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Statistics & Probability

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Statistics & Probability

Allan Variance Calculator.

Estimates the Allan variance and deviation of a dataset from a single sample of phase or frequency measurements, given the sample size and measurement interval.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the number of samples, averaging time, and phase noise.

  2. 2

    The calculator computes the Allan variance as phase noise squared divided by tau squared times (sample size minus one).

  3. 3

    The Allan deviation is the square root of the variance.

  4. 4

    Review the results and adjust inputs as needed.

(phase_noise^2) / (tau^2 * max(sample_size - 1, 1))

Frequently asked questions

What does Allan variance measure?

It quantifies frequency stability as a function of averaging time, helping identify noise types in clocks and oscillators.

Why use sample size minus one?

This approximates the degrees of freedom in the variance estimate, similar to sample variance.

Can I use this for any dataset?

This simplified version assumes white phase noise; for other noise types, more complex estimators are needed.

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Results

Formula checked

Allan Variance

0rad²/s²

Allan Deviation0.001005rad/s
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Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Estimates the Allan variance and deviation of a dataset from a single sample of phase or frequency measurements, given the sample size and measurement interval.

  1. Enter the number of samples, averaging time, and phase noise.
  2. The calculator computes the Allan variance as phase noise squared divided by tau squared times (sample size minus one).
  3. The Allan deviation is the square root of the variance.
  4. Review the results and adjust inputs as needed.

Formulas

The math behind this calculator, written out so you can verify the result.

Allan Variance (simplified)

σ_y²(τ) ≈ (σ_φ²) / (τ² (N-1))

Estimates variance from phase noise σ_φ, averaging time τ, and sample count N.

Real-world use cases

Where this calculation shows up in everyday life.

Oscillator stability

Compare short-term and long-term frequency stability of quartz or atomic clocks.

Example: Evaluate a 10 MHz oscillator with τ from 1 ms to 100 s.

Sensor noise characterization

Assess gyroscope or accelerometer noise for inertial navigation systems.

Example: Determine optimal averaging time for a MEMS gyro.

Tips and common mistakes

Tips

  • Use a larger sample size for more reliable estimates.
  • Choose tau values spanning decades to see noise type transitions.
  • Ensure phase noise is in radians, not degrees.

Common Mistakes to Avoid

  • Using sample size instead of sample size minus one.
  • Forgetting to square the phase noise.
  • Mixing units (e.g., degrees instead of radians).

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.