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Randomisation Block Size Calculator

Work out randomisation block size instantly with clear inputs, formula shown and shareable results.

About Randomisation Block Size Calculator

Block randomisation guarantees balance at the end of each block. Two arms with a multiplier of two gives blocks of four, so 120 participants need 30 blocks and imbalance can never exceed two. Small blocks balance tightly but become predictable to unblinded staff, which is why variable block sizes are usually preferred.

Formulas

Block size

size = arms x multiplier

Blocks needed

blocks = ceil(total participants / block size)

Worked example

With the default values below, Randomisation Block Size Calculator returns Block Size of 4. Change any input above and every figure here is recalculated in your browser.

Inputs used

Total participantsminimum 2
120
Treatment armsminimum 2
2
Block size as a multiple of the armsminimum 1
2

Results

Block Size
4 participants
Number Of Blocks Needed
30
Maximum Possible Imbalance
2 participants
Allocations Per Arm Per Block
2

Step by step

  1. 1Values used
  2. 2Block size
  3. 3Blocks needed
  4. 4Block Size= 4 participants
  5. 5Number Of Blocks Needed= 30
  6. 6Maximum Possible Imbalance= 2 participants
  7. 7Allocations Per Arm Per Block= 2

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 whole numbers, 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

Why not use very small blocks?

Because the last allocation in a block of two is fully predictable, which lets unblinded staff guess assignments and introduces selection bias.

What are variable block sizes?

Randomly alternating between, say, blocks of four and six. This preserves balance while defeating prediction.

Related Calculators

Randomisation Block Size Calculator – Calculate Block Size