Bloom Filter Optimal Bit-Array Size (m) & Hash Function Count (k) Calculator

Size probabilistic Bloom filters for caches, LSM-trees, and deduplication.

Bloom Filter Memory Size (MiB)
8.57 MiB
Optimal Hash Functions (k) 10 hashes
Bits Allocated per Key (m / n) 14.38 bits/key
Total Bit-Array Length (Millions) 71.89 M bits
Inputs
keys
Expected number of distinct keys inserted (n).
%
Target false-positive rate percentage (e.g., 0.1% = 0.001).
Results & Graph
Bloom Filter Memory Size (MiB)
8.57 MiB
Optimal Hash Functions (k)
10 hashes
Bits Allocated per Key (m / n)
14.38 bits/key
Total Bit-Array Length (Millions)
71.89 M bits

Bloom Filter Memory Size (MiB)

Graph 1 • Expected Elements N Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 MiB 6.9 MiB 13.9 MiB 50%: 4.28 MiB 4.3 50% 75%: 6.43 MiB 6.4 75% 100%: 8.57 MiB 8.6 100% 125%: 10.71 MiB 10.7 125% 150%: 12.85 MiB 12.8 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Bloom Filter Memory Size (MiB) 8.57 MiB Optimal Hash Functions (k) 10 hashes Bits Allocated per Key (m / n) 14.38 bits/key Total Bit-Array Length (Millions) 71.89 M bits
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Bloom Filter Memory Size (MiB)8.57 MiBOptimal Hash Functions (k)10 hashesBits Allocated per Key (m / n)14.38 bits/keyTotal Bit-Array Length (Millions)71.89 M bits
Summary: For 5,000,000 keys at 0.1% false-positive rate, allocate 8.57 MiB (14.4 bits/key) with k = 10 hash functions.
Summary: For 5,000,000 keys at 0.1% false-positive rate, allocate 8.57 MiB (14.4 bits/key) with k = 10 hash functions.
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Formula & Mathematical Methodology: Bloom Filter Sizing Systems Engineering Formula

mbits = −(n × ln(p)) / (ln 2)²
khashes = round((m / n) × ln 2)
m_bits = −(n × ln(p)) / (ln 2)²; k_hashes = round((m / n) × ln 2)
  • expectedElementsN: Expected Elements N (keys)
  • falsePositiveRatePct: False Positive Rate Pct (%)

Rounding: Binary/decimal capacities and engineering metrics retain full floating-point precision and round to 2 decimal places.

Worked Example: Architecture Sizing Example: Bloom Filter Sizing

Size probabilistic Bloom filters for caches, LSM-trees, and deduplication.

  1. Enter the workload parameters, model dimensions, or network link specifications.
  2. Compute the sizing equation: m_bits = −(n × ln(p)) / (ln 2)²; k_hashes = round((m / n) × ln 2).
  3. Inspect the primary capacity metric, headroom buffers, and 3 SVG visualizations.
Result: Calculates Bloom Filter Sizing via m_bits = −(n × ln(p)) / (ln 2)²; k_hashes = round((m / n) × ln 2).

Frequently Asked Questions

How does the Bloom Filter Optimal Bit-Array Size (m) & Hash Function Count (k) Calculator compute capacity?

It evaluates m_bits = −(n × ln(p)) / (ln 2)²; k_hashes = round((m / n) × ln 2) directly in your browser and plots three custom SVG diagrams.

Can I compare different cluster or model configurations side by side?

Yes. Use the "Compare (0/3)" button in the results panel to pin up to three configurations.

Does this tool upload any of my architecture parameters?

No. All calculations run 100% client-side in your browser.

Developer Tools · Cloud SRE & Distributed Systems

Bloom Filter Optimal Bit-Array Size (m) & Hash Function Count (k) Calculator: inputs, method, and how to read the result

Size probabilistic Bloom filters for caches, LSM-trees, and deduplication.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Expected Elements N: Expected number of distinct keys inserted (n).
  • False Positive Rate Pct: Target false-positive rate percentage (e.g., 0.1% = 0.001).

What the calculation includes

With the default values shown, Bloom Filter Memory Size (MiB) is 8.57 MiB. The calculation follows Bloom Filter Sizing Systems Engineering Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Expected Elements N from 5,000,000 keys to 5,500,000 keys changes Bloom Filter Memory Size (MiB) from 8.57 MiB to 9.43 MiB. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses industry-standard IEEE, IETF RFC, and GPU/cloud hardware sizing conventions.
  • Capacity planning estimate; benchmark under production traffic patterns before finalizing cluster or hardware procurement.

Scope: IEEE / IETF / Cloud Systems Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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