Torque Calculator
Torque is the rotational equivalent of force — it measures how much a force tends to rotate an object about an axis. This calculator computes torque in Newton-meters from force and lever arm distance, and converts to foot-pounds and inch-pounds.
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Formula
τ = F × r × sin(θ)
Torque (τ) equals force (F) times lever arm length (r) times the sine of the angle (θ) between the force and the lever arm. Maximum torque occurs when force is perpendicular to the lever arm (θ = 90°, sin = 1). 1 N·m = 0.7376 ft·lb = 8.851 in·lb.
How to use the Torque Calculator
- 1
Enter your force
Value should be in N.
- 2
Enter your lever arm length
Value should be in m.
- 3
Enter your angle between force and lever
Value should be in °.
- 4
Read your results instantly
Results update in real time as you type.
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What torque is and why it matters
Torque is what causes rotation. Just as force causes linear acceleration (F = ma), torque causes angular acceleration (τ = Iα, where I is moment of inertia and α is angular acceleration). Opening a door, tightening a bolt, steering a car, and pedaling a bicycle all involve torque.
The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. A longer lever arm produces more torque for the same force — this is the principle of the lever. Archimedes famously said, 'Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.'
Torque in engines and motors
Engine torque is the twisting force at the crankshaft, measured in N·m or ft·lb. Power = torque × angular velocity (P = τω). A diesel truck engine might produce 2,000 N·m of torque at low RPM — ideal for towing heavy loads. A high-revving sports car engine produces less torque but at much higher RPM, giving equivalent or greater power (P = τ × RPM × 2π/60).
Torque matters more than power for acceleration from a stop (where RPM is low). Power matters more for top speed. Torque multipliers — transmissions and gearboxes — trade RPM for torque, letting engines work in their efficient range.
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Torque wrenches and fastener specifications
Automotive and mechanical engineering specify bolt torques to achieve proper clamping force without overtightening (stripping threads) or undertightening (loose connections). A typical lug nut for a passenger car requires 90-120 N·m (65-90 ft·lb). Cylinder head bolts may require 150-200 N·m in sequence.
A torque wrench measures the torque applied to a fastener. The relationship between torque and bolt tension depends on friction (coefficient of friction between threads and surfaces). Lubricated bolts require less torque for the same tension — always check whether a spec assumes dry or lubricated threads.
Tips & Insights
Apply force perpendicular for max torque
Sin(90°) = 1 gives maximum torque. Pulling a wrench handle at an angle reduces effective torque by the sine of the angle.
1 N·m ≈ 0.738 ft·lb
To convert N·m to ft·lb, multiply by 0.7376. To convert ft·lb to N·m, multiply by 1.3558.
Longer handle = more torque
Doubling the wrench handle length doubles the torque for the same force. Extension bars on ratchets increase torque but risk over-tightening fasteners.
Worked Examples
Tightening a bolt
Torque = 200 × 0.25 × sin(90°) = 50 N·m ≈ 36.9 ft·lb.
Opening a door
Torque = 10 × 0.8 = 8 N·m. Pushing near the hinge (0.05 m) would need 160 N for the same torque.
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Frequently Asked Questions
What is torque?
Torque is the rotational equivalent of force. τ = F × r × sin(θ). It measures how much a force tends to rotate an object about a pivot point.
What is the unit of torque?
Newton-meters (N·m) in SI. Also foot-pounds (ft·lb) and inch-pounds (in·lb) in imperial units. 1 N·m = 0.7376 ft·lb.
What is a lever arm?
The lever arm (moment arm) is the perpendicular distance from the axis of rotation to the line of action of the force.
How is torque different from work?
Both are measured in N·m but mean different things. Work = force × distance in the direction of motion. Torque = force × perpendicular distance. Work is energy; torque is a rotational force (not energy).
Why do engines have a torque curve?
Engine torque varies with RPM. Most engines peak torque at mid-range RPM and have less at idle and redline. The torque curve shape determines how the vehicle responds at different speeds.
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