Hexagonal Miller direction indices to Miller-Bravais indices and back:
[uvw]⇔[UVTW]

[ u: v: w: ]

[ U: V: T: W: ]

Hexagonal Miller plane indices to Miller-Bravais indices and back:
(hkl)⇔(hkil)

( h: k: l: )

( h: k: i: l: )

Angle between two cubic directions:
[u1 v1 w1] ∠ [u2 v2 w2]

[ u1: v1: w1: ] [ u2: v2: w2: ]

cos(θ):  θ(°):  θ(rad): 

Angle between two hexagonal directions:
[U1 V1 T1 W1] ∠ [U2 V2 T1 W2]

a: c:

[ U1: V1: T1: W1: ] [ U2: V2: T2: W2: ]

cos(θ): θ(°): θ(rad):

Cubic lattice plane on which a given crystallographic direction is orthogonal:
(hkl) ⊥ [uvw]

( h: k: l: )

[ u: v: w: ]

Approximate hexagonal lattice plane on which a given crystallographic direction is orthogonal:
(hkl) ⊥ [uvw]

a: c:

( h: k: l: )

[ u: v: w: ]

This tool was written by Albes Koxhaj.