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Torque Unit Converter (N·m/lb·ft/oz·in)

Convert torque between Newton-metres, pound-feet, pound-inches, oz·in, kg·cm, kg·m, and dyne·cm.

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Formula

1N⋅m=0.7376lb⋅ft=141.6oz⋅in1 N·m = 0.7376 lb·ft = 141.6 oz·in

How It Works

This calculator converts between Newton-metres, pound-feet, pound-inches, ounce-inches, and kilogram-centimetres for mechanical engineers, roboticists, and motor designers. Per SI Brochure (BIPM), the Newton-metre is the SI unit of torque: 1 N·m = 1 kg·m^2/s^2. Key conversion factors per NIST SP 811: 1 N·m = 0.7376 lb·ft = 8.851 lb·in = 141.612 oz·in = 10.197 kgf·cm exactly. Torque spans 9 orders of magnitude: millinewton-metres for micro-motors (0.1-10 mN·m), Newton-metres for servos (0.5-50 N·m), and kilonewton-metres for industrial drives (1-100 kN·m). Hobby servos commonly specify oz·in (20-300 oz·in typical), while automotive uses lb·ft (200-500 lb·ft for engines). The relationship P = T × omega links torque to power: 1 N·m at 1 rad/s = 1 W.

Worked Example

Problem

A robot arm joint must lift a 2 kg payload at 0.5 m arm length with 2× safety factor. Select a servo motor and verify power at 60 RPM rotation.

Solution
  1. Static torque: T = m × g × r = 2 × 9.81 × 0.5 = 9.81 N·m
  2. With 2× safety factor: T_required = 19.6 N·m
  3. Convert to hobby servo units: 19.6 × 141.612 = 2776 oz·in
  4. Convert to kgf·cm: 19.6 × 10.197 = 200 kgf·cm
  5. Convert to lb·ft: 19.6 × 0.7376 = 14.5 lb·ft
  6. Angular velocity: omega = 60 RPM × 2*pi/60 = 6.28 rad/s
  7. Power: P = T × omega = 9.81 × 6.28 = 61.6 W (at rated load, no safety factor)
  8. Selection: Dynamixel MX-106 (8.4 N·m continuous, 10.0 N·m peak) - INSUFFICIENT; need MX-64 or external gearbox

Practical Tips

  • ✓Servo motor ratings per NEMA/IEC: stall torque (T_s) is maximum at zero speed, continuous torque (T_c) is sustained rating. Typical T_c = 0.3-0.5 × T_s. For safety, design for T_c > T_load with 50% margin
  • ✓Torque-speed relationship per motor physics: T = k_t × I where k_t is torque constant (N·m/A). For DC motors, k_t = k_e (back-EMF constant V/(rad/s)) by conservation of energy. Typical k_t values: 0.01-0.1 N·m/A for small motors
  • ✓Gearbox increases torque: T_out = T_in × ratio × efficiency. A 100:1 gearbox with 80% efficiency turns 0.1 N·m motor into 8 N·m output. Trade-off: speed reduces proportionally (1000 RPM input = 10 RPM output)

Common Mistakes

  • ✗Confusing kgf·cm with kg·m - they differ by 100x. A servo rated 5 kgf·cm produces 0.05 kg·m = 0.49 N·m, not 49 N·m. Always check if spec uses cm or m for lever arm
  • ✗Mixing up lb·ft and lb·in - they differ by 12x. A 10 lb·ft motor produces 120 lb·in. Automotive specs use lb·ft; servo/actuator specs often use lb·in or oz·in
  • ✗Ignoring that torque specs may be stall (maximum, zero speed) vs continuous (sustained operation) - operating at stall torque causes thermal damage. Use 50-70% of stall rating for continuous duty per NEMA guidelines

Frequently Asked Questions

Per SI Brochure: N·m (Newton-metre) is torque (force × distance), unit kg·m^2/s^2. N/m (Newton per metre) is spring stiffness (force/distance), unit kg/s^2. Completely different quantities despite similar notation. Torque rotates; stiffness resists linear displacement.
Historical US RC hobby industry standardized on oz·in. Typical ranges per Hitec/Futaba: micro servos 15-30 oz·in (0.1-0.2 N·m), standard servos 40-100 oz·in (0.3-0.7 N·m), high-torque 150-500 oz·in (1-3.5 N·m). Convert to N·m by dividing by 141.6. Industrial servos use N·m directly.
Static: T = m × g × r_cm (mass × gravity × center-of-mass distance). Dynamic: add T_accel = I × alpha (moment of inertia × angular acceleration). Total: T_motor > (T_static + T_dynamic) × safety_factor / gear_ratio / efficiency. Use 1.5-2× safety factor for varying loads. Include friction torque for geared systems.
Stall torque is maximum torque when motor shaft is held stationary (zero RPM, maximum current). Per NEMA MG-1: motor draws locked-rotor current (6-8× rated) at stall. Continuous operation at stall causes thermal failure in seconds. Use stall torque only for peak/transient loads < 1 second.

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