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API · /birthdayparadox-api

Birthday Paradox API

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Birthday-paradox and collision-probability maths as an API, computed locally and deterministically. The probability endpoint computes the chance that at least two of n people share a birthday among d equally likely days, P = 1 − Π(1 − i/d), evaluated in log space for accuracy — the famous result that just 23 people give about a 50.7 % chance, 50 people about 97 % and 70 people about 99.9 %. The people-needed endpoint inverts it: the smallest group size to reach a target probability (23 for 50 %, 57 for 99 %), with the √(2·d·ln(1/(1−p))) approximation. The collision endpoint generalises the birthday bound to any space — pass a number of buckets or a hash size in bits — and returns the collision probability P ≈ 1 − e^(−n²/2d), the rule behind hash collisions and UUID-uniqueness estimates, where a 50 % chance needs roughly 1.177·√d items. Days and buckets default to 365. Everything is computed locally and deterministically, so it is instant and private. Ideal for probability-education, security, cryptography, hashing, data-engineering and statistics app developers, collision-risk and birthday-problem tools, and teaching material. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the birthday/collision probability; for full distributions use a probability API.

#birthday-paradox #collision #probability #hashing #security #developer-tools
api.oanor.com/birthdayparadox-api
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Machine-readable spec so AI agents can integrate this API.

/api/birthdayparadox-api/openapi.json
/api/birthdayparadox-api/llms.txt

Discovery: GET /api/index.json lists every API.

API health

healthy
Uptime
100.00%
Server probes · 24h
Avg latency
84 ms
Server probes · 24h
Subscribers
4,858
active
Total calls
28
last 7 days
status Full status page → · 32 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

Free

Free

  • 5,050 calls / month
  • 2 requests / second
  • Hard cap (429 above quota, no overage)
  • 5,050 calls/month
  • 2 req/sec
  • Probability + people-needed + collision
  • No credit card
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Starter

€4.05 /month

  • 50,500 calls / month
  • 6 requests / second
  • Hard cap (429 above quota, no overage)
  • 50,500 calls/month
  • 6 req/sec
  • Custom day/bucket space, hash bits
  • Email support
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Pro

€11.30 /month

  • 232,000 calls / month
  • 15 requests / second
  • Hard cap (429 above quota, no overage)
  • 232,000 calls/month
  • 15 req/sec
  • Hash-collision & teaching pipelines
  • Priority support
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Mega

€37.00 /month

  • 1,295,000 calls / month
  • 40 requests / second
  • Hard cap (429 above quota, no overage)
  • 1,295,000 calls/month
  • 40 req/sec
  • Platform scale
  • Dedicated SLA
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Related APIs

Other APIs with overlapping tags.

Momentum & Collision API

Linear momentum, impulse and one-dimensional collisions as an API, computed locally and deterministically. The momentum endpoint computes the linear momentum p = m·v of a moving body, with its kinetic energy, and solves for whichever of the mass, velocity or momentum you leave out. The impulse endpoint applies the impulse-momentum theorem, J = F·Δt = m·Δv = Δp: from a force and a time it gives the impulse and, with a mass, the change in velocity; or from a mass and a velocity change it gives the impulse and the average force over a contact time — the physics of a bat hitting a ball or an airbag softening a crash. The collision endpoint solves a head-on collision between two bodies using conservation of momentum and a coefficient of restitution: e = 1 for a perfectly elastic collision (kinetic energy conserved), e = 0 for a perfectly inelastic one (the bodies stick together), or any value between for a partially inelastic collision — returning both final velocities, the conserved total momentum, the kinetic energy before and after, and the energy lost. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education and simulation tools, game and ballistics engines, vehicle-crash and sports apps, and engineering-dynamics software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is linear momentum and collisions; for rotational angular momentum and flywheel energy use a flywheel API.

