Torque Calculator

Torque (also called a moment of force) is the rotational equivalent of linear force. It measures how effectively a force causes an object to rotate about an axis. Torque τ = F × r × sin(θ), where F is the applied force, r is the distance from the pivot to the point of force application (the lever arm), and θ is the angle between the force vector and the lever arm. The SI unit of torque is the newton-metre (N·m).

τ = F × r × sin(θ). F is the force in newtons, r is the lever arm length in metres, and θ is the angle between the force direction and the lever arm (0° to 180°). When the force is perpendicular to the arm (θ = 90°), sin θ = 1 and torque is maximized: τ = F × r. When the force is parallel to the arm (θ = 0°), no torque is produced.

Power P = τ × ω, where ω is the angular velocity in rad/s. To convert RPM to rad/s: ω = 2π × RPM / 60. So P (watts) = τ (N·m) × 2π × RPM / 60. Example: 200 N·m at 3000 RPM gives P = 200 × 2π × 3000/60 ≈ 62,832 W ≈ 62.8 kW ≈ 84.2 hp.

Torque is a force × distance (N·m) that causes rotation. Power is the rate of doing work (watts). They are related by P = τ × ω: torque tells you the rotational strength, power tells you how fast that strength is being applied. A diesel engine at low RPM has high torque but moderate power; a sports car engine at high RPM converts moderate torque into high power.

Newton's second law for rotation states τ = I × α, where τ is the net torque (N·m), I is the moment of inertia (kg·m²), and α is the angular acceleration (rad/s²). This is the rotational equivalent of F = ma. A larger moment of inertia (more mass further from the axis) requires more torque to achieve the same angular acceleration.

The moment of inertia I is the rotational analogue of mass. It measures how resistant an object is to angular acceleration. I depends on both the mass and its distribution relative to the rotation axis: I = Σ mᵢrᵢ². For common shapes: solid disk I = ½mr², solid sphere I = 2mr²/5, thin ring I = mr². Concentrating mass closer to the axis reduces I (figure skater spinning faster by pulling arms in).

1 N·m = 0.737562 lb·ft. To convert from N·m to lb·ft: multiply by 0.7376. To convert from lb·ft to N·m: divide by 0.7376 (or multiply by 1.35582). Example: 300 N·m = 300 × 0.7376 ≈ 221 lb·ft. Engine torque specs are often given in lb·ft in US markets and N·m elsewhere - the conversion is essential for comparing specifications.

The lever arm (also called the moment arm) is the perpendicular distance from the pivot point (axis of rotation) to the line of action of the force. It is the r in τ = F × r × sin(θ). A longer lever arm produces more torque for the same force - this is why a longer wrench makes tightening a bolt easier. The effective lever arm is r × sin(θ), which equals the perpendicular distance from the pivot to the force vector.

Typical peak torques: compact car engine 150–250 N·m (110–185 lb·ft), sports car 300–600 N·m (220–440 lb·ft), diesel truck 1,000–3,000 N·m (740–2,200 lb·ft), electric car motor 300–700 N·m (available instantly at 0 RPM). Hand tightening a bolt: ~5–10 N·m. Bicycle crank: ~60–100 N·m peak.

Static torque causes no rotation (or the object is in equilibrium). Dynamic torque causes angular acceleration. For example, a wrench held stationary applies static torque against a bolt's resistance; once the bolt starts turning, the torque is dynamic. In engines, the torque curve shows dynamic torque available at different RPM. The torque × angular velocity product gives mechanical power in both cases.

In structural engineering, torque (moment of force) appears in beam bending (the bending moment is a torque about any cross-section), column buckling, shaft design, and bolt/fastener specifications. A beam loaded at mid-span has maximum bending moment at the centre, which equals force × span/4. Bolts are specified by tightening torque (e.g., M12 bolt to 80 N·m) to achieve the correct clamp force without yielding the fastener.