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.
61 examples found
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.
Angular Frequency and Period of a Torsional Pendulum
Natural angular frequency and oscillation period of a torsional pendulum, from its rotational stiffness and moment of inertia.