I recently derived a matrix which I believe to be the metric tensor in spherical polar coordinates in 3-D. Here were the components of the tensor that I derived. I will show my work afterwards: g11 = sin2(ø) + cos2(θ) g12 = -rsin(θ)cos(θ) g13 = rsin(ø)cos(ø) g21 = -rsin(θ)cos(θ) g22 = r2sin2(ø) + r2sin2(θ) g23 = 0 g31 = rsin(ø)cos(ø) g32 = 0 g33 = r2cos2(ø) The above is what I derived, but when I tried to verify to see if my answer was correct by checking various websites, I did not see any site have what I derived. Here is my work: The axes were: x1 = r x2 = θ x3 = ø The vector that I differentiated was: <rcos(θ)sin(ø) , rsin(θ)sin(ø) , rcos(θ)> I then differentiated the vector with respect to the various axes in order to derive my tangential basis vectors. Here were my basis vectors: er = <cos(θ)sin(ø) , sin(θ)sin(ø), cos(θ)> eθ = <-rsin(θ)sin(ø), rcos(θ)sin(ø) , -rsin(θ)> eø = <rcos(θ)cos(ø), rsin(θ)cos(ø) , 0> Finally, I did the dot product with these basis vectors to derive the components of my metric tensor. That is how I got what I derived, but I don't see any confirmation of this online. Can anyone please either verify if I am right with this metric tensor or tell me where I went wrong?