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Torque and Moment Calculator

Calculate torque (moment of force) from force, distance, and angle. Convert between N·m, lb·ft, and kgf·m units. Essential for engineering statics.

Enter Values

Distance from the pivot point to where the force is applied

Angle between force and moment arm (90° for perpendicular)

Result

Enter values above and click Calculate to see your result.

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Formula

τ = F × d × sin(θ)

Torque equals force times the perpendicular distance from the pivot. When the force is not perpendicular, multiply by sin(θ) where θ is the angle between the force vector and the moment arm.

Worked Example

Force: 100 N, Distance: 0.5 m, Angle: 90° Step 1: sin(90°) = 1 Step 2: τ = 100 × 0.5 × 1 = 50 N·m Step 3: = 5.0997 kgf·m = 36.878 lb·ft

Understanding Torque and Rotational Motion

Torque, often referred to as the moment of force, is the rotational equivalent of linear force. While a linear force causes an object to accelerate in a straight line, torque causes an object to rotate or twist around an axis or pivot point. It is a fundamental concept in physics and engineering, crucial for understanding how gears work, how levers amplify force, and even how engines generate power. The magnitude of torque depends on three key factors: the amount of force applied, the distance from the pivot point where the force is applied (known as the moment arm), and the angle at which the force acts relative to the moment arm. Only the component of the force perpendicular to the moment arm contributes to rotation, which is why the sine of the angle is included in the calculation. A larger force, a longer moment arm, or a force applied more perpendicularly to the moment arm will result in greater torque.
  • Torque measures the twisting or turning effect of a force.
  • It is essential for mechanical design, statics, and dynamics calculations.
  • The unit of torque is typically Newton-meters (N·m) in the SI system.
  • Maximizing torque often involves increasing the moment arm or applying force at a 90-degree angle.

Grasping the concept of torque is vital for anyone working with rotating machinery, levers, or even just tightening a bolt. Use our Torque and Moment Calculator to easily compute and visualize these rotational forces.

You can also calculate changes using our Beam Reaction Calculator.

Frequently Asked Questions

What is the difference between torque and moment?

In engineering statics, they are essentially the same: a force times a distance that causes rotation. "Torque" is more common for rotating shafts; "moment" is used for beam analysis and statics.

Why multiply by sin(θ)?

Only the component of force perpendicular to the moment arm creates rotation. When force is perpendicular (90°), sin(90°) = 1 and torque is maximized.

How do I convert N·m to lb·ft?

Multiply N·m by 0.7376 to get lb·ft. For example, 100 N·m = 73.76 lb·ft.

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