Torque calculator (force, power and rpm)
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Result
Calculate the torque of a force about an axis from the force, the lever arm and the angle between them. Other modes convert between torque, rotational speed in rpm and power, as for a motor or an engine, and use Newton’s second law for rotation, τ = I·α. Results are given in N·m, lbf·ft and kgf·m, with every step shown.
Step-by-step solution
Torque of a force
Other units
Key formulas
- Moments of inertia about G
- rod mL²/12, disc ½mR², ring mR², solid sphere (2/5)mR², hollow sphere (2/3)mR²
- Equation of motion
- ΣM = I·α
- Work and power
- W = T·θ, P = T·ω
How to calculate torque
- Measure the lever arm r from the axis of rotation to the point where the force acts.
- Find the angle θ between the force and the lever arm. Only the perpendicular part of the force, F·sin θ, turns the object.
- Multiply: τ = F·r·sin θ. With the force perpendicular to the lever (θ = 90°) this is simply F·r.
- For a rotating shaft, convert the speed to angular speed, ω = 2π·n/60 with n in rpm, and use P = T·ω. Rearranged, T = P/ω.
- For angular acceleration use τ = I·α, where I is the moment of inertia about the axis.
Questions and answers
What is the difference between torque and moment?
Both are a force times a perpendicular distance, in N·m. Torque is mostly used for turning and twisting, as on shafts and bolts, and moment for bending and for equilibrium in statics. The calculation is the same.
Why is torque not measured in joules?
Work is also force times distance, but there the distance is along the force; for torque it is perpendicular to it. To avoid confusion, torque is written in N·m and energy in J, even though the base units are the same.
How do I convert N·m to lbf·ft?
1 lbf·ft = 1.3558 N·m, so divide newton-metres by 1.3558: 100 N·m = 73.8 lbf·ft.
How are engine power and torque related?
P = T·ω. In practical units P (kW) = T (N·m) × n (rpm)/9549. An engine giving 250 N·m at 3000 rpm delivers 78.5 kW.
Practise it yourself
Practise Rigid-body rotation
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.