The weak mixing angle or Weinberg angle is a parameter in the Weinberg–Salam theory (by Steven Weinberg and Abdus Salam) of the electroweak interaction, part of the Standard Model of particle physics, and is usually denoted as θ_W. It is the angle by which spontaneous symmetry breaking rotates the original W⁰
and B⁰
vector boson plane, producing as a result the Z⁰
 boson, and the photon. Its measured value is slightly below 30°, but also varies, very slightly increasing, depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for.

The algebraic formula for the combination of the W⁰
and B⁰
vector bosons (i.e. 'mixing') that simultaneously produces the massive Z⁰
boson and the massless photon (γ) is expressed by the formula

     ${\displaystyle {\begin{pmatrix}\gamma ~\\{\textsf {Z}}^{0}\end{pmatrix}}={\begin{pmatrix}\quad \cos \theta _{\textsf {w}}&\sin \theta _{\textsf {w}}\\-\sin \theta _{\textsf {w}}&\cos \theta _{\textsf {w}}\end{pmatrix}}{\begin{pmatrix}{\textsf {B}}^{0}\\{\textsf {W}}^{0}\end{pmatrix}}.}$

The weak mixing angle also gives the relationship between the masses of the W and Z bosons (denoted as m_W and m_Z),

     ${\displaystyle m_{\textsf {Z}}={\frac {m_{\textsf {W}}}{\,\cos \theta _{\textsf {w}}}}\,.}$

The angle can be expressed in terms of the SU(2)_L and U(1)_Y couplings (weak isospin g and weak hypercharge g′, respectively),

     ${\displaystyle \cos \theta _{\textsf {w}}={\frac {\quad g~}{\ {\sqrt {g^{2}+g'^{\ 2}~}}\ }}\quad }$ and ${\displaystyle \quad \sin \theta _{\textsf {w}}={\frac {\quad g'~}{\ {\sqrt {g^{2}+g'^{\ 2}~}}\ }}~.}$

The electric charge is then expressible in terms of it, e = g sin θ_w = g′ cos θ_w (refer to the figure).