AbstractFor an integer n ⩾ 1, a graph G has an n‐constant crossing number if, for any two good drawings ϕ and ϕ′ of G in the plane, μ(ϕ) ≡ μ(ϕ′) (mod n), where μ(ϕ) is the number of crossings in ϕ. We prove that, except for trivial cases, a graph G has n‐constant crossing number if and only if n = 2 and G is either Kp or Kq,r, where p, q, and r are odd.