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.

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