Torque Calculator
Calculate Torque, Force, Distance, or Angle. Enter your known values to instantly solve for the missing variable.
Understanding Torque: The Physics of Rotational Force
Whether you are a mechanic tightening a cylinder head bolt with a wrench, or an engineering student designing a motor mechanism, understanding Torque is critical. Simply put, torque is a measure of how much a force acting on an object causes that object to rotate.
Our Torque Calculator removes the guesswork, allowing you to easily compute the rotational force by inputting your known variables. It automatically handles complex trigonometric angles and metric/imperial conversions behind the scenes.
Glossary of Torque Variables
- Torque (τ - Tau): The twisting force that causes rotation. It is standardly measured in Newton-meters (Nm) in the metric system, or Pound-feet (lb-ft) in the imperial system.
- Force (F): The linear push or pull applied to the object. It is measured in Newtons (N) or Pound-force (lbf).
- Lever Arm Distance (r): The distance from the axis of rotation (the pivot point) to the exact spot where the force is applied. Also known as the radius. Measured in Meters (m), Centimeters (cm), Feet (ft), or Inches (in).
- Angle (θ - Theta): The angle between the force vector and the lever arm. Measured in Degrees (°) or Radians (rad). Maximum torque is achieved at a 90° angle.
Method 1: Perpendicular Force (The Simple Formula)
When you apply force perfectly perpendicular (at a 90-degree angle) to a wrench or lever, all of your energy goes directly into rotating the object. Because the sine of 90° is exactly 1, the angle is dropped from the equation.
Perpendicular Torque Formula:
τ = F × r
Example: Imagine using a wrench that is 0.5 meters long. If you pull straight down on it with 100 Newtons of force, what is the torque?
τ = 100 N × 0.5 m
τ = 50 Nm (Newton-meters)
If you know the Torque, you can easily reverse the formula:
- To find Force: F = τ / r
- To find Lever Distance: r = τ / F
Method 2: Angled Force (The Full Formula)
In the real world, it is often impossible to apply force at a perfect 90° angle. If you push on a wrench at an awkward angle, some of your force pushes directly into the pivot point (doing no rotational work), while only the perpendicular component creates torque. We account for this using trigonometry (Sine).
Complete Angled Formula:
τ = F × r × sin(θ)
Example: You are applying 100 Newtons of force to that same 0.5-meter wrench, but this time at a 30-degree angle. (Note: sin(30°) = 0.5).
τ = 100 N × 0.5 m × sin(30°)
τ = 100 × 0.5 × 0.5 = 25 Nm
As the math proves, applying force at a 30° angle results in exactly half the torque (25 Nm) compared to pushing straight on perpendicularly (50 Nm)!
Why Unit Conversion Matters
A common pitfall in physics calculations is mixing imperial and metric units. You cannot directly multiply Pounds of force (lbf) by Centimeters (cm) and get a standard answer. Our calculator avoids these errors by standardizing all user inputs into base metric units before applying the Sine functions, ensuring a highly precise output every time.