# Joule-second

The joule-second (J s, or J∙s) is the mathematical product of an SI Derived Unit, the joule (J), and an SI Base Unit, the second (s). The joule-second describes the amount of action occurring in a physical system through a summation of energy (or heat, or work) over time. In mathematical terms, this summation of energy means that the quantity of energy becomes integrated over time.

## Base units

In SI base units the joule-second becomes kilogram-meters squared-per second or kg∙m2∙ s−1. Dimensional Analysis of the joule-second yields M L2 T−1. Note the denominator of seconds (s) in the base units.

## Confusion with joules per second

The joule-second should not be confused with the physical process of joules per second (J/s). In physical processes, when the unit of time appears in the denominator of a ratio, the described process occurs at a rate. For example, in discussions about speed, an object like a car travels a known distance of kilometers spread over a known number of seconds, and the car’s rate of speed becomes kilometers per second (km/s). In physics, work per time describes a system’s power; defined by the units of Watts (J/s), or joules per second.

## Other uses

The joule-second also appears as the unit of measure in classical mechanics for the angular momentum of a rotating object, and in quantum mechanics within the definition of Planck's constant. Angular momentum is the product of an object’s moment of inertia, in units of kg∙m2 and its rotational velocity in units of m∙s−1∙m−1, or simply s−1 (i.e., Hz). This product of moment of inertia and rotational velocity yields kg∙m2∙ s−1 or the joule-second. Planck's constant represents the energy of a wave, in units of joule, divided by the frequency of that wave, in units of s−1. This quotient of energy and frequency also yields the joule-second (J∙s).