api.oanor.com/momentum-api

Dice Probability API

Tabletop dice-probability maths as an API, computed locally and deterministically and exactly — the odds behind the rolls, not the rolls themselves. The advantage endpoint gives the D&D-style chances of beating a target on a d20 (or any die) rolling normally, with advantage (roll twice, keep the higher) or with disadvantage (keep the lower): needing an 11+ is 50 % normally, 75 % with advantage and 25 % with disadvantage, and it reports the average roll — advantage lifts a d20 from 10.5 to about 13.8. The pool endpoint handles success-counting systems (World of Darkness, Shadowrun): for a pool of dice that succeed on a face at or above a threshold it gives the chance per die, the expected number of successes and the exact binomial probability of getting exactly, or at least, a target number — six d10s succeeding on 7+ average 2.4 successes with a 45.6 % chance of three or more. The exploding endpoint gives the mean of an exploding ("acing", open-ended) die that re-rolls and adds on its maximum face — a d6 averages 4.2 instead of 3.5. Everything is computed locally and deterministically, so it is instant and private. Ideal for tabletop, virtual-tabletop, game-design and TTRPG app developers, odds-and-probability helpers, and game-master tools. Pure local computation — no key, no third-party service, instant. Exact maths, no simulation. Live, nothing stored. 3 compute endpoints. For random rolls use a dice-roller API.

api.oanor.com/dicepool-api

Betting Odds API

Betting-odds maths as an API, computed locally and deterministically. The convert endpoint translates a price between every format used by bookmakers — decimal (European), fractional (UK), American (moneyline) and the implied probability — give it any one and it returns all the others, with the implied probability that the odds represent (1 ÷ decimal). The payout endpoint computes the profit and total return for a stake at given decimal or American odds. The parlay endpoint combines several decimal-odds selections into one accumulator by multiplying them, returning the combined odds, the implied probability and the payout for a stake — every leg must win, so the payout grows fast while the probability shrinks. Decimal odds are the total return per unit staked, American odds are at least +100 for an underdog or −100 or lower for a favourite, and fractional odds look like 5/2. Everything is computed locally and deterministically, so it is instant and private. Ideal for sports-betting, fantasy, odds-comparison and gaming app developers, bet-slip and value tools, and probability education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is odds conversion; for probability distributions use a probability API.

api.oanor.com/odds-api

Probability API

Probability distributions and combinatorics as an API. The binomial endpoint gives the probability of exactly k successes in n trials (PMF), the cumulative probability up to k (CDF), and the mean, variance and standard deviation. The poisson endpoint does the same for the Poisson distribution from a rate λ. The normal endpoint computes the z-score, probability density, cumulative probability (CDF) and percentile for a value under a normal distribution with any mean and standard deviation — and runs in reverse, turning a probability into the value (the quantile / inverse CDF) and its z-score. The combinatorics endpoint computes combinations (nCr), permutations (nPr) and factorials with exact big-integer arithmetic. Everything is computed locally and deterministically, so it is instant and private. Ideal for data science and statistics, quality control and A/B-test planning, gaming and gambling odds, risk modelling, and statistics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 5 endpoints. This is probability theory; for descriptive statistics on a dataset use a statistics API and for general expression evaluation use a math API.

api.oanor.com/probability-api

Frequently asked questions

Quick answers about pricing, quotas, and integration.

How do I get an API key for Birthday Paradox API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Birthday Paradox API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Birthday Paradox API?
Free tier allows 1 request per second. Paid plans scale up to 50 requests per second on the Mega tier. Hard limits return HTTP 429 above the quota — no surprise overage charges.
How much does Birthday Paradox API cost?
Birthday Paradox API has a free tier with 100 calls / month. Paid plans start at €4.05 / month with higher quotas and faster rate limits.
Can I cancel my subscription anytime?
Yes. Plans are billed monthly and you can cancel anytime from your billing dashboard. No long-term contracts and no cancellation fee.
Is Birthday Paradox API GDPR-compliant?
All requests to Birthday Paradox API go through our EU-based gateway. Your upstream API key never leaves our server and no personal data is shared with the upstream provider beyond the request you send.

Pick an endpoint from the list on the left to see its details and try it.

Code snippets

Sign up to get an API key, then call any path under your slug.

curl https://api.oanor.com/birthdayparadox-api/SOME_PATH \
  -H "x-oanor-key: oanor_test_..."
const res = await fetch("https://api.oanor.com/birthdayparadox-api/SOME_PATH", {
  headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();
$ch = curl_init("https://api.oanor.com/birthdayparadox-api/SOME_PATH");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
$response = curl_exec($ch);
import requests
r = requests.get(
    "https://api.oanor.com/birthdayparadox-api/SOME_PATH",
    headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())

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