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Torque Calculator

Calculate torque from force and lever arm, bolt tightening specs, and power at RPM.

Torque = Force × Lever Arm — N·m and lb·ft

BrainyCalculators editorial insight — unique to this tool

Automotive lug nuts spec 80–100 lb·ft; over-torque strips threads. Engine torque × RPM ÷ 5252 = horsepower (US units). Bolt tightening sequences use torque wrenches calibrated in N·m on metric assemblies.

When to use this calculator

Use for rotational force calculations and unit conversion. Linear force → Force calculator.

Linear force and acceleration instead?

This page handles rotational torque. For F=ma problems, use the Force Calculator →

What is Torque?

Torque is rotational force: τ = F × r, critical for bolts, engines, and shafts. This calculator converts force-distance pairs and relates power at angular speed.

Use this page for twist and tightening specs. Linear force on a mass uses the Force Calculator; beam deflection uses distributed loads on members.

Power consumption links electrical kW; mechanical power-from-torque is a separate mode here.

Torque Formula

T = F × r   where F = force (N), r = lever arm length (m), T = torque (N·m)

Torque is also called the moment of force. It represents the rotational tendency produced by a force applied at a perpendicular distance from a pivot point. The SI unit is the Newton metre (N·m).

How the Torque Calculator Works

Formula, assumptions, and calculation steps for this engineering tool.

Methodology

Engineering calculators apply standard unit conversions and formula relationships after normalizing measurements to compatible units.

Calculation Steps

  1. Enter dimensions, loads, rates, or electrical values.
  2. Convert the inputs into the formula unit system.
  3. Apply the engineering equation or conversion factor.
  4. Return the result with units and supporting context.

Assumptions and Limits

  • Material behavior is assumed ideal unless fields specify otherwise.
  • Code checks, safety factors, and site conditions may require professional review.
  • Use a qualified engineer for design-critical decisions.

Frequently Asked Questions

Torque (also called moment of force) is the rotational equivalent of linear force. It measures how much a force tends to rotate an object about an axis or pivot. The formula is T = F × r, where F is the force applied perpendicular to the lever arm and r is the distance from the pivot (radius). The SI unit is the Newton metre (N·m).

Torque is a static or instantaneous twisting force (N·m), while power is the rate of doing work over time (Watts). They are related by the equation: Power (W) = Torque (N·m) × Angular velocity (rad/s). An engine can produce high torque at low RPM but low power, or low torque at high RPM with high power.

Multiply N·m by 0.737562 to get lbf·ft. For example, 100 N·m × 0.737562 = 73.76 lbf·ft. To convert lbf·ft to N·m, multiply by 1.35582.

Torque is measured using a torque wrench (which clicks at a set value) or a torque sensor/transducer. In engines, a dynamometer measures torque on a rotating shaft. Digital torque wrenches provide direct readouts in N·m, lbf·ft, or kgf·m.

Real-World Applications

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Fastener Tightening in Automotive & Engineering
Every critical fastener in a vehicle, aircraft, or machine has a manufacturer-specified tightening torque — from cylinder head bolts (100–200 N·m for most car engines) to wheel lug nuts (110–130 N·m typically) to brake caliper bolts (25–35 N·m). A torque wrench applies a precise torque to achieve the specified clamping force; under-torqued fasteners loosen under vibration and dynamic loading, while over-torqued fasteners yield, stretch, or shear the bolt threads. The torque calculator helps mechanics verify that a torque wrench setting in one unit (ft·lb) matches a workshop manual specification in another (N·m).
⚙️
Gearbox & Drivetrain Design
Mechanical engineers designing gearboxes, drive shafts, and pulleys calculate the torque transmitted through each component — and the resulting shear stress — to verify that selected materials and dimensions have adequate strength. A 5 kW motor running at 1,500 RPM produces 31.8 N·m of output torque; a 3:1 reduction gearbox multiplies this to approximately 95 N·m (minus efficiency losses) at the output shaft. Torque calculations define minimum shaft diameter and gear tooth width requirements.
🏎️
Engine Performance Analysis
Automotive engineers and tuners use engine torque and power curves to understand performance characteristics — torque curves show at which RPM the engine produces peak pulling effort, while power (torque × angular velocity) determines top-speed capability. The torque calculator converts between imperial horsepower and metric kilowatts, and between ft·lb and N·m, enabling comparison between engine specifications published in different countries' technical literature.
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Biomechanics & Physical Therapy
Physiotherapists and biomechanists calculate joint torques — the rotational forces acting on anatomical joints (knee, hip, elbow, shoulder) — from external loads applied at measured distances from the joint centre. Understanding joint torque is essential for designing rehabilitation exercises, specifying safe lifting limits, and analysing movement patterns that predispose athletes to injury. A force of 100N applied 0.4m from the knee joint produces 40 N·m of torque — comparable to peak quadriceps torque during walking.
🌬️
Wind Turbine & Renewable Energy Engineering
Wind turbine gearboxes must transmit enormous torques from the low-speed rotor shaft (15–20 RPM) to the high-speed generator shaft (1,500 RPM). A 2 MW wind turbine at 15 RPM produces approximately 1,270 kN·m of rotor torque — the gearbox must be designed to handle this continuously and withstand torque spikes from wind gusts. The torque calculator provides unit conversions between the kN·m, MN·m, and ft·lb notation used in different national and international turbine standards.
🏗️
Structural Engineering & Moment Analysis
Structural engineers calculate bending moments (torque about a cross-section) in beams, columns, and connections to verify that structural members have sufficient bending strength. A beam loaded at mid-span produces a maximum bending moment at mid-span equal to (force × span) / 4; this moment must be less than the section's plastic moment resistance. Torque and moment calculations in structural engineering use the same underlying mathematics — force multiplied by perpendicular distance — as mechanical torque.

