Stern-Gerlach Experiment

Measure a spin along a new axis and it snaps to up or down — never in between. The experiment that revealed quantum measurement and spin.

Stern-Gerlach ExperimentLive

spin measurement & projection

Controls

Presets

Analyzer angle θ (°)

Speed1×

Atoms prepared spin-up are measured along an axis tilted by θ. Quantum mechanics says each atom randomly comes out up or down, with probability cos²(θ/2) for up — never a fraction. At 90° it is a perfect coin flip; at 180° it always flips. The running tally converges to the Born-rule probability.

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Data Inspector

P(up) theory0.750

Measured up0.0%

Atoms1

Governing equation

P (↑) = cos^{2} \frac{θ}{2} = 0.750, P (↓) = sin^{2} \frac{θ}{2} = 0.250, θ = 6 0^{\circ}

Reading this result: Tilted by 60°, the analyzer still favors up: theory predicts P(up) = cos²(θ/2) ≈ 0.75, and the tally converges there.

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How it works

Atoms prepared spin-up are sent through an analyzer tilted by an angle θ. Each atom emerges up with probability cos²(θ/2) and down otherwise — a discrete, random outcome, not a smooth fraction. At 90° it is a fair coin flip; at 180° every atom flips. Running many atoms, the tally converges to the Born rule, the core of quantum measurement.

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Frequently asked questions

Is this Stern-Gerlach spin experiment tool really free?▾

Yes. Stern-Gerlach Experiment runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

Can I save or share my simulation?▾

Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.

How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.