Engineering Symbols

Angle, angular acceleration

Thermal diffusivity

Coefficient of thermal expansion

Temperature coefficient of resistance

Angle, velocity ratio, pipe area ratio

Current gain of a transistor (BJT)

Ratio of reinforcement in concrete design

Specific weight (unit weight)

Shear strain (dimensionless)

Ratio of specific heats Cp/Cv (adiabatic index)

Specific gravity or surface tension

Circulation (line integral of velocity)

Gamma function - generalization of factorial

Beam or structural deflection

Infinitesimally small change in a quantity

Skin depth of current penetration

Logarithmic decrement

Change in a quantity: ΔT = temperature change, ΔP = pressure drop, ΔV = volume change

Normal strain (dimensionless) - elongation per unit length

Permittivity of a dielectric

Emissivity of a surface (0–1)

Damping ratio (ζ < 1: underdamped, ζ = 1: critically damped, ζ > 1: overdamped)

Thermal efficiency of a heat engine or cycle

Dynamic (absolute) viscosity

Efficiency of a power converter

Plane angle - the most common angle symbol

Temperature difference or temperature (sometimes)

Phase angle between voltage and current

Wavelength of a wave

Thermal conductivity

Slenderness ratio (sometimes, alongside KL/r)

Eigenvalue

Dynamic (absolute) viscosity

Coefficient of friction (sliding or static)

Micro- prefix: × 10⁻⁶ (e.g., μm = micrometre, μA = microamp)

Poisson's ratio - lateral strain / axial strain

Kinematic viscosity (ν = μ/ρ)

Ratio of circumference to diameter of a circle: 3.14159…

Density - mass per unit volume

Electrical resistivity

Radius of curvature (of a beam)

Normal stress - force per unit cross-sectional area

Standard deviation

Stefan-Boltzmann constant: 5.67 × 10⁻⁸ W/(m²·K⁴)

Summation - sum of a series of terms (e.g., Σ Fᵢ = net force)

Shear stress - tangential force per unit area

Time constant (RC or RL circuit, or thermal)

Torque (sometimes, especially in dynamics)

Phase angle between voltage and current waveforms

Strength reduction factor in LRFD design (φ = 0.90 for flexure)

Internal friction angle of soil

Diameter of a circular cross-section (prefix, not multiplication)

Stream function

Angle of twist of a beam or shaft

Angular velocity - rate of rotation

Angular frequency (ω = 2πf)

Ohm - SI unit of electrical resistance

Safety factor in Allowable Stress Design (ASD)

Sum of a series: ∑ᵢ aᵢ = a₁ + a₂ + … + aₙ

Definite or indefinite integral - area under a curve; reverse of differentiation

Partial derivative - rate of change with respect to one variable while others are held constant (e.g., ∂T/∂x)

Vector differential operator - used for gradient (∇f), divergence (∇·F), and curl (∇×F)

Unbounded quantity - used in limits, boundary conditions, and long-distance approximations

Result is close but not exactly equal - used in engineering estimates and rounding

y ∝ x means y = k·x for some constant k - indicates a linear relationship without specifying the constant

Positive square root of a quantity: √9 = 3

Product of a series: ∏ᵢ aᵢ = a₁ × a₂ × … × aₙ

Rate of change of a function with respect to x - same as f′(x)

Derivative of function f - same as df/dx. f″ is the second derivative.

Magnitude of x - always positive: |−5| = 5, |5| = 5

× 10¹² (one trillion). Example: TW = terawatt

× 10⁹ (one billion). Example: GHz = gigahertz

× 10⁶ (one million). Example: MPa = megapascal

× 10³ (one thousand). Example: kN = kilonewton, kPa = kilopascal

× 10² (one hundred). Example: hPa = hectopascal (used in weather)

× 10¹ (ten). The least-used SI prefix in engineering - occasional exceptions are decaliter (daL) for bulk liquid measure and decanewton (daN), sometimes seen on European tension/force gauges

× 10⁻¹ (one-tenth). Example: dL = deciliter

× 10⁻² (one-hundredth). Example: cm = centimeter

× 10⁻³ (one-thousandth). Example: mm = millimeter, mA = milliamp, mV = millivolt

× 10⁻⁶ (one-millionth). Example: μm = micrometre, μF = microfarad, μs = microsecond

× 10⁻⁹. Example: nm = nanometer, nF = nanofarad, ns = nanosecond

× 10⁻¹² Example: pF = picofarad, ps = picosecond

× 10⁻¹⁵. Example: fs = femtosecond, common in laser and photonics work

Length - the base unit of length in the International System of Units

Mass - the base unit of mass

Time - the base unit of time

Electric current - the base unit of electric current

Thermodynamic temperature - absolute temperature scale (0 K = absolute zero)

Force - 1 N = 1 kg·m/s². The weight of ~102 g on Earth's surface.

Stress and pressure - 1 Pa = 1 N/m²

Fluid pressure

Energy and work - 1 J = 1 N·m = 1 kg·m²/s²

Power - 1 W = 1 J/s. Rate of energy transfer.

Electric potential difference (voltage) - 1 V = 1 J/C

Electrical resistance - 1 Ω = 1 V/A

Capacitance - 1 F = 1 C/V. Practical capacitors are usually pF to μF.

