Torque Calculator

About Torque Calculator

Our Torque Calculator helps you calculate torque using multiple methods: force and distance, power and angular velocity, angular acceleration with moment of inertia, or calculate moment of inertia from mass and radius. Perfect for engineers, physics students, mechanics, and anyone working with rotational motion and forces.

How to Use the Torque Calculator

1. Select your calculation method (Force, Power, Angular, or Moment)
2. Enter the required values for your chosen method
3. Click "Calculate" to get instant results
4. View detailed solution steps and additional metrics
5. See rotation direction (CW/CCW) for torque calculations
6. Use the formulas reference card for quick lookup

What is Torque?

Torque (τ) is the rotational equivalent of force. It measures the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Torque is calculated as the product of force and the perpendicular distance from the axis of rotation. The SI unit of torque is the Newton-meter (N⋅m).

Calculation Methods

1. Force Method (Basic Torque)

Calculate torque from force, distance, and angle:

Formula: τ = r × F × sin(θ)

• τ: Torque in Newton-meters (N⋅m)
• r: Distance from axis of rotation in meters (m)
• F: Applied force in Newtons (N)
• θ: Angle between force and lever arm in degrees (°)

When the force is perpendicular to the lever arm (θ = 90°), sin(90°) = 1, and the formula simplifies to τ = r × F. This produces maximum torque for a given force and distance.

2. Power Method

Calculate torque from power and rotational speed:

Formula: τ = P / ω

• τ: Torque in Newton-meters (N⋅m)
• P: Power in Watts (W)
• ω: Angular velocity in radians per second (rad/s)

You can input either RPM (revolutions per minute) or angular velocity directly. The calculator converts RPM to rad/s using: ω = (RPM × 2π) / 60.

3. Angular Acceleration Method

Calculate torque from moment of inertia and angular acceleration:

Formula: τ = I × α

• τ: Torque in Newton-meters (N⋅m)
• I: Moment of inertia in kg⋅m²
• α: Angular acceleration in rad/s²

This is Newton's second law for rotation. It relates the net torque to the angular acceleration of an object, similar to how F = ma relates force to linear acceleration.

4. Moment of Inertia Method

Calculate moment of inertia for a point mass:

Formula: I = m × r²

• I: Moment of inertia in kg⋅m²
• m: Mass in kilograms (kg)
• r: Distance from axis of rotation in meters (m)

This formula applies to a point mass or a thin ring. Different shapes have different moment of inertia formulas (e.g., solid cylinder: I = ½mr², solid sphere: I = ⅖mr²).

Understanding Torque Direction

Torque has both magnitude and direction, making it a vector quantity:

• Positive Torque: Counterclockwise (CCW) rotation
• Negative Torque: Clockwise (CW) rotation
• Zero Torque: No rotation or balanced forces

The right-hand rule determines torque direction: point your fingers in the direction of the radius vector, curl them toward the force vector, and your thumb points in the torque direction.

Key Concepts

Moment of Inertia

Moment of inertia (I) is the rotational equivalent of mass. It measures an object's resistance to changes in rotational motion. Objects with mass farther from the axis of rotation have higher moments of inertia and are harder to spin or stop spinning.

Angular Velocity

Angular velocity (ω) measures how fast an object rotates, expressed in radians per second (rad/s) or revolutions per minute (RPM). One complete revolution equals 2π radians or 360 degrees.

Angular Acceleration

Angular acceleration (α) measures the rate of change of angular velocity, expressed in rad/s². It's analogous to linear acceleration but for rotational motion.

Power and Torque Relationship

Power is the rate of doing work. In rotational systems, power equals torque times angular velocity: P = τω. This relationship is crucial in engine and motor design, where high torque at low RPM provides strong acceleration, while high RPM with moderate torque provides high top speed.

Practical Applications

• Automotive Engineering: Engine torque specifications, wheel lug nut tightening, transmission design
• Mechanical Engineering: Bolt tightening specifications, shaft design, gear systems
• Robotics: Motor selection, joint design, gripper force calculations
• Physics Education: Rotational dynamics, angular momentum, mechanical advantage
• Construction: Crane operations, structural analysis, tool specifications
• Sports Science: Biomechanics analysis, equipment design, performance optimization
• Aerospace: Control surface actuation, gyroscope design, satellite orientation

Common Torque Values

• Car Wheel Lug Nuts: 80-140 N⋅m (depending on vehicle)
• Bicycle Pedal: 5-10 N⋅m (typical pedaling force)
• Spark Plug: 20-30 N⋅m
• Oil Drain Plug: 25-35 N⋅m
• Small Car Engine: 150-250 N⋅m peak torque
• Large Truck Engine: 1000-2000 N⋅m peak torque
• Electric Motor (Small): 0.1-10 N⋅m
• Industrial Motor: 100-10,000 N⋅m

Torque vs. Work vs. Energy

While torque is measured in N⋅m, the same units as work and energy (Joules), they represent different physical quantities:

• Torque: A force that causes rotation (N⋅m)
• Work: Force applied over a distance (J = N⋅m)
• Energy: Capacity to do work (J)

Work done by torque equals torque times angular displacement: W = τθ (where θ is in radians). For one complete revolution (2π radians), work = τ × 2π.

Design Considerations

• Lever Arm Length: Longer lever arms produce more torque for the same force (e.g., longer wrench handle)
• Force Application Angle: Maximum torque occurs when force is perpendicular to the lever arm
• Material Strength: Components must withstand applied torques without deformation or failure
• Torque Multiplication: Gear systems can multiply torque at the expense of speed
• Friction Losses: Real systems lose energy to friction, reducing effective torque
• Dynamic vs. Static Torque: Starting torque (static) often differs from running torque (dynamic)

Torque Measurement Tools

• Torque Wrench: Mechanical tool that clicks or indicates when target torque is reached
• Torque Screwdriver: Precision tool for small fasteners
• Dynamometer: Measures engine or motor torque output
• Torque Sensor: Electronic device for continuous torque monitoring
• Strain Gauge: Measures shaft twist to calculate torque

Safety and Best Practices

• Always use calibrated torque tools for critical applications
• Follow manufacturer torque specifications for fasteners
• Apply torque gradually and smoothly, not in sudden jerks
• Consider thread lubrication effects on torque requirements
• Re-torque fasteners after initial settling period when specified
• Account for temperature effects on torque specifications
• Use proper technique: pull, don't push torque wrenches

Frequently Asked Questions

Advanced Topics

• Gyroscopic Torque: Torque required to change the orientation of a spinning object
• Torsional Vibration: Oscillating torque in rotating shafts
• Torque Ripple: Variation in torque output, common in electric motors
• Preload Torque: Initial torque applied to create tension in bolted joints
• Breakaway Torque: Torque needed to overcome static friction and start rotation
• Cogging Torque: Magnetic resistance to rotation in motors without current

Calculation Examples