Units in Physics (mechanical, electricity, magnetism, light and optics) including Si units.

April 28, 2007 by aaron

This is a reference list with notes of all SI and derived units in physics. The notes provide a brief explanation of some of the more confusing elements, but be warned that the full explanation could take many pages, and may be explained elsewhere on this website.

Physics has only 5 base units. (Plus the SI units Mole and Candela, but these are rarely used in Physics.)

Name Abbreviation (Symbol) Standard Unit Notes
Name Abbreviation (Symbol) Standard Unit Notes
Length l, x (for distances) Meter (m) A meter is defined as the distance light travels in a vacumm in \frac{1}{299 792 458} of a second (in physics it is customary to use metric measurements although the basic principles apply if you to use feet instead of meters)
Mass m, M (when used with measurements in meters) Kilogram (kg) A kilogram is defined as the weight of a specific platinum-iridium cylinder
Time t Second (s) Seconds are defined as 9,192,631,770 vibrations of radiation from a cesium atom
Temparature T Kelvin (K) A degree kelvin is defined as \frac{1}{273.16} of the distance between absolute 0 and the triple point of water
Electric Current I Ampere (A) An ampere is the amount of charge (C) passing through a surface per second, and is defined as the current which produces a force of 2*10^{-7} newtons per meter of length between two infinitely long, perfectly straight and parallel conductors with an infinitely small cross section separated by one meter in a vacuum..

Each of these base units is defined on fundamental constants, and all other units are based on these five units. At times it useful to break longer equations down to their most basic units to determine if the equation makes sense. The most common combinations of these basic units are given their own symbols and names. These common units are as follows.

Name (alphabetically) Abbreviation (Symbol) Unit – Derivation Notes
Name (alphabetically) Abbreviation (Symbol) Unit – Derivation Notes
Acceleration a \frac{\text{m}}{\text{s}^2} (meters per second squared) Acceleration is literally the rate of change of the rate of change of an object’s position.
Angle \theta,\varphi radian A radian is defined as the angle an arc length, equal to the circle’s radius, makes with the center of the circle.
Capacitance C Farad (F) \frac{\text{C}}{\text{V}} (Charge over the Potential)
Charge Q ), q ,e (of elementary particles) Coulomb (C) \text{A*s} (Amperes times seconds) Literally the charge is the amount of current that flows over the entire time period.
Density \rho \frac{\text{kg}}{\text{m}^3} Density is the amount of mass in every cubed unit length
Displacement s, d (distance), h (height) meters – m Displacement is the total change in length in any single direction. Sometimes it is used as the absolute change in distance –if you were walk all the way around the earth less one meter, your displacement would be one meter
Electric Field E \frac{\text{V}}{\text{m}} (Electric potential per meter) An electric field is the amount of electric potential over any given area.
Electric Flux \Phi_e \text{V*M}(Electric Potential time meters) Electric flux is the electric field through some area.
Electromotive Force (emf) \scr{E} or \epsilon Volt (V) Electromotive force is a potential difference in volts.
Electron Volt eV \text{e*J} The Electron Volt is the amount of energy change of a charge-field system when a charge of magnitude e is moved through a potential difference of 1V. It is used in place of the Joule (energy).
Energy E (total),U (potential),K (kinetic) Joule (J) kg * \frac{\text{m}^2}{\text{s}^2}
Entropy S \frac{\text{J}}{\text{K}}
Force F Newton (N) kg \frac{\text{m}}{\text{s}^2}, \frac{\text{J}}{\text{m}}
Frequency f,v Hertz (Hz) \frac{\text{cycles}}{\text{s}}
Heat Q Joule (J) Joule is used for work, heat and energy, but remember that Joule is a unit of energy not of energy transfer. This means that heat can have a Joule of energy, but can’t be measured in Newtons.
Magnetic Field B Tesla (T) \frac{\text{Wb}}{\text{m}^2}
Magnetic Flux \Phi_m Weber (Wb) \text{kg} \frac{\text{m}^2}{\text{A}} \text{s}^2
Momentum p \text{kg} \frac{\text{m}}{\text{s}}
Potential (Electric) V or \delta V Voltage (V) \frac{\text{J}}{\text{C}} Potential is the amount of excess charge. It can be compared with potential energy.
Power P, \scrP \frac{\text{j}}{\text{s}} Power is the amount of work done in any given time.
Pressure P Pascal (Pa) \frac{\text{N}}{\text{m}^2}
Resistance R Ohm \frac{\text{V}}{\text{A}} Resistance is the amount of energy that is lost in the transfer of energy through an object.
Torque \tau \text{N*m} Torque is usually shown with units N*m even though it is technically joules.
Velocity v \frac{\text{m}}{\text{s}} Velocity is the speed and direction of an object.
Wavelength \lambda Meter (m)
Work W Joule (J) \text{N*m} Work is the amount of force outputted over some distance.

For of the derived units such as electric flux there are multiple possible unit definitions. The two standard definitions for electric flux are Vmand \frac{Nm^2}{C}as the following derivation from the former to the latter shows they are both correct.

V*m = \frac{J}{C}m = \frac{\frac{kg*m^2}{s^2}}{As}*m = \frac{kg*m^3}{As^3} = \frac{Nm^2}{As} = \frac{Nm^2}{C}

This derivation only used units given in the above table, but there are other ways.

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