Formula Database | Formula Sheet
This is our growing database of formulas. Here you can find formulas and copy them directly to LaTeX or Microsoft Word 2007+. The formulas with a ⌨ icon feature calculators that allow you to solve for an unknown variable. For additional features including cloud formula storage and searching this database, check out If you would like to help us build this free resource, please contact us.


Mechanical Engineering


Acceleration (rectilinear)
Angular momentum of a particle
Circular planar motion of a particle in polar coordinates
Coefficient of restitution
Conservation of linear momentum
Damped natural frequency
Differential equations of motion (rectilinear)
Equation of motion for damped forced vibration
Equation of motion for damped free vibration
Equation of motion for undamped forced vibration
Equation of motion for undamped free vibration
Gravitational potential energy
Hooke's law
Inertia tensor
Kinetic energy (fixed-axis rotation)
Kinetic energy (planar motion)
Kinetic energy (translation)
Linear impulse
Linear momentum
Moment of inertia
Newton's first law of motion
Newton's second law of motion
Newton's second law of motion (variable-mass systems)
Newton's third law of motion
Parallel axis theorem
Planar motion of a particle in Cartesian coordinates
Relative acceleration
Relative acceleration on a rigid body due to rotation
Relative acceleration with respect to a rotating coordinate system
Relative velocity
Relative velocity on a rigid body due to rotation
Relative velocity with respect to a rotating coordinate system
Velocity (rectilinear)



Area (geometry)

Area of a circle
Area of a parallelogram
Area of a rectangle
Area of a regular hexagon
Area of a regular octagon
Area of a regular polygon
Area of a square
Area of a trapezoid
Area of a triangle
Area of an ellipse
Surface area of a cone
Surface area of a cube
Surface area of a cylinder
Surface area of a rectangular prism
Surface area of a regular tetrahedron
Surface area of a sphere


Chain rule
Chain rule (Leibniz notation)
Derivative definition
Inverse power rule
Linearity of differentiation
Linearity of differentiation (Leibniz notation)
Linearity of integration
Power rule
Product rule
Product rule (Leibniz notation)
Quotient rule
Riemann sum
Second fundamental theorem of calculus
Simpson's rule

Mathematical constants

Euler's number
Golden ratio
Imaginary unit
Pi (Archimedes' constant)

Taylor series

Arctangent Taylor series
Cosine Taylor series
Exponential Taylor series
Geometric Taylor series
Natural logarithm Taylor series
Sine Taylor series

Trigonometric function derivatives

Derivative of arccosecant
Derivative of arccosine
Derivative of arccotangent
Derivative of arcsecant
Derivative of arcsine
Derivative of arctangent
Derivative of cosecant
Derivative of cosine
Derivative of cotangent
Derivative of secant
Derivative of sine
Derivative of tangent

Trigonometric functions


Trigonometric identities

Cosine double-angle formula
Cosine sum and difference identity
Cosine triple-angle formula
Cotangent double-angle formula
Cotangent triple-angle formula
Pythagorean identity
Pythagorean identity (cotangent and cosecant)
Pythagorean identity (tangent and secant)
Sine double-angle formula
Sine sum and difference identity
Sine triple-angle formula
Tangent double-angle formula
Tangent sum and difference identity
Tangent triple-angle formula
Trigonometric functions shifts and periodicity
Trigonometric functions symmetry

Trigonometric laws and theorems

Law of cosines
Law of cotangents
Law of sines
Law of tangents
Pythagorean theorem
Pythagorean theorem hypotenuse solution

Volume (geometry)

Volume of a cone
Volume of a cube
Volume of a cylinder
Volume of a rectangular prism
Volume of a regular tetrahedron
Volume of a sphere
Volume of an ellipsoid


Physical constants

Avagadro constant
Boltzmann constant
Electron mass
Elementary charge
Gravitational constant
Impedance of free space
Neutron mass
Planck constant
Planck length
Planck mass
Planck temperature
Planck time
Proton mass
Speed of light in a vacuum
Vacuum permeability
Vacuum permittivity