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Focused engineering tools for fast, well-defined problems.
23 calculators · Engineering Mechanics
Engineering Mechanics
23 calculatorsDomain overview →
Statics & Equilibrium
- Resultant Force CalculatorVector sum of coplanar forces: resultant components, magnitude and direction, with the zero-resultant case reported honestly.
- Moment of a Force CalculatorMoment of a planar force about a chosen point, M = r × F, positive counter-clockwise, with the perpendicular lever arm.
- 2D Equilibrium CalculatorSupport reactions of a planar rigid body from ΣFx = 0, ΣFy = 0 and ΣM = 0, with an explicit determinate, indeterminate or inconsistent verdict.
- Static Friction CalculatorMaximum static friction μs·N against the required equilibrium force, distinguishing sticking, impending slip and no static equilibrium.
Mass Properties
- Centroid CalculatorArea and geometric centroid of a single shape or a composite section, with cutouts as negative signed areas.
- Center of Mass CalculatorTotal mass and centre of mass of discrete planar point masses, or of a composite body built from shapes with densities, with each contribution shown.
- Area Moment of Inertia CalculatorCentroidal Ix, Iy and Ixy in m⁴ for standard shapes, with parallel-axis translation and principal values.
- Mass Moment of Inertia CalculatorMass moment of inertia in kg·m² for standard rigid bodies, with the axis stated for every case.
- Huygens–Steiner (Parallel-Axis) Theorem CalculatorTransfer a centroidal inertia to a parallel axis with the Huygens–Steiner theorem, also known as the parallel-axis theorem, in the area form I_c + A·d² or the mass form I_G + m·d².
- Radius of Gyration CalculatorRadius of gyration k = √(I/A) for an area or k = √(I/m) for a mass, undefined when the divisor is not positive.
Particle Mechanics
- Constant Acceleration CalculatorExact constant-acceleration kinematics: the standard 1D relations with explicit solve modes, and 2D propagation of position, velocity and speed.
- Projectile Motion CalculatorIdeal projectile motion: launch components, apex, flight time to a chosen landing elevation, range, impact velocity and impact angle.
- Circular Motion CalculatorParticle circular motion: v = rω, normal and tangential acceleration, total acceleration, period, frequency and the vectors at a chosen angle.
- Newton's Second Law CalculatorΣF = m·a for a planar particle, with explicit modes for the resultant force, the mass or the acceleration from several known forces.
- Work–Energy CalculatorWork of a constant force, particle kinetic energy and the work–energy theorem, with an honest verdict when no physical final speed exists.
- Impulse–Momentum CalculatorPlanar impulse and linear momentum: p = m·v, J = F·Δt and J = Δp, kept as distinct quantities throughout.
- Collision CalculatorDirect 1D impact of two particles from momentum conservation and the coefficient of restitution, with the kinetic-energy loss.
- Curvilinear Motion CalculatorPlanar curvilinear kinematics in normal–tangential or polar coordinates, with the components, the total acceleration and the Coriolis-like polar term named explicitly.
Rigid-Body Mechanics
- Rotational Kinematics CalculatorConstant angular-acceleration relations between θ, ω, α and t, with one explicit unknown per mode.
- Rotational Dynamics CalculatorΣM_G = I_G·α for a planar rigid body, solved for the moment, the mass moment of inertia or the angular acceleration.
- Rigid-Body Work–Energy CalculatorT = ½m|v_G|² + ½I_Gω² with the translational and rotational parts kept apart, and T₂ − T₁ = W_net solved either way.
- Rigid-Body Impulse–Momentum CalculatorJ = m(v_G2 − v_G1) and K_G = I_G(ω₂ − ω₁) for one planar rigid body, including constant loads acting over a duration.
- Rolling Without Slipping CalculatorPure-rolling kinematics with the contact and top point velocities, and the incline case with the static friction the no-slip constraint demands.