Torque & Moment of Inertia Calculator

Enter force (N) and lever arm (m), choose a shape to compute its moment of inertia, and get torque, angular acceleration, and rotational kinetic energy (if ω is provided). Private by design — everything runs locally in your browser.

Inputs

Force F (N)

Lever arm r_⊥ (m)

Lever arm = perpendicular distance to the axis (i.e., r·sinθ).

Angular speed ω (rad/s, optional for KE)

Axis & shape

Radius R (m)

Mass M (kg)

Assumes the applied force is the net torque contributor and the axis is fixed. For non-perpendicular forces, use r⊥ = r·sinθ as the lever arm.

Results

Moment of inertia I (from shape):

–

—

Torque τ (about axis):

–

τ = F · r_⊥

Angular acceleration α:

–

α = τ / I

Rotational kinetic energy (if ω > 0):

–

K = ½ I ω²; Power P = τ ω

How Torque, Moment of Inertia, and Rotation Fit Together

Rotational dynamics mirrors linear motion: force causes acceleration, and torque causes angular acceleration. The torque about an axis is τ = r⊥F, where r⊥ is the perpendicular distance from the axis to the line of action of the force; this is commonly called the lever arm. The rotational equivalent of mass is the moment of inertia I, which depends on how mass is distributed relative to the axis.

For standard shapes, useful formulas about their symmetry axes are: solid sphere I = (2/5)MR², solid cylinder or disk I = (1/2)MR², thin rod about its center I = (1/12)ML², and thin rod about one end I = (1/3)ML². Once you know I, the angular acceleration from an applied torque is simply α = τ/I. If the object spins at angular speed ω, its rotational kinetic energy is K = ½ I ω², and the instantaneous power delivered by a torque is P = τ ω.

Notes: This calculator assumes a rigid body and a fixed rotation axis with the applied force creating the net torque. Real systems may have opposing torques (friction, drag, gravity on offset masses). If your force is not perpendicular, compute r⊥ = r·sinθ before entering. SI units are used throughout: N, m, kg, rad/s, J.