ForHosting KIT · Developer Utilities

Hash bits for collision resistance

Storing 1,000,000 items with at most a one-in-a-million chance of any collision takes 59 bits of hash, the smallest width that meets the birthday bound. You also see the hash space and the estimated risk at that width. Free in your browser.

Free
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Run — free How it works & API

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Worked example

If you enter

Items: 1,000,000
Max probability: 0.000001

You get

Bits needed: 59
Approximate collision probability: 0.0000008674
Hash space: 2^59

When you pick a hash length for identifiers, cache keys, content digests, or short codes, the hard question is not only “is the digest long enough for preimage security?” but “how many items can I store before two hashes collide by chance?” This calculator answers that sizing problem with the classic birthday bound. You supply the expected number of items and the maximum collision probability you will accept; it returns the smallest integer bit width that keeps the approximate pair-collision risk at or below that target, plus the implied hash space size and the approximate probability at that width.

Birthday bound and why hash length grows with the square of the set size

A uniform random hash of b bits maps every item into a space of size two to the power b. With only one item there is nothing to collide with, but as soon as you insert many values the number of unordered pairs grows like n choose two. Each pair collides with probability about one over the space size, so the expected number of colliding pairs is roughly n times n minus one over two times two to the b.

When that expectation is small, it is also a good approximation of the probability of at least one collision. Rearranging for a target probability p yields the closed sizing rule bits equals the ceiling of log base two of n times n minus one over two p. Equivalently, bits is about twice the log of n minus the log of p, minus one.

That square-root structure is the famous birthday paradox in engineering clothes: to keep collisions rare while holding a billion items you need far more than thirty bits of hash, and cryptographic collision resistance against an adversary who can try two to the sixty-four hashes classically pushes designers toward one-hundred-twenty-eight-bit or larger digests.

This tool uses the birthday bound approximation only—it does not model non-uniform hashes, truncated HMAC constructions, or multi-collision attacks beyond the basic pair bound—so treat the answer as a planning lower bound for random-looking digests, then add margin for implementation quirks and threat models that go beyond chance collisions.

What you can do with it

Identifier and short-code length planning

Product engineers size truncated hash or random ID bit widths so expected collisions among projected user or object counts stay under a written risk budget.

Cache keys and content digests

Platform teams pick digest lengths for caches and deduplication indexes by sweeping item counts and target probabilities instead of guessing round numbers.

Teaching the birthday bound

Instructors and interview prep tools demonstrate why collision risk scales with n squared and recover classic sixty-four-bit classroom thresholds deterministically.

FAQ

Is the hash bits calculator free?

The browser tool runs free on your device.

Does this replace a cryptographic security review?

No. It sizes chance pair collisions for uniform hashes only. Algorithm choice, truncation, adversarial collision search, and preimage strength still need a separate security analysis.

Why do hash collisions appear sooner than expected?

Because what matters is the number of pairs, not the number of items. Pairs grow roughly with the square of the item count, and each pair can collide, so the risk rises much faster than the count does. This is the birthday paradox.

Does the result hold for any hash function?

It assumes a uniform, random-looking hash and the basic pair bound. It does not model uneven hashes, truncated keyed hashes or multi-collision attacks, so treat it as a planning floor and add margin for your own threat model.

How much does doubling the items change the bits needed?

By about two bits. The bits needed are roughly twice the base-2 logarithm of the item count, minus the logarithm of your target probability, minus one, so each doubling of items adds close to two bits.

Related tools

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/dev/hash-bits-for-collision

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/dev/hash-bits-for-collision \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"items":1000000,"max_probability":0.000001}'

const res = await fetch("https://api.kit.forhosting.com/dev/hash-bits-for-collision", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "items": 1000000,
    "max_probability": 0.000001
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/dev/hash-bits-for-collision",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "items": 1000000,
    "max_probability": 0.000001
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/dev/hash-bits-for-collision", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"items":1000000,"max_probability":0.000001}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"items":1000000,"max_probability":0.000001}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/dev/hash-bits-for-collision", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "items": 1000000,
  "max_probability": 0.000001
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "dev.hash_bits_for_collision",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Technical notes

The same pure arithmetic runs free in the browser and as a billed API item, so teaching demos, design docs, and automation scripts share one deterministic contract with no sampling noise and no language model.

Input contract, validation rules, and response fields

Example: one million items with a target of one in a million yields on the order of fifty-nine bits and a hash space of two to that power. Classic classroom checks such as roughly four billion items at fifty percent collision risk recover the familiar sixty-four-bit figure. POST a JSON body with two required fields. items is a positive integer from one through one quadrillion (one times ten to the fifteen) describing how many values you expect to hash or store; aliases n, count, and num_items are accepted. max_probability is a finite number strictly between zero and one giving the largest collision probability you will tolerate under the bound; aliases p, probability, target_probability, and max_collision_probability work the same way. Missing fields, non-integers for items, non-finite probabilities, zero or negative counts, probabilities of zero or one or outside the published range all fail with invalid_input and are not billed. On success the response echoes items and max_probability, returns bits_needed as the smallest non-negative integer bit width, approximate_collision_probability as the birthday-bound estimate at that width (using one minus exp of minus lambda when lambda is not tiny), hash_space as the string two caret bits_needed, and a short formula string documenting the sizing rule.

When to use the calculator, pricing, and honest limits of the model

Use the free browser tool while drafting identifier schemes, choosing truncated hash lengths for URLs or database keys, or teaching why doubling the set size costs about one extra bit rather than zero. The model assumes ideal uniform independent hashes and the standard pair birthday approximation; it will not warn you about structured inputs that break uniformity, about second-preimage or length-extension issues, or about adversarial collision search that is cheaper than brute force for a broken hash family. Each successful request is one billable item at $0.002; failed validation does not consume balance. Always interpret bits_needed as “how wide must a random-looking digest be so that chance pair collisions among n items stay under p,” then validate the actual algorithm and truncation policy separately.

Technical questions

How do I calculate hash bits for collision resistance?

Send integers items (or n) and a max_probability p strictly between 0 and 1. The API returns bits_needed = ceil(log2(n*(n-1)/(2*p))) under the birthday bound, plus approximate probability and hash_space.

What formula does the birthday bound use?

Collision probability is approximated as n(n-1)/(2·2^b). Solving for the smallest integer b that keeps that value at or below your target p yields the bits_needed field.

What if items is 1?

With a single item there is no pair to collide, so bits_needed is 0 and approximate_collision_probability is 0. Counts below 1 are rejected as invalid_input.

Read the full KIT documentation →

Run — free