The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements d s_N, d s_T, and d s_B along the normal, tangent, and binormal vectors respectively, is defined as the quantity d s_N | = | sqrt(d s_T^2 + d s_B^2) | = | sqrt(κ^2 + τ^2)d s where κ is the curvature and τ is the torsion.

curvature | Gaussian curvature | Lancret equation | space curve | torsion