Electroweak Mixing Angle Calculator

The electroweak mixing angle θW (also called the Weinberg angle) is a fundamental parameter of the Standard Model that describes how the electromagnetic and weak forces mix to produce the physically observed photon, W boson, and Z boson.

From the boson masses: cos(θW) = MW/MZ, where MW and MZ are the W and Z boson masses. Equivalently, sin²(θW) = 1 − cos²(θW). This calculator also supports computing θW directly from a given sin²θW value.

Using the measured on-shell boson masses (MW≈80.377 GeV, MZ≈91.1876 GeV), θW ≈ 28.18°, corresponding to sin²θW ≈ 0.2231. Different precision-physics renormalization schemes quote slightly different values, commonly around sin²θW ≈ 0.231.

In the Standard Model, the W and Z bosons acquire their masses through the Higgs mechanism, but with different couplings to the Higgs field, since the Z boson is a mixture of the original electroweak gauge bosons while the W boson is not. This mass difference is exactly what the mixing angle parameterizes.

It is often called the Weinberg angle after physicist Steven Weinberg, who together with Abdus Salam and Sheldon Glashow developed the unified electroweak theory in the 1960s and 1970s, work recognized with the 1979 Nobel Prize in Physics.

The 'from boson masses' mode directly reflects the physical definition (cos θW = MW/MZ), useful when you know the measured boson masses. The 'from sin²θW' mode is useful for coursework and problem sets that instead give a target sin²θW value and ask you to find the corresponding angle.

It sets the relative strength of the weak neutral current's coupling to different particle types, and determines how the original SU(2)×U(1) gauge bosons combine into the physically observed photon, W, and Z bosons. It is one of the most precisely measured Standard Model parameters.

Yes, like other Standard Model couplings, sin²θW runs (changes) slowly with the energy scale at which it is measured, due to quantum loop corrections, one reason different experiments and renormalization schemes quote slightly different numerical values.

It is one of the most precisely measured parameters in particle physics, determined to about 4-5 significant figures from a combination of collider measurements (Z-pole asymmetries, W mass measurements) and precision low-energy experiments.

Yes, together with the weak coupling constant, it determines the electromagnetic coupling (fine structure constant) through the relation e = g·sin(θW), directly connecting the unified electroweak coupling strengths to the more familiar electric charge.