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Bootstrap Sample Size Calculator

Determine the number of bootstrap resamples needed for stable estimates.

About Bootstrap Sample Size Calculator

Bootstrap intervals need enough resamples for the tails to be well populated. Two thousand is the practical minimum for a 95 per cent interval, and ten thousand is standard for publication. Too few resamples makes the interval endpoints unstable between runs, which is a Monte Carlo artefact rather than genuine statistical uncertainty.

Formula

Bootstrap Sample Size

B ≈ α(1−α) ÷ precision²; each tail should contain at least about 50 resamples

Monte Carlo error
Uncertainty from resampling itself, distinct from sampling uncertainty

Worked example

With the default values below, Bootstrap Sample Size Calculator returns Bootstrap Resamples Needed of 1,901. Change any input above and every figure here is recalculated in your browser.

Inputs used

Confidence levelaccepts 50–99.9 %
95 %
Desired Monte Carlo precisionaccepts 0.01–10 %
0.5 %
Original sample sizeminimum 2
500

Results

Bootstrap Resamples Needed
1,901
Recommended Practical Number
10,000
Resamples Falling in Each Tail
250.0
Monte Carlo Standard Error
0.002179
Guidance
Enough resamples in each tail for a stable percentile interval

Step by step

  1. 1Values used
  2. 2Bootstrap Sample Size
  3. 3Bootstrap Resamples Needed= 1,901
  4. 4Recommended Practical Number= 10,000
  5. 5Resamples Falling in Each Tail= 250.0
  6. 6Monte Carlo Standard Error= 0.002179
  7. 7Guidance= Enough resamples in each tail for a stable percentile interval

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Bootstrap Sample Size calculated?

B ≈ α(1−α) ÷ precision²; each tail should contain at least about 50 resamples Bootstrap intervals need enough resamples for the tails to be well populated. Two thousand is the practical minimum for a 95 per cent interval, and ten thousand is standard for publication.

Why does Bootstrap Sample Size matter?

Too few resamples makes the interval endpoints unstable between runs, which is a Monte Carlo artefact rather than genuine statistical uncertainty.

What values do I need to enter?

This calculator takes 3 inputs: Confidence level, Desired Monte Carlo precision, Original sample size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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