The change in position of an object from its initial point.Displacement is the vector quantity that describes the change in position of an object from its initial point to its final point. Unlike distance, which is a scalar measuring the total path length traveled, displacement only cares about the straight-line separation between start and end, including direction. It is a fundamental concept in kinematics, forming the basis for defining velocity and acceleration, and it plays a central role in mechanics, wave theory, and even electromagnetism where it appears in the displacement current.
The concept of displacement as a vector was formalized in the 19th century, building on earlier work by Galileo and Newton on motion. The term 'displacement' in its modern sense became standard with the development of vector analysis by Hamilton and Gibbs in the late 1800s.
Displacement is calculated as Δr = r_final - r_initial, where r is the position vector. It obeys vector addition, so displacements can be combined by adding their components. In calculus, instantaneous velocity is the time derivative of displacement, and acceleration is the second derivative. In oscillatory systems, displacement from equilibrium is the key variable, as in Hooke's law F = -kx, where x is the displacement.
Displacement is used everywhere from engineering (measuring structural deformation) to seismology (tracking ground motion during earthquakes) and GPS navigation (calculating position changes). In fluid dynamics, displacement thickness describes how a boundary layer pushes the outer flow outward.
In a closed loop, the total displacement is always zero, regardless of the distance traveled — which is why a hiker who walks 10 kilometers in a circle ends up with zero displacement from the starting point.
| a | variable | acceleration — acceleration metre per second squared |
| f | variable | frequency — frequency hertz |
| x | variable | displacement from equilibrium — displacement metre |
| x | variable | Displacement from equilibrium — displacement metre |
| t | variable | Time — time second |
| F | variable | External driving force per unit mass — force per unit mass metre per second squared |
| \omega | constant | Characteristic oscillation frequency of the system — angular frequency = varies radian per second |
| \ddot{x} | operator | Second derivative with respect to time — second time derivative |
| h | variable | displacement of the oscillator — displacement metre |
| Ξ | variable | damping coefficient — damping coefficient per second |
| ω | variable | angular frequency of the undamped oscillator — angular frequency radian per second |
| h'' | operator | second derivative of h with respect to time — second time derivative |
| h' | operator | first derivative of h with respect to time — first time derivative |
