
related topics 
{math, energy, light} 
{math, number, function} 
{rate, high, increase} 
{ship, engine, design} 
{theory, work, human} 
{line, north, south} 
{style, bgcolor, rowspan} 

In physics and science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions (usually mass, length, time, electric charge, and temperature) which describe it; for example, speed has the dimension length / time, and may be measured in meters per second, miles per hour, or other units. Dimensional analysis is based on the fact that a physical law must be independent of the units used to measure the physical variables. A straightforward practical consequence is that any meaningful equation (and any inequality and inequation) must have the same dimensions in the left and right sides. Checking this is the basic way of performing dimensional analysis.
Dimensional analysis is routinely used to check the plausibility of derived equations and computations. It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena, and to categorize types of physical quantities and units based on their relations to or dependence on other units, or their dimensions if any.
The basic principle of dimensional analysis was known to Isaac Newton (1686) who referred to it as the "Great Principle of Similitude".^{[1]} The 19thcentury French mathematician Joseph Fourier made important contributions^{[2]} based on the idea that physical laws like F = ma should be independent of the units employed to measure the physical variables. This led to the conclusion that meaningful laws must be homogeneous equations in their various units of measurement, a result which was eventually formalized in the Buckingham π theorem. This theorem describes how every physically meaningful equation involving n variables can be equivalently rewritten as an equation of n − m dimensionless parameters, where m is the number of fundamental dimensions used. Furthermore, and most importantly, it provides a method for computing these dimensionless parameters from the given variables.
A dimensional equation can have the dimensions reduced or eliminated through nondimensionalization, which begins with dimensional analysis, and involves scaling quantities by characteristic units of a system or natural units of nature. This gives insight into the fundamental properties of the system, as illustrated in the examples below.
Contents
Full article ▸


related documents 
Dynamical system 
Lorentz transformation 
Quantum entanglement 
Quantum superposition 
Wave equation 
Statistical mechanics 
Mathematical formulation of quantum mechanics 
Symmetry 
Noether's theorem 
Platonic solid 
Shape of the Universe 
Kepler's laws of planetary motion 
List of relativistic equations 
Kinetic energy 
Proxima Centauri 
Variable star 
Wave 
Tau Ceti 
Gamma ray burst 
Nonlinear optics 
Phonon 
Phase transition 
Eclipse 
Event horizon 
Electric field 
Holographic principle 
Orbital resonance 
Longitude 
Galaxy formation and evolution 
Electromagnetic field 
