Torque Calculator

Torque is rotational force measured in N·m or lb·ft. It's crucial for fasteners, engines, and mechanical systems.

Higher torque means more rotational force.

Common conversions: 1 N·m = 0.7376 lb·ft = 10.197 kg·cm = 8.851 lb·in.

Engine specs often use N·m (metric) or lb·ft (imperial).

To calculate torque, multiply the applied force by the perpendicular distance from the axis of rotation: τ = F × r. Force is measured in newtons (N) and the lever arm in meters (m), giving torque in newton-meters (N·m).

For example, a 100 N force applied 0.5 m from the pivot produces 100 × 0.5 = 50 N·m.

When the force is not perpendicular, use τ = r × F × sin(θ), where θ is the angle between the force vector and the moment arm; the effective torque is maximized at 90°.

According to HyperPhysics (Georgia State University), torque is formally the cross product of the position vector and force vector.

The SI unit of torque is the newton-meter (N·m), the product of the newton (unit of force) and the meter (unit of length).

The BIPM and NIST note that although N·m is dimensionally equivalent to the joule, torque is never expressed in joules to avoid confusion with energy. In imperial systems, torque is measured in pound-feet (lb·ft) or pound-inches (lb·in).

Standard conversions:

• 1 N·m = 0.7376 lb·ft = 8.851 lb·in = 10.197 kg·cm
• 1 lb·ft = 1.3558 N·m

The newton itself is defined as 1 kg·m/s² (F = ma), so torque carries base units of kg·m²/s².

Power equals torque multiplied by angular velocity: P = τ × ω, where ω is in radians per second. Since angular velocity relates to rotational speed by ω = 2πf = RPM × 2π/60, the practical formula becomes Power (kW) = Torque (N·m) × RPM / 9549.

For example, an engine producing 300 N·m at 3000 RPM delivers 300 × 3000 / 9549 = 94.25 kW.

In imperial units, Horsepower = Torque (lb·ft) × RPM / 5252.

Khan Academy explains that this is why torque and power curves always intersect at 5252 RPM on a dyno chart when using lb·ft and mechanical horsepower.

Torque measures rotational force, while horsepower measures the rate of doing work — how quickly that force is applied over time. They are linked by P = τ × ω, meaning power rises with both torque and rotational speed.

A diesel truck engine generates high torque at low RPM for towing and pulling, whereas a high-revving sports car engine produces peak horsepower at high RPM for top-end acceleration.

Encyclopaedia Britannica describes power as work per unit time, and work as force applied through a distance.

In practical terms, torque gets a heavy load moving, and horsepower keeps it accelerating once in motion.

To convert newton-meters to pound-feet, multiply by 0.7376; to convert pound-feet back to newton-meters, multiply by 1.3558.

For example, 100 N·m × 0.7376 = 73.76 lb·ft, and 50 lb·ft × 1.3558 = 67.79 N·m.

Other useful factors, consistent with NIST unit-conversion tables, include:

• 1 N·m = 8.851 lb·in
• 1 N·m = 10.197 kg·cm

Because 1 foot equals 12 inches, 1 lb·ft also equals 12 lb·in.

Getting conversions right matters: mixing up lb·ft and lb·in has caused fasteners to be tightened to twelve times or one-twelfth of the intended specification.

Torque calculations underpin countless engineering and everyday tasks.

• Mechanics use torque wrenches to tighten wheel lug nuts and cylinder-head bolts to exact specifications, preventing loosening from vibration or thread failure.
• Automotive engineers rate engines by peak torque — a factor in acceleration and towing capacity, with passenger cars typically producing 200–300 N·m.
• In robotics, servo and stepper motors are selected by their torque output to move joints and payloads.
• Wind turbines convert aerodynamic force into rotational torque on the drive shaft, and IEEE literature covers electric-motor torque control extensively.
• Structural engineers analyze the moment (torque about a point) on beams and bolted connections to ensure safety under load.

• The most frequent error is confusing pound-feet with pound-inches; since 1 lb·ft = 12 lb·in, mixing them yields a 12x error that can strip threads or leave bolts dangerously loose.
• Another mistake is using the total force instead of only its perpendicular component — remember τ = r × F × sin(θ), so an angled force delivers less torque.
• Measuring the lever arm from the wrong point (not the true rotation axis) also skews results.
• When computing power, forgetting to convert RPM to rad/s (ω = RPM × 0.10472) produces wildly wrong figures.
• Finally, never express torque in joules; NIST and BIPM reserve the joule strictly for energy despite the shared base units.

Torque increases in direct proportion to the lever arm length because τ = F × r. Doubling the distance from the pivot doubles the torque produced by the same force — this is the principle of mechanical advantage.

A mechanic applying 200 N at the end of a 0.3 m wrench generates 60 N·m, but the same force on a 0.6 m breaker bar generates 120 N·m.

Khan Academy describes this as trading distance for force: a longer arm lets a smaller effort overcome a larger resistive moment.

This is why breaker bars, cheater pipes, and long handles are used to loosen seized fasteners.

Bolt torque estimates the tightening effort needed to achieve a target clamping preload, commonly approximated by T = K × D × F, where:

• T is torque
• K is the friction coefficient (about 0.2 for dry steel)
• D is the nominal bolt diameter
• F is the desired preload force

Because friction from lubrication or plating strongly affects K, always follow manufacturer or ISO fastener specifications rather than estimates alone.

Typical dry values for Grade 8.8 fasteners are roughly:

• M8 = 25 N·m
• M10 = 50 N·m
• M12 = 85 N·m

Use a calibrated torque wrench and tighten in the correct sequence to distribute load evenly across a joint.