Bloom Filter Optimal Bit Array Size (m), Hash Functions (k) & False Positive Rate Calculator

Design a probabilistic Bloom filter’s exact memory footprint (MB) and hash function count k.

Bloom Filter Memory Footprint
5.713 MiB
Optimal Bits per Element (m / n) 9.585 bits/key
Optimal Hash Functions (k) 7 hashes
Total Bit Array Length (Millions of Bits) 47.925 Mbits
Inputs
⚡ Scenarios:
items
Expected number of distinct keys inserted into the Bloom filter (n).
%
Target false-positive probability p in percent (e.g., 1.0% = 0.01, 0.1% = 0.001).
Results & Graph
Bloom Filter Memory Footprint
5.713 MiB
Optimal Bits per Element (m / n)
9.585 bits/key
Optimal Hash Functions (k)
7 hashes
Total Bit Array Length (Millions of Bits)
47.925 Mbits

Bloom Filter Memory Footprint

Graph 1 • Bloom Filter Bit Size & Hashes • Domain Architecture & Live Telemetry Maps Expected Inserted Items N, Target False Positive Pct through Bloom Filter Bit Size & Hashes Formula.
Source / Tx Target / Rx Bloom Filter Bit Size & Hashes Propagation Path Bloom Filter Memory Footpr 5.713 MiB Optimal Bits per Element (: 9.585 bits/key Optimal Hash Functions (k): 7 hashes
Graph 2 • Bloom Filter Memory Footprint Across Expected Inserted Items N Sweep (40% → 160%) Evaluates m_bits = −[ n × ln(p) ] / (ln 2)²; BitsPerItem = m / n = −2.08137 × ln across 7 operating points (current input highlighted).
0 MiB 5.03 MiB 10.06 MiB 2.29 2.00Mitems 3.43 3.00Mitems 4.57 4.00Mitems 5.71 5.00Mitems 6.86 6.00Mitems 8.00 7.00Mitems 9.14 8.00Mitems
Graph 3 • Joint Sensitivity: Expected Inserted Items N × Target False Positive Pct Compares Bloom Filter Memory Footprint when Target False Positive Pct is shifted +25% (solid) vs. −25% (dashed).
0 MiB 4.34 MiB 8.68 MiB --- Target False Positive Pct @ 75% 3.81 -30% 4.62 -15% 5.44 +0% 6.25 +15% 7.07 +30%
Summary: Storing 5,000,000 keys at 1% false-positive rate requires 9.59 bits/item (5.71 MiB total bit array) and k = 7 hash functions.
Summary: Storing 5,000,000 keys at 1% false-positive rate requires 9.59 bits/item (5.71 MiB total bit array) and k = 7 hash functions.
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Formula & Mathematical Methodology: Bloom Filter Bit Size & Hashes Formula

mbits = −[ n × ln(p) ] / (ln 2)²
BitsPerItem = m / n = −2.08137 × ln(p)
OptimalHashesk = round((m / n) × ln 2)
m_bits = −[ n × ln(p) ] / (ln 2)²; BitsPerItem = m / n = −2.08137 × ln(p); OptimalHashes_k = round((m / n) × ln 2)
  • expectedInsertedItemsN: Expected number of distinct keys inserted into the Bloom filter (n).
  • targetFalsePositivePct: Target false-positive probability p in percent (e.g., 1.0% = 0.01, 0.1% = 0.001).

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Bloom Filter Bit Size & Hashes Worked Example

Design a probabilistic Bloom filter’s exact memory footprint (MB) and hash function count k.

  1. Enter the input measurement, system configuration, or astronomical parameter.
  2. Apply the standard conversion or analytical equation: m_bits = −[ n × ln(p) ] / (ln 2)²; BitsPerItem = m / n = −2.08137 × ln(p); OptimalHashes_k = round((m / n) × ln 2).
  3. Inspect the primary metric, secondary equivalents, and 3 real-time SVG graphs.
Result: Computes Bloom Filter Bit Size & Hashes via m_bits = −[ n × ln(p) ] / (ln 2)²; BitsPerItem = m / n = −2.08137 × ln(p); OptimalHashes_k = round((m / n) × ln 2).

Frequently Asked Questions

How does the Bloom Filter Optimal Bit Array Size (m), Hash Functions (k) & False Positive Rate Calculator perform the calculation?

It evaluates m_bits = −[ n × ln(p) ] / (ln 2)²; BitsPerItem = m / n = −2.08137 × ln(p); OptimalHashes_k = round((m / n) × ln 2) directly in your browser and renders three custom SVG charts in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this tool work offline?

Yes. All calculations run 100% locally in your browser with full offline PWA support.

Developer Tools · Networking & Systems Performance

Bloom Filter Optimal Bit Array Size (m), Hash Functions (k) & False Positive Rate Calculator: inputs, method, and how to read the result

Design a probabilistic Bloom filter’s exact memory footprint (MB) and hash function count k.

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 Inserted Items N: Expected number of distinct keys inserted into the Bloom filter (n).
  • Target False Positive Pct: Target false-positive probability p in percent (e.g., 1.0% = 0.01, 0.1% = 0.001).

What the calculation includes

With the default values shown, Bloom Filter Memory Footprint is 5.713 MiB. The calculation follows Bloom Filter Bit Size & Hashes Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Expected Inserted Items N from 5,000,000 items to 5,500,000 items changes Bloom Filter Memory Footprint from 5.713 MiB to 6.284 MiB. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official NIST Special Publication 811, IEEE/RFC systems engineering, APA psychometric, and USNO astronomical formulas.
  • Empirical metallurgy and calendar conversions represent standard reference-condition approximations.

Scope: Global NIST, IEEE, APA & Astronomical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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