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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In vector calculus, the surface gradient is a vector differential operator that is similar to the conventional gradient. The distinction is that the surface gradient takes effect along a surface.For a surface S in a scalar field u, the surface gradient is defined and notated as nabla_S u = nabla u - mathbf{hat n} (mathbf{hat n} cdot nabla u) where mathbf{hat n} is a unit normal to the surface. Examining the definition shows that the surface gradient is the (conventional) gradient with the component normal to the surface removed (subtracted), hence this gradient is tangent to the surface.