Common Mistakes

1
Confusing torque (N·m) with energy (J) — they have the same SI units but different meanings
Torque in Newton-metres and energy in Joules are both dimensionally kg·m²/s² in SI base units, but they are fundamentally different quantities. Torque is a vector (it has a direction — the axis of rotation) associated with a force causing rotation; energy is a scalar associated with work done or stored. They should never be added or directly compared. The numerical equality (1 N·m of torque and 1 J of energy have the same number) is coincidental and stems from the perpendicular relationship assumed in both definitions.
2
Applying force at a non-perpendicular angle without the sin(θ) correction
The full torque formula is τ = F × r × sin(θ), where θ is the angle between the force vector and the lever arm. Only when the force is applied exactly perpendicular to the moment arm (θ = 90°, sin(θ) = 1) does the formula simplify to τ = F × r. Applying a 100N force at 60° to a 0.5m wrench handle produces τ = 100 × 0.5 × sin(60°) = 43.3 N·m — not the 50 N·m calculated assuming perpendicularity. When tightening fasteners at awkward angles, the effective torque is significantly less than the applied force would suggest.
3
Measuring moment arm from the wrong reference point
The moment arm must be measured from the axis of rotation (pivot point) to the point of force application — not along the lever or the force vector. A common error is measuring the full physical length of a wrench from handle tip to socket, when the effective moment arm is the perpendicular distance from the bolt centre (the pivot) to the line of action of the hand force. If the wrench is held at an angle, the effective moment arm is shorter than the physical wrench length.
4
Confusing ft·lb (foot-pounds of torque) with lb·ft — they are the same unit with different notation conventions
In American engineering, torque is most commonly expressed as "ft·lb" (foot-pounds) or "lb·ft" — both notations refer to the same unit (force in pounds multiplied by moment arm in feet). Confusion arises with "ft·lb" used for energy (foot-pound-force), but in the torque context both are equivalent. The distinction from the SI system is more important: 1 ft·lb = 1.356 N·m. Converting engine torque specs from US car manuals (ft·lb) to European workshop documentation (N·m) requires this factor.
5
Not accounting for friction when applying torque to fasteners
Approximately 50% of torque applied to a bolt fastener is consumed overcoming thread and underhead friction — only about 50% contributes to creating clamping force (the actual purpose of tightening). Lubricated fasteners require significantly less torque to achieve the same clamping force as dry fasteners. Using a dry torque specification on a lubricated fastener over-torques the bolt; using a dry specification on a dry fastener with a damaged thread (high friction) under-clamps the joint. Always use the manufacturer's specified torque for the specified fastener condition (dry, lubricated, thread-locked).

Torque Unit Conversion Quick Reference

From To Multiply By
N·m ft·lb × 0.7376
ft·lb N·m × 1.3558
N·m in·lb × 8.8507
kgf·m N·m × 9.8067
N·m kgf·cm × 10.197

References

  1. Shigley, J.E. et al. Shigley's Mechanical Engineering Design. McGraw-Hill, 2014.
  2. BIPM. The International System of Units (SI), 9th edition. bipm.org, 2019.
  3. Norton, R.L. Machine Design: An Integrated Approach. Prentice Hall, 2013.
  4. SAE International. J1875: Torque-Angle Tightening. sae.org, 2023.
  5. Bhandari, V.B. Design of Machine Elements. McGraw-Hill, 2019.

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