Let γ : [0, 1] → S 2 be a non-degenerate curve in R 3 , that is to say, det γ(θ), γ ′ (θ), γ ′′ (θ) = 0. For each θ ∈ [0, 1], let V θ = γ(θ) ⊥ and let π θ : R 3 → V θ be the orthogonal projections. We prove that if A ⊂ R 3 is a Borel set, then for a.e. θ ∈ [0, 1] we have dim(π θ (A)) = min{2, dimA}.More generally, we prove an exceptional set estimate. For A ⊂ R 3 and 0 ≤ s ≤ 2, define Es(A) := {θ ∈ [0, 1] : dim(π θ (A)) < s}. We have dim(Es(A)) ≤ 1 + s − dim(A). We also prove that if dim(A) > 2, then for a.e. θ ∈ [0, 1] we have H 2 (π θ (A)) > 0.2020 Mathematics Subject Classification. 42B15, 42B20.