Angular momentum converter
Convert angular momentum between SI units and multiples of ħ, the quantum that everything spinning comes in.
That's 1,000,000,000,000,000,000,000,000,000,000,000× as much as a rotating molecule, while a spinning bicycle wheel is 3× more. That is about 9.483×10³³ quanta of ħ.
What it means
How much spin is that?
Angular momentum has the same dimensions as action, which is why the same constant, ħ, quantizes both.
Every unit
Your angular momentum in every unit
Learn
Three things worth knowing
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ħ = h ÷ 2π
The reduced Planck constant is 1.055 × 10⁻³⁴ J·s. Spin comes in half-integer multiples of it, which is what makes electrons obey the exclusion principle that keeps atoms from collapsing into one another.
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Conserved, always
Angular momentum is conserved because space looks the same in every direction. That is Noether’s theorem, and it is why a skater spins faster with their arms in.
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Not the same as moment of inertia
Angular momentum is inertia times angular velocity: L = Iω. The inertia alone (kg·m²) says nothing about how fast anything is turning.
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Popular angular momentum conversions
Background
About angular momentum
Angular momentum is what keeps a bicycle upright and a planet in orbit. In SI it is kg·m²/s, identical in dimensions to the joule-second of action.
At the quantum scale it comes in steps of ħ = 1.055 × 10⁻³⁴ J·s. An electron carries exactly ħ/2 of spin — not approximately, exactly.