For a particle of spin- j the following uncertainty relation holds σ σ J x 2 + σ σ J y 2 + σ σ J z 2 ≥ ≥ j , where J l are angular momentum components. The relation can be derived from ⟨ ⟨ J x 2 + J y 2 + J z 2 ⟩ ⟩ = j ( j + 1 ) , and ⟨ ⟨ J x ⟩ ⟩ 2 + ⟨ ⟨ J y ⟩ ⟩ 2 + ⟨ ⟨ J z ⟩ ⟩ 2 ≤ ≤ j . The relation can be strengthened as σ σ J x 2 + σ σ J y 2 + F Q [ ϱ ϱ , J z ] / 4 ≥ ≥ j , where F Q [ ϱ ϱ , J z ] is the quantum Fisher information.