The maximum extent of a vibration or oscillation, measured from its equilibrium.Amplitude is the maximum displacement of a wave or oscillation from its equilibrium position. For a sound wave, amplitude corresponds to loudness; for a light wave, it relates to brightness; for a seismic wave, it determines the strength of shaking. Amplitude is a fundamental measure of the energy carried by a wave, as the energy is proportional to the square of the amplitude.
The concept of amplitude has been used since ancient times to describe the size of vibrations, but it was formalized in the 17th century by Galileo Galilei and later by Isaac Newton in their studies of pendulums and waves. In the 20th century, quantum mechanics extended the idea to probability amplitudes.
In a mechanical wave, such as a vibrating string or a water wave, amplitude is the distance from the rest position to the crest or trough. In quantum mechanics, the amplitude of a wave function is related to the probability of finding a particle in a given state. Larger amplitudes mean more energy and more pronounced effects, whether that is a louder sound or a stronger signal in a detector.
Amplitude is used in everything from audio engineering to set volume levels, to seismology to measure earthquake magnitudes, and in gravitational wave detectors to quantify the tiny ripples in spacetime.
In gravitational wave astronomy, the amplitude of a wave from a merging black hole pair is so small that it stretches the entire Earth by less than the width of a proton.
| ψ | variable | perturbation amplitude — wave function |
| A | variable | initial amplitude — amplitude |
| ω_I | variable | imaginary part of frequency (decay rate) — decay rate per second |
| ω_R | variable | real part of frequency (oscillation frequency) — angular frequency per second |
| φ | variable | phase offset — phase |
| F | variable | value of the decaying quantity at position x — amplitude varies |
| F_0 | variable | initial value at x = 0 — amplitude varies |
| x | variable | independent variable (position, time, etc.) — position metre |
| α | variable | decay constant (rate of decay per unit x) — decay constant per metre |
| P(k) | variable | Perturbed power spectrum — power spectrum cubic metre |
| P_0(k) | variable | Background power spectrum — power spectrum cubic metre |
| A | variable | Amplitude of the bump — amplitude |
| k | variable | Wavenumber — wavenumber per metre |
| k_0 | variable | Central wavenumber of the bump — wavenumber per metre |
| σ | variable | Width of the bump in log-k — width |
| exp | operator | Exponential function — exponential |
| log | operator | Natural logarithm — logarithm |
| ω | variable | angular frequency — angular frequency radian per second |
| k | variable | spring constant — spring constant newton per metre |
| m | variable | mass — mass kilogram |
| A | variable | amplitude — amplitude metre |
| E | variable | total energy — energy joule |
| √ | operator | square root operation — square root |
| A | variable | Polarization vector — polarization vector |
| Δ | variable | Amplitude of the field — amplitude volt per metre |
| e_x | variable | Unit vector along x-axis — unit vector |
| e_y | variable | Unit vector along y-axis — unit vector |
| i | operator | Complex number with square -1 — imaginary unit |
| x | variable | input point — input variable |
| x' | variable | another input point — input variable |
| σ | variable | signal amplitude — amplitude |
| ℓ | variable | length scale — length scale |
| exp | operator | raises e to the given power — exponential function |
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