Grad

360° = 2π (radian measure) = 400 grads.

Grads are more often seen in Europe than in the US. Radian measure is the purest mathematical measure of angle, being unitless; grads and degrees are equally arbitrary.

Short for the gradient of a quantity. In an orthogonal coordinate system with coordinates {u₁,u₂,u₃}, where a line element ds is given by

ds²=h₁² du₁² + h₂² du₂² + h₃² du₃²

grad φ = (1/h₁)(δ φ/δ u₁) i₁ + (1/h₂)(δ φ/δ u₂) i₂ +(1/h₃)(δ φ/δ u₃) i₃

In cartesian coordinates

{u₁,u₂,u₃} = {x,y,z}
{h₁,h₂,h₃} = {1,1,1}

'Grad' is usually represented by an triangle 'pointing' downwards

See also div.