EngineeringFormulaMechanical Engineering
Torque Calculator
Calculate torque from an applied force and the perpendicular lever-arm distance.
Torque is the rotational equivalent of linear force: it equals the applied force multiplied by the perpendicular distance from the pivot to the line of action of that force. Enter the force and lever-arm distance to calculate the resulting torque. This calculator uses the perpendicular-lever-arm form T = F × r; if your force is applied at an angle, convert it to the perpendicular component first or use r × F × sin(θ).
F · Applied force, perpendicular to the lever arm.
r · Perpendicular distance from the pivot to the line of action of the force.
Solution
Enter the required values to calculate torque.
T = F × r
Formula Sheet
- TTorque
- FForce
- rLever Arm
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| T | Torque | Rotational force produced about the pivot. | N·m, lb·ft |
| F | Force | Applied force, perpendicular to the lever arm. | N, kN, lbf |
| r | Lever Arm | Perpendicular distance from the pivot to the line of action of the force. | mm, cm, m, in, ft |
How to Use This Calculator
- 01Enter the applied Force and the perpendicular Lever Arm distance, choosing the unit that matches your source data (N or lbf; m, ft, or in).
- 02Select Calculate to compute the resulting torque.
- 03Review the formula substitution to see exactly how the force and lever-arm values combine.
- 04Mix unit systems freely between the two inputs if needed - the calculator converts each to a common base before computing, so a force in lbf and a lever arm in meters still produce a correct result.
- 05If your input is a physical arm length and the force is not at 90°, multiply the force by sin(θ), or multiply the arm by the perpendicular distance to the force line of action before entering it.
How the Formula Works
Torque is the rotational equivalent of force: instead of producing straight-line acceleration, it produces angular acceleration about a pivot. It's calculated as the applied force multiplied by the perpendicular distance from the pivot to the line of action of that force - T = F × r.
Because torque scales linearly with lever-arm length, the same force produces more torque the farther it's applied from the pivot - the reason a longer wrench makes a stubborn bolt easier to turn. This calculator computes the magnitude of torque for a force already perpendicular to the lever arm; a force applied at any other angle only contributes its perpendicular component (F × sin θ).
Worked Example 01
Calculating torque from force and lever arm
Known
- Force (F): 250 N
- Lever Arm (r): 0.5 m
Formula
T = F × r
Substitution
T = 250 × 0.5
Result
T = 125 N·m
A 250 N force applied at a 0.5 m perpendicular distance from the pivot produces 125 N·m of torque.
Worked Example 02
Calculating torque in US customary units
Known
- Force (F): 50 lbf
- Lever Arm (r): 2 ft
Formula
T = F × r
Substitution
T = 50 × 2
Result
T = 100 lb·ft (≈ 135.58 N·m)
A 50 lbf force at a 2 ft lever arm produces 100 lb·ft of torque - the calculator converts both inputs to newtons and meters internally, giving the same result in SI units.
Applications
- 01Mechanical power transmission and shaft design
- 02Torque wrench and fastener specifications
- 03Motor and engine torque analysis
- 04Quick lever-arm checks where the perpendicular force component is already known
Assumptions
- 01Force is applied perpendicular to the lever arm.
- 02The lever arm is treated as rigid.
Where This Model Stops
- 01Does not account for force applied at an angle - resolve the perpendicular component of the force first, or use a full torque-vector calculation.
- 02Not valid for systems with multiple simultaneous forces or moments - those require vector summation.
- 03Does not estimate bolt preload, thread friction, wrench calibration, shaft stress, or fastener safety factors.
References
- [1]
Torque
Standard mechanical engineering and physics fundamentals
T = F × r is a foundational relationship in rotational mechanics.
Frequently Asked Questions
What if the force isn't applied perpendicular to the lever arm?
Only the component of force perpendicular to the lever arm contributes to torque. Multiply the force by the sine of the angle between the force and the lever arm before using this calculator.
What's the difference between torque and moment?
Torque and moment describe the same physical quantity - a rotational effect produced by a force. "Torque" is more commonly used for rotating shafts and fasteners, while "moment" is more common in structural engineering.
How is this different from the Torque Wrench or Bolt Torque calculators?
This page calculates pure rotational effect from force and lever arm. The Torque Wrench Calculator is for applying a specified wrench torque, while the Bolt Torque Calculator estimates tightening torque related to fastener preload and friction.