Mechanical Engineering Formulas & Equations

 List of common useful mechanical engineering formulas and equations has been produced hereunder. The list covers important topics of mechanical engineering with basic definition, equation and formula.

Detailed basic and fundamental concepts of mechanical engineering have been defined in separate section. 

Stress

Force per unit area in a solid. The area is perpendicular to the force for tensile stress and parallel to it for shear stress. Unit: newtons per square meter (Pascal).

Strain

The change in shape or size of a stressed body divided by its original shape or size, e.g. ‘linear strain’, ‘shear strain’, ‘volumetric strain’.

Young’s modulus of elasticity

A measure of the rigidity of a material. The ratio of stress to strain in the elastic region.

Stiffness

The ability of a metal, etc., to resist elastic deformation. It is proportional to the appropriate modulus of elasticity.

Modulus of rigidity

The ratio of shear stress to shear strain within the elastic limit.

Thermal strain's Formula

Strain in a body due to a temperature gradient.

Thermal stress in compound bar

Stress in a body due to a temperature gradient.

Ultimate tensile strength

The maximum tensile stress a material will withstand before failure.

Moment

The moment of a force (or other vector quantity) about a point is the product of the force and the perpendicular distance from the line of action of the force to the point.

Torque

The algebraic sum of couples, or moments of external forces, about the axis of twist. Also called ‘torsional moment’

Power

The rate of doing work. Unit: watt (W).

Horsepower

Angular Torque

Average velocity

Acceleration

The rate of change of velocity with respect to time

Linear velocity

The rate of change of position of a point with respect to time. Unit: meters per second

Angular velocity

Linear acceleration

Relationships between initial velocity u, final velocity v, displacement s, time t and constant acceleration a

Relationships between initial angular velocity ω1, final angular velocity ω2, angle θ, time t and angular acceleration a

Momentum Formula

The product of mass and velocity of a body, i.e. mv.

Impulse Formula

Impulse is defined as the change of momentum produced in either body.

Force

That quantity which produces acceleration in a body measured by the rate of change of momentum. Unit: newton (N).

Weight

Centripetal acceleration

Centripetal force

A body constrained to move in a curved path reacts with a force (centrifugal force) directed away from the center of curvature. It is equal and opposite to the force deviating the body from a straight line called the ‘centripetal force’. Both are equal to the mass multiplied by the ‘centripetal acceleration’.

Density

The mass of a unit volume of a substance. The unit is kilograms per meter cubed.

Work done

Efficiency

A non-dimensional measure of the perfection of a piece of equipment, e.g. for an engine, the ratio of power produced to the energy rate of the fuel consumed, expressed as a fraction or as a percentage.

Power

The rate of doing work. Unit: watt (W).

Potential energy & kinetic energy

The capacity of a body for doing work. Types are: kinetic, potential, pressure, chemical, electric, etc.

Kinetic energy of rotation

Frictional force

Angle of repose

Efficiency of screw jack

SHM Equations

Simple pendulum

Compound pendulum

Force ratio

Movement ratio

Efficiency

Kelvin temperature

Quantity of heat energy

New length

New surface area equations

New volume

Pressure

At a point in a fluid, pressure is the force per unit area acting in all directions. That is, it is a scalar quantity; e.g. in a cylinder with a piston, pressure P is the force on the piston divided by the cylinder area.

Absolute pressure

Absolute pressure = gauge pressure + atmospheric pressure

Metacentric height, GM

Bernoulli’s equation

Coefficient of discharge

The rate of actual to theoretical flow of a fluid through an orifice, nozzle, Venturi meter, etc.

Characteristic gas equation formula

I hope this list of mechanical engineering formulas and equations proves useful for our valued readers. We'll be adding more formulas to this list in future. Any recommendations and remarks are welcomed in comments section.