Quaternion Multiplication Calculator

Calculate the Hamilton product of two quaternions with detailed breakdown

Input Quaternions

Quaternion Q1

w

x (x)

y (y)

z (z)

Quaternion Q2

w

x (x)

y (y)

z (z)

Results

Q1 * Q2 =

1.0000i

Q2 * Q1 =

1.0000i

These quaternions commute (Q1*Q2 = Q2*Q1)

Component Values (Q1 * Q2)

w component

0.000000

x component (i)

1.000000

y component (j)

0.000000

z component (k)

0.000000

Hamilton Product Formula

For q1 = (w1, x1, y1, z1) and q2 = (w2, x2, y2, z2):

w = w1*w2 - x1*x2 - y1*y2 - z1*z2
x = w1*x2 + x1*w2 + y1*z2 - z1*y2
y = w1*y2 - x1*z2 + y1*w2 + z1*x2
z = w1*z2 + x1*y2 - y1*x2 + z1*w2

Based on: i^2 = j^2 = k^2 = ijk = -1