  We determine the critical equation of state of the three-dimensional O(4)
universality class. We first consider the small-field expansion of the
effective potential (Helmholtz free energy). Then, we apply a systematic
approximation scheme based on polynomial parametric representations that are
valid in the whole critical regime, satisfy the correct analytic properties
(Griffiths' analyticity), take into account the Goldstone singularities at the
coexistence curve, and match the small-field expansion of the effective
potential. From the approximate representations of the equation of state, we
obtain estimates of several universal amplitude ratios.
  The three-dimensional O(4) universality class is expected to describe the
finite-temperature chiral transition of quantum chromodynamics with two light
flavors. Within this picture, the O(4) critical equation of state relates the
reduced temperature, the quark masses, and the condensates around T_c in the
limit of vanishing quark masses.
