Calculate Torque

Online calculator and formulas for calculating torque

Torque Calculator

Calculate rotational force

Calculates the Torque (M) from the acting Force (F) and the Lever arm (r). Torque describes the rotational effect of a force.

Result
Torque (M):

Example Calculation

Example: Wrench
Problem:

A force of 40 N is applied perpendicular to the lever arm on a 25 cm long wrench. What is the torque at the bolt head?

Given:
  • Force F = 40 N
  • Lever arm r = 25 cm = 0.25 m
  • Force acts perpendicular
  • Find: Torque M
Solution:
\[M = F \times r\]
\[M = 40 \text{ N} \times 0.25 \text{ m}\]
\[M = 10 \text{ Nm}\]
Practical Applications
Mechanical engineering: Bolt connections, gears, motors
Automotive engineering: Wheel nuts, engine torque, brake systems
Everyday life: Wrenches, door handles, levers
Lever Principle

Golden rule of mechanics: What you save in force, you must add in distance. A longer lever requires less force for the same torque.

\[\text{Longer lever} \Rightarrow \text{Less force}\] \[\text{Shorter lever} \Rightarrow \text{More force}\]

Formulas for torque

Torque describes the rotational effect of a force around a pivot point. It is measured in Newton meters (Nm) and is the product of force and lever arm.

Basic torque formula

Torque when force acts perpendicular to the lever arm.

\[\displaystyle M = F \cdot r\]
M = Torque [Nm]
F = Force [N]
r = Lever arm [m]
General formula

Torque at any angle between force and lever arm.

\[\displaystyle M = F \cdot r \cdot \sin(\alpha)\]
α = Angle between force and lever arm
For perpendicular application: sin(90°) = 1
Rearranged for force

Calculation of required force for a given torque.

\[\displaystyle F = \frac{M}{r}\]
Rearranged for lever arm

Calculation of required lever arm for a given force.

\[\displaystyle r = \frac{M}{F}\]
Important Notes
  • Torque is maximum when force acts perpendicular to the lever arm
  • The longer the lever arm, the less force is needed for the same torque
  • 1 Newton meter = 1 N × 1 m = 1 kg·m²/s²
  • Torque is a vector quantity with direction

Detailed description of torque

Physical Fundamentals

Torque indicates the force generated at the pivot point when the lever is moved by a force at the other end of the lever. The longer the lever, the less force is needed to generate the rotational force or torque.

Usage Instructions

To calculate, enter the required values and click the 'Calculate' button. The calculator computes torque for force acting perpendicular to the lever arm.

Application Areas

Mechanical Engineering

Bolt connections, gears, motors, couplings. Important for designing drive systems and fastening elements.

Automotive Engineering

Tightening torques for wheel nuts, engine torque, brake systems. Crucial for safety and functionality.

Everyday Life and Tools

Wrenches, door handles, levers, nutcrackers. The lever principle simplifies many daily tasks.

Understanding the Lever Principle

Torque explains why a longer wrench makes it easier to loosen a bolt:

Short lever (10 cm)

For 10 Nm torque:
\[F = \frac{10 \text{ Nm}}{0.1 \text{ m}} = 100 \text{ N}\]

Long lever (50 cm)

For 10 Nm torque:
\[F = \frac{10 \text{ Nm}}{0.5 \text{ m}} = 20 \text{ N}\]

Conclusion: A 5 times longer lever reduces the required force by a factor of 5!


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