length — from formula anatomyLength is a measure of the spatial extent of an object or the distance between two points. In physics, it is one of the seven base quantities in the International System of Units (SI), with the meter as its unit. Length appears in nearly every formula, from simple kinematics (distance = speed × time) to the wavelength of light and the size of a system in thermodynamics.
Length measurement is as old as civilization; the meter was introduced during the French Revolution (1790s) as a fraction of the Earth's meridian. The current definition based on the speed of light was adopted in 1983.
Length is defined operationally: it is what a ruler measures. In modern physics, the meter is defined by the distance light travels in a vacuum in 1/299,792,458 of a second, tying length to the speed of light. In geometry and calculus, length can be generalized to arc length along curves, computed via integrals.
Essential for engineering, construction, navigation, and all experimental physics — from measuring particle trajectories to astronomical distances.
The Planck length (about 1.6 × 10⁻³⁵ meters) is the smallest meaningful length in quantum gravity, below which our current laws of physics break down.
| V | variable | Potential energy — potential energy joule |
| r | variable | Radial distance from source — distance metre |
| g | variable | Coupling strength (not a universal constant) joule metre |
| λ | variable | Screening length (range of interaction) — length metre |
| Δφ | variable | Phase shift — phase shift radian |
| λ | variable | Wavelength of light — wavelength metre |
| Δn | variable | Change in refractive index — refractive index change |
| L | variable | Path length through medium — length metre |
| r | variable | distance between two points — distance metre |
| ν | variable | smoothness parameter |
| l | variable | length scale parameter — length metre |
| σ | variable | variance amplitude — variance square metre |
| Γ | operator | Gamma function, generalizes factorial — gamma function |
| K_ν | operator | Modified Bessel function of the second kind of order ν — modified bessel function second kind |
| P | variable | orbital period — period second |
| a | variable | semi-major axis of the orbit — length metre |
| M | variable | mass of the central body — mass kilogram |
| G | constant | constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| sqrt | operator | takes the square root — square root |