What it does
A spinner is a fair way to choose at random, as long as you know how big each part is. On a spinner the chance of landing on a sector is its angle ÷ 360°: a 90° sector comes up a quarter of the time. This page lets you design your own spinner and then test it:
- set up to six sectors by their angles, and see each probability as a fraction and a decimal,
- spin once (with an animated pointer), or 10 or 1 000 times at once,
- compare the share of landings with the theory in a table and a bar chart, where a black mark shows each probability,
- at the Class 12 level, give each sector a number of points and get the expected score per spin, E(X) = Σ P × points, next to the average your spins actually scored.
It goes with the Class 9 maths chapter on probability (experiments, outcomes and chance), Class 10 probability, and Class 12 random variables and expected value.
For listing every outcome of dice, coins and cards, use the sample space builder; for several stages one after another, draw a probability tree. Randomness that builds up over many trials is also behind radioactive decay dice.
How to use it
- Under Design the sectors type each sector’s angle in degrees. Add a sector (up to six) or remove one with ×.
- If the angles do not add up to 360°, the page still shares the circle in proportion and says so; Fit to 360° rounds them so they do. Make all equal gives a fair spinner.
- Press Spin once to watch the pointer, or Spin 10 and Spin 1 000 to run many spins quickly. Clear the tally starts the count again.
- Read Theory against experiment: the “Share” column and the bars are what happened; the “P (theory)” column and the black marks are what should happen in the long run.
- Switch to Class 12 to show a points box for each sector and the expected value.
A worked example
The page starts with Red 120°, Blue 120°, Green 90° and Yellow 30°. The probabilities are 120/360 = 1/3, 1/3, 90/360 = 1/4 and 30/360 = 1/12, and they add up to 1.
Spin 10 times and the shares can be far off (Yellow might not come up at all). Spin 1 000 more and each share is usually within a few percentage points of its probability.
At Class 12 level the points are 1, 2, 5 and 10. The expected score is 1/3 × 1 + 1/3 × 2 + 1/4 × 5 + 1/12 × 10 = 0.333 + 0.667 + 1.25 + 0.833 = 3.083 points per spin.
Tips
- The probability of not landing on a sector is 1 minus its probability: (360° − angle) ÷ 360°.
- To make a sector with probability p, give it p × 360°: 1/3 needs 120°, 2/5 needs 144°.
- Experimental probability never has to equal the theory exactly; it gets closer, on the whole, as the number of spins grows.
Check yourself
Four fresh questions each time: probability from an angle, angle from a probability, “not” a sector, and an expected score. You can type a fraction like 1/4 or a decimal. Nothing is saved.
FAQ
Are the spins really random? They come from a pseudo-random number generator in your browser, which is good enough for experiments like these. Nothing is sent anywhere.
Is this from the NCERT book? It covers the same topics with fibub’s own spinner. fibub is not part of NCERT.
Where the numbers come from
- Geometric probability (sector angle ÷ 360°), experimental probability and expected value E(X) = Σ p·x are standard school maths. Written for fibub; spins use a seeded pseudo-random generator in the browser.
- Checked by hand (120°, 120°, 90°, 30° sectors with 1, 2, 5, 10 points: probabilities 1/3, 1/3, 1/4, 1/12 and expected score 3.083) and by 200 000 seeded spins landing within 1 % of each probability.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.