Bloom Filter False Positive Simulator All tools
Interactive simulator

Bloom Filter False Positive Simulator

Use bit occupancy, false-positive curve, and optimal hash-count views to balance memory and accuracy.

Parameters
Inserted items n
item

Number of inserted elements.

Bit array size m
bit

Length of the bit array.

Hash count k
-

Number of hash functions per item.

Query count
query

Number of lookups used for expected false hits.

Results
False-positive rate
Bit occupancy
Optimal hash count
Expected false hits
Bit-array occupancy
False-positive curve
Hash-count sensitivity
Model and equations

$$p=\left(1-e^{-kn/m}\right)^k,\quad k_{opt}=\frac{m}{n}\ln 2$$

A Bloom filter avoids false negatives but allows false positives. If deletion or counts are needed, use variants such as Counting Bloom filters.

How to read it

The bit-array view shows occupancy rising as items are inserted.

The FPR curve shows the benefit of more memory.

The hash view shows why too few or too many hashes both hurt.

Learn Bloom Filter False Positive by dialogue

🙋
When reading Bloom Filter False Positive, where should I look first? Moving Inserted items n changes both the plots and the result cards.
🎓
Start with False-positive rate, but do not treat the number as the whole answer. Use Bit-array occupancy to confirm the assumed state, then read False-positive curve for the distribution or trend. The bit-array view shows occupancy rising as items are inserted.
🙋
I can see why Inserted items n changes False-positive rate. How should I judge the influence of Bit array size m?
🎓
Move Bit array size m in small steps and watch Bit occupancy. That reveals which term is controlling the result. A Bloom filter avoids false negatives but allows false positives. If deletion or counts are needed, use variants such as Counting Bloom filters. A single operating point is not enough; sweep the realistic scatter range.
🙋
What is Hash-count sensitivity for? It feels like the ordinary curve already tells the story.
🎓
Hash-count sensitivity is for finding boundaries where the condition becomes risky or margin collapses quickly. The FPR curve shows the benefit of more memory. In Memory sizing for cache existence checks, the important question is often what happens after a small change, not only the nominal value.
🙋
So if False-positive rate is within the target, can I accept the condition?
🎓
Treat this as a first-pass review. It helps with False-hit estimates for duplicate or URL-set tests and Initial bit and hash-count selection, but final decisions still need standards, measured data, detailed analysis, and vendor limits. The hash view shows why too few or too many hashes both hurt.

Practical use

Memory sizing for cache existence checks.

False-hit estimates for duplicate or URL-set tests.

Initial bit and hash-count selection.

FAQ

Start with False-positive rate and Bit occupancy. Then use Bit-array occupancy to confirm the assumed state and False-positive curve to read distribution or bias. The bit-array view shows occupancy rising as items are inserted
Move Inserted items n alone, then move Bit array size m by a comparable amount and compare the change in False-positive rate. Hash-count sensitivity shows combinations where margin or performance changes quickly.
Use it for Memory sizing for cache existence checks. Instead of trusting a single point, widen the input range and check whether False-positive rate keeps enough margin before moving to detailed analysis.
A Bloom filter avoids false negatives but allows false positives. If deletion or counts are needed, use variants such as Counting Bloom filters. Final decisions still require standards, measured data, detailed analysis, and vendor limits.