The degree per second (symbolized deg/s or deg · s^{-1}) is a unit of angular (rotational) speed. This quantity can be defined in either of two senses: average or instantaneous.

Average angular speed is obtained by measuring the angle in degrees through which an object rotates in a certain number of seconds, and then dividing the total angle by the time. If *u*_{avg} represents the average angular speed of an object (in degrees per second) during a time interval *t* (in seconds), and the angle through which the object rotates in that time is equal to *q* (in degrees), then:

*u*_{avg} = *q* / *t*

Instantaneous angular speed is more difficult to intuit, because it involves an expression of motion over an "infinitely short" interval of time. Let *p* represent a specific point in time. Suppose an object is in rotational motion at about that time. The average angular speed can be measured over increasingly short time intervals centered at *p*, for example:

[*p*-4, *p*+4]

[*p*-3, *p*+3]

[*p*-2 , *p*+2]

[*p*-1, *p*+1]

[*p*-0.5, *p*+0.5]

[*p*-0.25, *p*+0.25]

.

.

.

[*p*-*x*, *p*+*x*]

.

.

.

where the added and subtracted numbers represent seconds. The instantaneous angular speed, *u*_{inst}, is the limit of the measured average speed as *x* approaches zero. This is a theoretical value, because it cannot be obtained except by inference from measurements made over progressively shorter time spans.

Also see angular degree, angular speed, angular velocity, radian per second, International System of Units (SI), and Table of Physical Units.

*This was last updated in*May 2008

*Posted by:*Margaret Rouse

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