Inductance - 1 H = 1 V·s/A

Frequency - 1 Hz = 1 cycle per second (1/s)

Magnetic flux density - 1 T = 1 kg/(A·s²)

Electric charge - 1 C = charge carried by ~6.24 × 10¹⁸ electrons

Plane angle - dimensionless SI unit. 2π rad = 360°. 1 rad ≈ 57.3°

Solid angle - dimensionless SI derived unit. A full sphere subtends 4π sr

Amount of substance - used in chemistry and materials engineering. 1 mol = ~6.022 × 10²³ elementary entities (Avogadro's number)

Luminous intensity - used in optics and lighting engineering to rate light sources

Applied force - push or pull on a body

Bending moment - tendency of a force to bend a member

Mass (careful: same symbol, different context)

Shear force in a beam - force perpendicular to the beam axis

Young's modulus (elastic modulus) - stiffness: E = stress/strain

Second moment of area (moment of inertia) - resistance to bending

Elastic section modulus - S = I/c, where c = distance from neutral axis to extreme fibre

Spring constant - stiffness: F = kx

Thermal conductivity

Column slenderness ratio - K=effective length factor, L=length, r=radius of gyration. Used to classify columns for buckling.

Electric current - flow of electric charge per unit time

Electrical resistance - opposition to current flow: R = V/I

Electric potential difference - energy per unit charge

AC impedance - complex opposition to current: Z = R + jX

Frequency of an AC signal or wave - cycles per second

Ratio of real power to apparent power: PF = cos φ (0–1). Unity PF = purely resistive load.

Wire size standard - higher AWG number = smaller wire. 12 AWG is standard for 20A circuits.

Volume of fluid passing a cross-section per unit time

Mass of fluid passing a cross-section per unit time: ṁ = ρQ

Average fluid velocity across a pipe or duct cross-section

Velocity of a body - rate of change of position

Dimensionless ratio of inertial to viscous forces: Re = ρvL/μ. Re < 2300: laminar; Re > 4000: turbulent.

Dimensionless ratio of inertial to gravitational forces: Fr = v/√(gL). Used for open-channel flow and ship-hull design.

Dimensionless ratio of flow velocity to the local speed of sound: Ma = v/c. Ma < 1: subsonic; Ma = 1: sonic; Ma > 1: supersonic.

Dimensionless drag coefficient - quantifies drag relative to dynamic pressure and reference area

Fluid pressure - force per unit area

Point load or applied load (sometimes)

Absolute thermodynamic temperature

Torque (careful - same symbol)

Heat transferred to/from a system

Ratio of useful work output to heat input: η = W/Q_H

Rate of heat conduction through a material per unit temperature gradient

Convective heat transfer coefficient - Newton's law of cooling: Q = hAΔT

Heat capacity at constant pressure - energy per unit mass per degree

Heat capacity at constant volume - energy per unit mass per degree with no expansion work done

Total heat content of a system: H = U + PV. Used to track energy in constant-pressure processes.

Measure of a system's disorder or unavailable energy - always non-decreasing for an isolated system (2nd law)

Total kinetic and potential energy of a system's molecules - careful, same letter as U-value below

Energy transferred by a system through boundary movement, e.g. gas expansion against a piston

Watt - SI unit of power (careful, same letter as thermodynamic work)

Resistance to heat flow through a material - R = L/k for a single layer, R-value on insulation labels

Electrical resistance (careful - same letter as thermal resistance)

Overall heat transfer coefficient through a building element - lower = better insulation

Location tolerance - defines a zone within which the center, axis, or center plane of a feature of size is permitted to vary from true (theoretically exact) position.

Form tolerance - specifies a tolerance zone defined by two parallel planes within which the surface must lie.

Form tolerance - specifies a tolerance zone within which the considered line/axis must lie.

Form tolerance - specifies a tolerance zone bounded by two concentric circles within which each circular element of the surface must lie.

Form tolerance - specifies a tolerance zone bounded by two concentric cylinders within which the surface must lie.

Profile tolerance - specifies a 2D tolerance zone around any line of the feature.

Profile tolerance - specifies a 3D tolerance zone around the entire surface of the feature.

Orientation tolerance - specifies that a feature must be perfectly at 90 degrees to a datum.

Orientation tolerance - specifies that a feature must be at a specified angle (other than 90°) to a datum.

Orientation tolerance - specifies that a feature must be perfectly parallel to a datum.

Location tolerance - specifies that the median points of a feature must lie within a cylindrical zone centered on a datum axis. (Note: Removed in ASME Y14.5-2018, but still common in older drawings/ISO).

Runout tolerance - specifies the 2D tolerance zone for each circular cross-section when the part is rotated 360 degrees about the datum axis.

Runout tolerance - specifies the 3D tolerance zone for the entire surface when the part is rotated 360 degrees about the datum axis.

Modifier - indicates that a tolerance applies when the feature contains the maximum amount of material (e.g., smallest hole, largest pin).

Modifier - indicates that a tolerance applies when the feature contains the least amount of material (e.g., largest hole, smallest pin).

Indicates that the following dimension is a diameter (e.g., ⌀25). Used widely in all technical drawings.