Moment of Force Converter

Convert moment of force (torque) between N·m, kN·m, kgf·m, lbf·ft, and other units with scientific precision.

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Moment of Force Units Explained

Newton Meter (N·m)

The SI unit of moment of force (torque). Represents the rotational effect of a 1-newton force applied at a perpendicular distance of 1 meter. M = F × r.

Common uses: International standards, engineering design, scientific research, mechanical specifications.

Kilonewton Meter (kN·m)

Moment of force in kilonewtons. 1 kN·m = 1000 N·m. Used for large torques in heavy machinery.

Common uses: Industrial equipment, large motors, hydraulic systems, heavy machinery.

Kilogram-Force Meter (kgf·m)

Moment using kilogram-force units. 1 kgf·m ≈ 9.807 N·m. Still used in some regions and older standards.

Common uses: Regional standards, legacy equipment specifications, some mechanical designs.

Pound-Force Foot (lbf·ft)

Moment in US customary units. 1 lbf·ft ≈ 1.356 N·m. Common in US mechanical engineering.

Common uses: US automotive, machinery, industrial equipment, American engineering standards.

Moment of Force Calculation

Moment of force is the product of force and perpendicular distance from the pivot point: M = F × r × sin(θ)

  • M: Moment of force (N·m)
  • F: Applied force (Newtons)
  • r: Perpendicular distance from pivot (meters)
  • θ: Angle between force and lever arm

Equilibrium of Moments

For an object in rotational equilibrium, the sum of clockwise moments equals the sum of counterclockwise moments:

  • Equilibrium condition: ΣM_clockwise = ΣM_counterclockwise
  • Example: A seesaw balances when both sides have equal moments (weight × distance)
  • Mechanical advantage: Longer lever arm produces greater moment with same force

Typical Moment of Force Values

  • Opening a door: 1-5 N·m
  • Wrench on bolt: 10-100 N·m
  • Car engine torque: 100-400 N·m
  • Truck engine torque: 500-2000 N·m
  • Electric motor (1 hp): 0.75-1.5 N·m
  • Electric motor (10 hp): 7-15 N·m
  • Industrial press: 1000-10,000 N·m
  • Crane hook load: 10,000-100,000 N·m

Relationship between Moment and Work

When a moment causes rotation, work is performed:

  • Work: W = M × θ (moment × angular displacement in radians)
  • Power: P = M × ω (moment × angular velocity)
  • Energy: E = ½ × I × ω² (rotational kinetic energy)

Practical Moment Measurement

Moments are commonly measured and specified as:

  • Torque wrench: Calibrated to specific moment values (Nm, kgf·m)
  • Motor nameplate: Rated torque in N·m or lbf·ft
  • Fastener specs: Bolt tightening torque in appropriate units
  • Dynamometer testing: Measures moment output of engines/motors

Common Applications

Moment of force calculations are essential in:

  • Mechanical Design: Shaft and bearing sizing, coupling selection
  • Motor Selection: Matching torque requirements to motor ratings
  • Fastening: Bolt torque specifications and tightening procedures
  • Structural Analysis: Beam bending moments, stress calculations
  • Heavy Equipment: Crane operation, lifting, load handling
  • Power Transmission: Gear torque, chain drives, belt drives
  • Vehicle Engineering: Engine performance, drivetrain design

Vector Nature of Moment of Force

Moment of force is a vector quantity with direction determined by the right-hand rule:

  • Positive moment: Counterclockwise rotation (conventional sign)
  • Negative moment: Clockwise rotation
  • Right-hand rule: Curl fingers in direction of rotation, thumb points in moment direction
  • Vector cross product: M = r × F (position × force)