Torque Calculator

General Physics

Select the variable to calculate and enter the other values.

Result
Calculated Torque

45 N·m

33.190246 lbf·ft

Practical Examples

See how the Torque Calculator is used in real-world scenarios. Load an example to see how it works.

Tightening a Car's Lug Nut

example

Calculating the torque needed to tighten a lug nut on a car wheel.

Type: torque

Force: 150 N

Distance: 0.3 m

Torque: undefined undefined

Angle: 90°

Child on a See-Saw

example

Calculating the force a child needs to exert to balance a see-saw.

Type: force

Force: undefined undefined

Distance: 1.5 m

Torque: 300 Nm

Angle: 90°

Opening a Stubborn Jar Lid

example

Finding the distance from the edge to apply force when the maximum torque is known.

Type: distance

Force: 50 N

Distance: undefined undefined

Torque: 5 Nm

Angle: 80°

Wrench at an Angle

example

Calculating torque when the wrench is not perpendicular to the bolt.

Type: torque

Force: 100 N

Distance: 0.25 m

Torque: undefined undefined

Angle: 60°

Other Titles
Understanding Torque: A Comprehensive Guide
Dive deep into the principles of torque, its calculation, applications, and the physics behind it.

What is Torque?

  • Defining Rotational Force
  • The Key Components: Force, Distance, and Angle
  • Units of Measurement
Torque, also known as the moment of force, is the measure of the force that can cause an object to rotate about an axis. Just as a force causes an object to accelerate in linear kinematics, torque causes an object to acquire angular acceleration. It is a vector quantity, meaning it has both a direction and a magnitude.
The Formula for Torque
The magnitude of torque is defined by the formula τ = r F sin(θ), where τ (tau) is the torque, 'r' is the length of the lever arm (the distance from the axis of rotation to the point where the force is applied), 'F' is the magnitude of the applied force, and θ (theta) is the angle between the force vector and the lever arm. For maximum torque, the force should be applied perpendicularly (at a 90-degree angle) to the lever arm, as sin(90°) = 1.

Simple Analogy

  • Imagine opening a door. You push on the side of the door farthest from the hinges. Pushing near the hinges requires much more force to get the same opening effect. The distance from the hinges (the pivot point) is your lever arm.

Step-by-Step Guide to Using the Torque Calculator

  • Selecting the Calculation Type
  • Entering Input Values and Units
  • Interpreting the Results
Our calculator is designed to be flexible, allowing you to solve for torque, force, or distance. Here's how to use it effectively:
1. Choose What to Calculate
Start by using the 'Variable to Calculate' dropdown to select whether you want to find 'Torque', 'Force', or 'Lever Arm Distance'. The input fields will adjust accordingly.
2. Provide the Known Values
Fill in the required fields. For example, if you are calculating torque, you will need to input the Force, Lever Arm Distance, and the Angle. Make sure to select the correct units for each measurement from the dropdowns next to the input fields.
3. Get Your Result
Click the 'Calculate' button. The result will be displayed instantly, along with conversions to other common units for your convenience.

Example Calculation

  • To find the torque from a 150 N force applied at a 0.3 m distance at a 90° angle, you would select 'Torque', enter Force=150 N, Distance=0.3 m, Angle=90°, and click Calculate. The result is 45 N·m.

Real-World Applications of Torque

  • Automotive Engineering
  • Construction and Machinery
  • Everyday Life
Torque is a fundamental concept in physics and engineering with countless applications.
In Automotive
Engine specifications often list a torque rating (e.g., 400 N·m @ 2500 RPM), which indicates the engine's rotational power. It's also critical when tightening bolts and nuts to a specific torque value to ensure a secure fit without damaging parts.
In Tools and Sports
A simple wrench uses torque to turn a bolt. A cyclist applies torque to the pedals to turn the wheels. Even a baseball player swinging a bat is applying torque to make the bat rotate and hit the ball with maximum force.

Did You Know?

  • Electric motors produce their maximum torque at low RPMs, which is why electric cars are known for their quick acceleration from a standstill.

Common Misconceptions and Correct Methods

  • Torque vs. Work
  • The Importance of the Angle
  • Direction of Torque
It's easy to confuse torque with similar physics concepts.
Torque is not Work
Although both torque and work have the same units in the SI system (Newton-meter), they are different concepts. Work is force applied over a distance (Force × Distance), resulting in energy transfer. Torque is a force applied at a distance from a pivot that causes rotation. No movement is required for torque to exist, but movement is required for work to be done.
Angle Matters
A common mistake is to ignore the angle and simply multiply force by distance. The force component that is perpendicular to the lever arm is what creates torque. If you push or pull parallel to the lever arm (an angle of 0° or 180°), you create zero torque.

Key Takeaway

  • Always apply force perpendicularly to a wrench for maximum effect. Leaning into it at a strange angle reduces the effective torque you can apply.

Mathematical Derivation and Examples

  • The Vector Cross Product
  • Right-Hand Rule
  • Solved Problems
For a deeper understanding, torque is formally defined as the cross product of the position vector (r) and the force vector (F): τ = r × F.
The Right-Hand Rule
The direction of the torque vector is determined by the right-hand rule. If you curl the fingers of your right hand in the direction of rotation that the torque would cause, your thumb points in the direction of the torque vector. A counter-clockwise torque is typically considered positive, and a clockwise torque is negative.
Example Problem
A mechanic applies a force of 20 lbf to the end of a 1.5 ft wrench at an angle of 75 degrees. What is the torque applied to the bolt?
τ = r F sin(θ)
τ = 1.5 ft 20 lbf sin(75°)
τ ≈ 1.5 20 0.966
τ ≈ 28.98 lbf·ft

Final Note

  • Understanding the vector nature of torque is crucial for solving complex problems in 3D space, especially in fields like robotics and aerospace engineering.