Calculate torque in newton-meters from force and distance, with conversions to imperial units
Perpendicular distance from the rotation axis to where force is applied
Torque (symbol τ, tau) is the rotational equivalent of linear force. It measures the turning effect of a force applied at a distance from a rotation axis. The same force applied farther from the pivot creates more torque.
τ = F × r × sin(θ)
Where θ is the angle between force and lever arm. For perpendicular force (90°), sin(θ) = 1, simplifying to τ = F × r.
Right-hand rule: Point your fingers in the direction of the lever arm, curl them toward the force direction—your thumb points in the direction of the torque vector (clockwise/counterclockwise axis).
Torque (N·m) and energy (Joules) are both calculated as force × distance, giving them identical dimensional units. However:
Torque (N·m)
Energy (Joules)
Convention: To avoid confusion, torque is always written as N·m (newton-meter), never as J (Joules), even though they're dimensionally equivalent.
| Application | Torque (N·m) | Torque (ft-lbs) |
|---|---|---|
| Bicycle pedal (casual) | 40 | 29.5 |
| Car wheel lug nut | 100-120 | 74-89 |
| Motorcycle wheel bolt | 60-80 | 44-59 |
| Spark plug (gasoline engine) | 25-30 | 18-22 |
| Oil drain plug (car) | 30-40 | 22-29 |
| Compact car engine (max) | 180-200 | 133-148 |
| V8 sports car (max) | 500-700 | 369-516 |
| Diesel truck engine | 1,500-2,000 | 1,106-1,475 |
Torque is rotational force (how hard you twist), while horsepower is the rate of doing work (how fast you can sustain that twist). Formula: HP = (Torque × RPM) / 5252. An engine can have high torque but low horsepower if it spins slowly (diesel truck), or low torque but high horsepower if it spins fast (motorcycle).
A torque wrench has an internal clutch mechanism calibrated to a specific torque value. When you reach that value, the clutch slips and produces an audible click, preventing over-tightening. Digital torque wrenches use strain gauges and beep/display the reading instead.
Yes! Torque = Force × Distance, so doubling the wrench length doubles the torque for the same applied force. This is why "cheater bars" (pipe extensions) make it easier to loosen stuck bolts. However, using excessive leverage can strip threads or break fasteners.
Only the perpendicular component of force creates torque. The formula becomes τ = F × r × sin(θ), where θ is the angle between the force vector and the lever arm. At 90° (perpendicular), sin(90°) = 1 gives maximum torque. At 0° (parallel), sin(0°) = 0 gives zero torque.
Electric motors produce maximum torque from 0 RPM because electromagnetic force is available immediately. Internal combustion engines need to build RPM before developing peak torque (typically 3,000-5,000 RPM) because they rely on combustion cycles. This is why electric cars accelerate so quickly from a standstill.
You're tightening lug nuts to specification (100 N·m) using a torque wrench with a 0.5 meter lever arm. How much force should you apply?
Given:
Solve for force:
τ = F × r
100 = F × 0.5
F = 100 ÷ 0.5
F = 200 Newtons (~45 lbs)
Practical tip: If you double the wrench length to 1.0 m, you'd only need 100 N (~22 lbs) of force to achieve the same 100 N·m torque. This is why torque wrench specs assume a specific handle length!
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