Work

In physics, work refers to the dot product of force and distance vectors .

$W={\mathbf {F}}\cdot {\mathbf {d}}$

Or:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W = Fd \cos\theta}

Where θ is the angle that separates the vectors. The second form of the equation is the expanded form of the "dot product" in the first equation. In physics, the dot product "a · b" (read "a dot b") can be rewritten as "|a| |b| cos θ".

When the force is not constant, the correct expression uses integration:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \bold{F} \cdot \mathrm{d}\bold{s}}

Work is a transfer of energy; if W is positive, there is a transfer of energy to the system, and if W is negative there is a transfer of energy from the system.

Its units are that of force multiplied by distance, in SI this is Newton · Meter, or Joule. The aberrant unit kWh (kilowatt-hour) is sometimes used; this unit is the product of kilowatt, or 1,000 Watts (Joules per second), and hour, or 3,600 seconds.