Moment of Force & Lever Arm Calculator

Vector Statics, Lever Arms & Moment of Force Metrology

The moment of a force () quantifies its capacity to produce rotation about a specific pivot point:

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• Moment of Force Equations (ISO & Statics Standards)**:

= \×

M = r \× F \× \\θ = F \× d_\

d_\ (Perpendicular Distance) = r \× \\θ \ ()

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• Unit Conversion Multipliers to N\·m:

• 1\ N\·: SI base unit of moment

• 1\ kN\·: 1,000\ N\·

• 1\ ft\·: \1.355818\ N\· \ 1\ N\· = \0.737562\ ft\·

• 1\ in\·: \0.112985\ N\· \ 1\ N\· = \8.85075\ in\·

• 1\ kgf\·: 9.80665\ N\·

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• Standard Mechanical Statics Benchmarks**:

• Wrench Tightening (200 N @ 0.50m): = 100.0\ N\· \ \73.76\ ft\·

• Wheel Lug Nut (400 N @ 0.35m): = 140.0\ N\· \ \103.26\ ft\·

• Angled Lever: = 207.85\ N\· \ \153.30\ ft\·

• Cantilever Beam (5 kN @ 3m): = 15.0\ kN\· \ \11,063\ ft\·

How to Use This Calculator

Enter your Applied Force Magnitude (F in Newtons) (e.g. 200 in N), Lever Arm Distance from Pivot (r in meters) (e.g. 0.50 in m), Angle of Applied Force (θ in degrees) (e.g. 90 in °), To Moment of Force Unit — choose from Newton-Meters (N·m - SI Base Unit), Kilonewton-Meters (kN·m - Structural Engineering), Foot-Pounds Force (ft·lbf - Imperial / US), and Mechanical Statics Benchmark — choose from Custom Moment of Force, Wrench Bolt Tightening (200 N @ 0.50m, θ=90°) → M = 100.0 N·m | 73.76 ft·lbf | 885.1 in·lbf, Cantilever Beam Tip Load (5,000 N @ 3.0m, θ=90°) → M = 15.0 kN·m (11,063 ft·lbf). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Perpendicular lever arm d_perp = r * sin(theta)

Moment of force M = r F sin(theta) (in N*m)

Worked Example

A mechanic using a 0.50-meter breaker bar pushes with 200 Newtons of force at 90° to loosen a stubborn lug nut, generating exactly 100.0 N·m (73.76 ft·lbf) of turning moment.

Understanding Your Result

Force in Newtons (N): 1 N = 1 kg·m/s². Reference values: 1 kg object at Earth's surface weighs 9.81 N, atmospheric pressure 101,325 Pa (N/m²). Pressure benchmarks: car tire 30–35 psi (207–241 kPa), blood pressure systolic 120 mmHg (16 kPa), deep sea at 3,000m depth ~300 atm (30 MPa). Torque = Force × moment arm length — doubling the wrench length doubles the torque for the same applied force. Always verify whether gauge or absolute pressure is required for the application.