Pick what to solve and enter known values. Add unit choices and optional resistance losses. Get net torque, inertia, and acceleration results fast here.
Sample calculations using τ_net = I · α.
| Case | Applied torque | Resisting torque | Inertia | Computed α |
|---|---|---|---|---|
| A | 12.0 N·m | 2.0 N·m | 0.20 kg·m² | 50.0 rad/s² |
| B | 8.0 lbf·ft | 1.0 lbf·ft | 1.80 lb·ft² | 3.85 rad/s² |
| C | 150 N·cm | 0 N·cm | 50,000 g·cm² | 0.30 rad/s² |
Numbers are rounded for readability. Your results may vary with unit choices and sign conventions.
This calculator uses the rotational form of Newton’s second law:
Where τ is torque, I is moment of inertia about the rotation axis, and α is angular acceleration.
If computed signs look wrong, reverse the sign of torques or acceleration to match your chosen direction convention.
Torque, inertia, and angular acceleration connect through tau_net = I × alpha. This relation predicts how quickly a rotor speeds up when you know the net turning effort and the axis inertia.
The calculator accepts up to three applied torques to model multiple motors, belts, or stages. Use positive values for your chosen rotation direction and negative values for opposing effects, such as braking, back-driving, or windage drag.
Moment of inertia measures resistance to angular acceleration and depends on mass distribution. For the same tau_net, a flywheel with I = 0.50 kg·m² accelerates five times slower than a rotor with I = 0.10 kg·m². Concentrating mass near the rim increases I strongly because radius is squared.
When I is unknown, the estimator uses standard rigid-body models. Solid disk or cylinder: I = 0.5 m R². Thin rod about center: I = (1/12) m L². Hollow cylinder: I = 0.5 m (R² + r²). Enter mass and geometry carefully; small radius errors can create large inertia errors.
Real systems face losses from bearings, seals, gear mesh, and external loads. Add resisting torque so tau_net = tau_applied − tau_resist. If tau_resist exceeds tau_applied, alpha becomes negative, meaning the system decelerates. This is common in coast-down tests and when loads change during operation.
You can mix common torque units (N·m, N·cm, lbf·ft, lbf·in) and inertia units (kg·m², g·cm², lb·ft², slug·ft²). For example, 1 lbf·ft equals about 1.356 N·m. Choose decimals to match sensor resolution and keep reports consistent.
Use the tool for motor sizing, robotic joints, turntables, lab rigs, and drivetrain tuning. A quick check: doubling tau_net should double alpha, while doubling I should halve alpha. Also confirm signs: if torque and acceleration directions disagree, flip the sign of one input to match your convention. If tau_net is 10 N·m and I is 0.20 kg·m², alpha is 50 rad/s², or about 2865 deg/s². To estimate ramp time, use t = Δω/alpha; reaching 300 rad/s then needs about 6 seconds under constant net torque conditions. With typical laboratory motor setups.
Applied torque is the sum of torques you add from motors or forces. Net torque subtracts resisting torque from losses or loads. Net torque is the value used in tau_net = I × alpha.
Yes. Choose “Moment of inertia (I)” and enter at least one applied torque, any resisting torque, and the measured angular acceleration. The calculator computes I = tau_net / alpha.
A negative result means your net torque is opposite your chosen positive direction. This usually happens when resisting torque is larger than applied torque, or when you entered a braking torque as positive.
Pick the option that matches your object and rotation axis. A solid disk fits wheels and flywheels, a rod model fits beams, and hollow cylinder fits pipes. Use correct radius or length, because I scales with distance squared.
Conversions use standard constants, including 1 lbf·ft ≈ 1.3558 N·m and 1 inch = 0.0254 m. Small rounding differences may appear if you display many decimals.
Use constant-acceleration kinematics: t = Δω / alpha. If you know starting and target angular speed, compute the change in ω and divide by alpha. This provides a first estimate before accounting for speed-dependent losses.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.