waveform is a Chi-squared distributed random variable with (2*F) DOF, where F is the number of time-data frames.

We can use the equations that define the Chi-squared distribution to determine the probability of meeting tolerance. When frames of data are assumed to be independent, the DOF equals 2x the number of frames. The DOF calculator provided by Vibration Research can be used to assess the probability of a random vibration test being within tolerance. Enter the DOF, lines, and max frequency and automatically calculate the probability of satisfying tolerance and the time to acquire the DOF.

For DOF calculations to be accurate, the time waveform must be stationary.

Note: If frames are overlapped or window functions are applied, the frames are no longer independent. As such, the DOF of the average is no longer a multiple of the number of frames. Learn more in the Statistical Degrees-of-Freedom (DOF) technical note.

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