Example engineering calculations
Worked, unit-aware calculation worksheets across structural, mechanical, electrical and more. Open any example into your own workspace to edit and reuse. New to Calculeaf? Start with your first worksheet or the examples guide.
515 examples
2×2 Matrix Determinant
Determinant of a 2×2 matrix computed from its four scalar entries.
Vector Dot Product and Angle Between Two Vectors
Dot product of two 3D vectors given by components, and the angle between them.
Vector Cross Product Magnitude
Cross product of two 3D vectors given by components, and the magnitude of the resulting vector.
Arithmetic Series Sum
Sum of the first n terms of an arithmetic sequence with a given first term and common difference.
Geometric Series Sum
Sum of the first n terms of a geometric sequence with a given first term and common ratio.
Diffraction Grating Angle
Diffraction angle for a given order of a light beam passing through a diffraction grating.
Young's Double-Slit Fringe Spacing
Spacing between adjacent bright interference fringes on a screen in the classic double-slit experiment.
Magnetic Force Between Two Parallel Current-Carrying Wires
Force per unit length between two long, parallel wires each carrying a steady current.
Electric Field of a Point Charge
Electric field strength at a distance from an isolated point charge, from Coulomb's law.
Electric Field Energy Density in a Capacitor
Energy stored per unit volume in the electric field between capacitor plates.
Malus's Law Polarizer Transmitted Intensity
Intensity of polarized light transmitted through a polarizing filter oriented at an angle to the incoming polarization.
Beat Frequency of Two Close Tones
Audible beat frequency produced when two sound tones of slightly different frequency are played together.
Relativistic Time Dilation
Elapsed time measured by a stationary observer for a clock moving at a significant fraction of the speed of light.
Room Reverberation Time (Sabine Equation)
Time for sound in a room to decay by 60 dB after the source stops, estimated from room volume and total absorption.
Fundamental Frequency of a Vibrating String
Fundamental (and harmonic) frequency of a taut string, from its length, tension, and mass per unit length.
Moment of Inertia of a Solid Disc
Rotational moment of inertia of a uniform solid disc about its central axis.
Moment of Inertia of a Solid Sphere
Rotational moment of inertia of a uniform solid sphere about a diameter.
Angular Momentum of a Rotating Body
Angular momentum of a rigid body spinning at a known rotation frequency, given its moment of inertia.
Rotational Kinetic Energy
Kinetic energy stored in a rigid body spinning at a known rotation frequency.
Torque from Moment of Inertia and Angular Acceleration
Torque required to produce a given angular acceleration in a rotating shaft or body.
Parallel Axis Theorem
Moment of inertia of a body about an offset axis, computed from its moment of inertia about its own center of mass.
Gravitational Field Strength (Surface Gravity)
Gravitational acceleration at the surface of a spherical body, from Newton's law of universal gravitation.
Elastic Collision Final Velocities (1D, Two Bodies)
Post-collision velocities of two bodies colliding elastically head-on, from conservation of momentum and kinetic energy.
Projectile Range with a Launch Height Above the Landing Point
Horizontal range of a projectile launched from an elevated point above the level landing surface.