An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight r −b for functions in $${\mathbb{R}^n}$$ . The exact Hardy constant c b  = c b (n) is found and generalized minimizers are given. The constant c b vanishes on a countable set of b, which extends the known case n = 2, b = 0 which corresponds to the trivial Hardy inequality in $${\mathbb{R}^2}$$ . Analogous inequalities are proved in the case c b  = 0 under constraints and, with error terms, for a bounded domain.