(1) In geometry, a unit of angle measurement. A full circle equals 360 degrees.

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(2) In mathematics, the degree is the highest exponent in a polynomial. For example the degree of $2x^3-4x^2+2$ equals three. NURBS geometry is fundamentally built from polynomials, meaning the concept carries over.

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(3) In NURBS geometry, degrees are used to classify the smoothness of a shape. A degree=1 curve is a polyline, degree=2 curves are used to represent conic sections such as ellipses and parabolas, while higher degrees are smoother still. The most common degrees are 1, 2, 3, and 5, but Rhino supports shapes with degrees up to 11.

Note that NURBS surfaces may have different degrees in their u and v directions.