MathBench

Spinner Wheel

Type your options, spin, and let an unbiased random pick — dressed up in a satisfying spin — make the decision. Equal odds for every wedge, and the fairness is inspectable.

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Click “Spin the wheel”.

How this calculator works

Each line in the box becomes an equal wedge of the wheel. Clicking spin does two things in a strict order: first the winner is drawn from an unbiased random number generator; then, and only then, the wheel is animated through four to six full rotations to stop with the pointer on that wedge. The animation is presentation — the selection would be equally fair with no wheel at all, but decisions go down easier with a little suspense.

Repeat a line to weight an option (two lines of "Pizza" out of ten total gives pizza a 20% wedge share and a 20% chance — the geometry and the probability always agree). Tick "remove winner" for raffle-style drawing without replacement. For the skeptical, the wheel's SVG carries data-winner-index and data-final-rotation attributes after each spin — check that the pointer's landing wedge matches the drawn index.

The formula

P(any single entry) = 1/n        (n entries, equal wedges of 360°/n)
P(entry listed k times) = k/n

Winner index: unbiased integer in [0, n) via rejection sampling
Final rotation = 4–6 full turns + (360° − wedge-center angle)
  → pointer lands on the pre-drawn winner

Random integers come from crypto.getRandomValues (W3C Web Cryptography API) with the same rejection-sampling technique as our team picker — see that page for the modulo-bias explanation, and Knuth's The Art of Computer Programming Vol. 2 for the underlying theory of unbiased selection.

Worked example

With the default 8 dinner options on the wheel:

  1. Each wedge spans 360° ÷ 8 = 45°
  2. Each option's probability: 1/8 = 12.5%
  3. Suppose the RNG draws index 2 (Sushi): the wheel must stop with the pointer at 2 × 45 + 22.5 = 112.5° — so it rotates some whole number of turns plus 247.5°
  4. Expected waits: dinner picked in one spin, always — but if you spun repeatedly, each option would win about 125 times per 1,000 spins

Add a second "Pizza" line (9 entries): pizza's chance rises to 2/9 ≈ 22.2%, everything else drops to 1/9 ≈ 11.1%, and the wheel redraws to show exactly that.

Assumptions & tips

  • Weight with duplicate lines, openly. Weighting by repetition keeps the odds visible on the wheel itself — anyone can count wedges. Hidden weights are how spinner apps get accused of rigging.
  • Use remove-winner for gift exchanges. Spin once per prize; each winner leaves the wheel. The odds automatically follow the names-in-a-hat arithmetic.
  • Long labels get trimmed on the wheel but the result panel shows the full text. Keep entries short if the audience reads the wheel on a projector.
  • Decisions, not stakes. Cryptographic randomness or not, a browser wheel has no audit trail — run regulated drawings on systems built for them.
  • Need teams instead of one winner? The random team picker shares this page's RNG and splits the whole list at once.

Frequently asked questions

Is the spin actually random, or is the animation deciding?

The winner is chosen by the browser's cryptographic random number generator the instant you click — before the wheel moves — and the animation is then steered to land on that result. This is the honest architecture: a wheel that "decides" by where friction happens to stop it would depend on frame timing and be neither verifiable nor fair. The page exposes the chosen index in the wheel's data attributes, so you can confirm the pointer landed where the RNG said.

Does every entry really have the same chance?

Yes — each of n entries is selected with probability exactly 1/n, using rejection sampling to avoid modulo bias. The wedges are drawn equal-sized to match. If you want weighted odds, enter a name multiple times: two entries out of ten gives that name a 20 percent chance, and the math stays visible.

What is "remove winner after spin" for?

Drawing without replacement — raffle style. Each spin removes the winner from the wheel, so nobody wins twice and the remaining odds rise for everyone left. Ten entries becomes a sequence of picks at 1/10, 1/9, 1/8… which is exactly how names-from-a-hat behaves. Leave it off for repeatable decisions like "who buys coffee".

Can I use this for anything serious, like a customer giveaway?

The randomness is cryptographic quality, which is more than fair enough. What a browser page cannot give you is an audit trail — there is no server, no log, and no proof after the fact of who was on the wheel. For legally regulated drawings, use a system that records entries and results; for offices, classrooms, and streams, this is exactly the right tool.

Why does the wheel spin several times before stopping?

Pure theater, honestly labeled as such. The wheel turns four to six full rotations with an ease-out curve because a spin that snapped instantly to the answer would feel rigged even though it is not. The suspense is adjustable in no way whatsoever — that is part of the joke.

Sources

  1. Web Cryptography API — World Wide Web Consortium (W3C) Recommendation, 26 January 2017. §10.2.1, the getRandomValues method. w3.orgDefines crypto.getRandomValues, which draws the winning wedge index before the wheel starts moving, and requires it to return cryptographically random values — the standard behind this page's fairness claim.
  2. FIPS 186-5: Digital Signature Standard (DSS) — National Institute of Standards and Technology, 3 February 2023. Appendix A.4, Random Values Mod n. nvlpubs.nist.govContrasts modular reduction (A.4.1) with the discard method (A.4.2) — the standards-body basis for redrawing rather than reducing, which is what makes each wedge exactly 1/n rather than approximately so.
  3. Fast Random Integer Generation in an Interval — Daniel Lemire, ACM Transactions on Modeling and Computer Simulation, volume 29, number 1, pages 1–12, 2019. DOI 10.1145/3230636. arxiv.orgQuantifies the modulo bias that equal-looking wedges would otherwise hide, and the rejection bound used by this page's winner-drawing routine. Linked to the author's arXiv copy; the published version sits behind the ACM paywall.
  4. The Art of Computer Programming, Volume 2: Seminumerical Algorithms — Donald E. Knuth, 3rd edition, Addison-Wesley, 1997. §3.4.2, Random Sampling and Shuffling. The theory of unbiased selection named in this page's formula section, including sampling without replacement — the model behind the remove-winner option's 1/n, 1/(n−1), 1/(n−2) sequence. Cited bibliographically: no free full text to link.

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