perdegree

Perdegree is a term used to describe the rate of change of a quantity with respect to angular position measured in degrees. It denotes how much a quantity changes per one degree of rotation.

Formalism: If Q is a function of the angle θ and θ is measured in degrees, the perdegree of Q with respect to θ is the derivative dQ/dθ, with units of Q per degree. If θ is in radians, the per-degree rate relates via dQ/dθ_deg = dQ/dθ_rad × (π/180). To avoid ambiguity, one should specify that θ is in degrees when reporting perdegree values.

Examples and usage: If Q(θ) = 2θ and θ is in degrees, then the perdegree rate is dQ/dθ = 2, meaning Q increases by 2 units per degree. In robotics and servo systems, a sensor output that depends on rotor angle can be described by its perdegree sensitivity, providing a straightforward measure of how the signal changes with each degree of rotation.

Applications and limitations: Perdegree is not an official SI unit and has no formal metrological status. It is used informally in technical documentation or analyses where angular position is naturally expressed in degrees. For precision and interoperability, practitioners typically convert to per-radian figures or explicitly state the degree convention and unit. See also derivative, angular position, degrees, radians, and calibration.