What is torque and how is it different from force?

Torque is rotational force - the tendency of force to cause rotation: • Force: Causes linear motion (push/pull) • Torque: Causes rotational motion (twist/turn) • Formula: τ = F × r × sin(θ) • Units: Newton-meters (Nm), foot-pounds (ft-lb) Think of torque as 'twisting force' - like turning a wrench or opening a door.

How does the angle affect torque calculation?

The angle between force and lever arm is crucial: • 90° (perpendicular): Maximum torque, sin(90°) = 1 • 0° (parallel): Zero torque, sin(0°) = 0 • 45°: Torque = 0.707 × (F × r) • Formula: τ = F × r × sin(θ) For maximum efficiency, apply force perpendicular to the lever arm.

What are common applications of torque calculations?

Torque is essential in many engineering applications: • Automotive: Engine torque, wheel lug nuts, transmission • Mechanical: Bolt tightening specifications • Construction: Structural joint assembly • Manufacturing: Machine tool operations • Aerospace: Control surface actuators • Daily life: Door handles, bottle caps, steering wheels

How do I determine the correct torque specification?

Torque specifications ensure proper assembly: • Manufacturer specs: Always check official documentation • Material properties: Steel, aluminum, plastic have different limits • Thread pitch: Finer threads need less torque • Lubrication: Oil/grease reduces required torque • Safety factor: Don't exceed 90% of yield strength • Tools: Use calibrated torque wrenches for precision

What's the difference between torque and work?

Torque and work are related but different concepts: • Torque: Rotational force (Nm), doesn't require motion • Work: Energy transfer (Joules), requires motion • Relationship: Work = Torque × Angular displacement • Power: Work/time = Torque × Angular velocity You can apply torque without doing work (holding a stationary wrench under load).

Torque Calculator for Mechanical Engineering

Calculate torque, force, and distance using torque equations for mechanical engineering applications.

Calculate:

Required Fields

Enter Force and Distance (angle is optional, defaults to 90°)

Force (F) - Newtons

Distance (r) - Meters

Angle (θ) - Degrees

Angle between force and lever arm (0-90°). Default is 90° for perpendicular force.

Torque (τ) - Newton⋅meters

Quick Examples

Key Formulas

Torque: τ = F × r × sin(θ)

Force: F = τ / (r × sin(θ))

Distance: r = τ / (F × sin(θ))

Units: N⋅m = N × m

Usage Tips

• Torque is measured in Newton⋅meters (N⋅m)
• Force is measured in Newtons (N)
• Distance is the perpendicular distance (lever arm)
• Angle is between force direction and lever arm
• 90° angle gives maximum torque
• 0° angle produces zero torque

Understanding Torque

The Physics

τ = F × r × sin(θ)

Torque equals Force times Distance times sine of angle

Torque (τ) is rotational force - it causes objects to rotate around an axis. The effectiveness depends on:

• Force magnitude: Larger force = more torque
• Lever arm length: Longer distance = more torque
• Angle of application: Perpendicular (90°) = maximum torque

Real-World Applications

Automotive: Wheel lug nuts, engine bolts, torque specifications
Machinery: Motor shaft design, gear systems, coupling analysis
Construction: Structural connections, crane operations, lifting equipment
Tools: Wrench effectiveness, screwdriver design, torque wrenches

💡 Engineering Tips

• Maximum torque occurs when force is perpendicular to the lever arm (90°)
• Doubling the lever arm doubles the torque for the same force
• Use longer handles for higher torque with less effort
• Torque specifications prevent over-tightening and component damage
• Consider safety factors when designing for torque loads

How to Calculate Torque

Choose calculation type

Select whether to calculate torque, force, or distance based on what values you know.

Enter known values

Input the measured values for force, distance, and angle of application.

Set angle of application

Enter the angle between force direction and lever arm (90° for perpendicular force).

Calculate result

The calculator applies τ = F × r × sin(θ) to find the torque value.

Analyze rotational effect

Interpret the torque result for your mechanical system design.

Pro Tips

Maximum torque occurs when force is applied perpendicular to the lever arm (90°)
Longer lever arms produce more torque with the same applied force
Torque direction follows the right-hand rule for rotational systems
Consider friction and mechanical advantage in real-world applications
Use consistent units throughout your calculations (N⋅m, lb⋅ft, etc.)

Understanding Your Torque Results

Low Torque (< 10 N⋅m)

Suitable for small fasteners, precision instruments, and light-duty applications. Common in electronics and small machinery.

Moderate Torque (10-100 N⋅m)

Typical for automotive applications, medium-sized bolts, and general mechanical systems. Most hand tools operate in this range.

High Torque (100-1000 N⋅m)

Heavy-duty applications like large automotive components, industrial machinery, and structural connections.

Very High Torque (> 1000 N⋅m)

Industrial applications requiring specialized tools. Common in heavy machinery, large engines, and structural steel connections.

Torque Calculator - Frequently Asked Questions

Torque at a glance

Relate torque, force, lever arm, and application angle. Helpful for wrenching, machinery, and design checks.

Mechanics made easy

Torque Calculator: Force, Distance, Power & RPM

Convert between torque, power, and speed. Compute moment from force and lever arm.

Moment basics

τ = F × r and unit conversions.

Power relation

P = τ × ω (with RPM).

Units

N·m, lb·ft, kW, hp ready.

Torque topics

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Explore mechanics

Round out calculations.

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Important: This torque calculator is designed for educational and preliminary mechanical analysis purposes using fundamental torque relationships and idealized rigid-body mechanics. While calculations are mathematically accurate for basic torque applications, real-world mechanical systems involve complex factors including material deformation, friction, dynamic loading, safety factors, and specific application requirements that are not captured by simplified torque formulas. For mechanical design, fastener selection, equipment specification, or any application involving safety-critical torque requirements, always follow manufacturer specifications, applicable safety standards, and consult qualified mechanical engineers who can account for the specific loading conditions, safety margins, and regulatory requirements of your mechanical application.

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