Torque Calculator

Enter the total force, the radius of the applied force, and the angle at which it is applied to calculate the total torque on an object. This calculator can also determine the radius, force, or angle given the other variables.

• All Physics Calculators
• All Torque Calculators
• Counter Balance Weight Calculator
• Net Torque Calculator

Torque Formula and Calculator Guide

Torque measures the turning effect of a force about a pivot, shaft, axle, or hinge. For a given force, torque increases when the force is applied farther from the center of rotation and when the force acts more nearly perpendicular to the radius.

\tau = rF\sin(\theta)

In this equation, τ is torque, r is the radius or lever arm, F is the applied force, and θ is the angle between the radius line and the force direction.

When the force is perfectly perpendicular to the radius, the sine term becomes 1, so torque reaches its maximum value for that same force and distance.

\tau_{\max} = rF

Another useful way to think about torque is with the perpendicular distance from the pivot to the line of action of the force, often called the moment arm or lever arm.

\tau = Fd_{\perp}

d_{\perp} = r\sin(\theta)

What Each Calculator Input Means

Rearranged Torque Equations

If you know any three values, the missing value can be found by rearranging the torque formula.

r = \frac{\tau}{F\sin(\theta)}

F = \frac{\tau}{r\sin(\theta)}

\theta = \sin^{-1}\left(\frac{\tau}{rF}\right)

If you are solving for angle, the value inside the inverse sine must be between 0 and 1 when using torque magnitude. If it is larger than 1, the inputs are not physically consistent and should be checked for unit or entry errors.

How the Angle Changes Torque

The angle matters because only the component of force that acts perpendicular to the radius produces rotation.

\sin(0^\circ)=0

\sin(30^\circ)=0.5

\sin(45^\circ)\approx0.707

\sin(60^\circ)\approx0.866

\sin(90^\circ)=1

How to Use the Torque Calculator Correctly

1. Enter any three known values: radius, force, angle, or torque.
2. Choose the correct unit system before calculating.
3. Use the radius, not the diameter.
4. Make sure the angle is measured between the radius and the force direction.
5. If your angle is given in radians, select radians instead of degrees.
6. Keep units consistent. Avoid mixing newtons with feet or pounds-force with meters unless you convert first.

Examples

If a force of 120 N is applied 0.35 m from the pivot at an angle of 60°, the torque is:

\tau = 0.35 \times 120 \times \sin(60^\circ) \approx 36.37\ \text{N}\cdot\text{m}

If you need 250 N·m of torque with a 0.5 m lever arm and a 90° force angle, the required force is:

F = \frac{250}{0.5 \times \sin(90^\circ)} = 500\ \text{N}

If a system produces 40 N·m of torque with a 0.25 m radius and a 200 N force, the angle is:

\theta = \sin^{-1}\left(\frac{40}{0.25 \times 200}\right) = \sin^{-1}(0.8) \approx 53.13^\circ

Common Real-World Uses of Torque

• Tightening or loosening bolts with a wrench
• Estimating motor or engine output at a shaft
• Analyzing gears, pulleys, and crank handles
• Calculating loads on doors, levers, and hinges
• Checking rotational force in robotics and machinery
• Studying statics and dynamics in engineering and physics

Important Unit Notes

The most common torque units are newton-meters and pound-feet. They represent the same type of quantity, but they are not interchangeable without conversion.

1\ \text{lb}\cdot\text{ft} \approx 1.35582\ \text{N}\cdot\text{m}

1\ \text{N}\cdot\text{m} \approx 0.73756\ \text{lb}\cdot\text{ft}

Torque and energy share the same base units in SI, but they are not the same concept. Torque describes a turning tendency, while energy describes the capacity to do work.

Common Mistakes When Calculating Torque

• Using the full length of an object instead of the actual perpendicular distance to the force line of action
• Entering diameter where the formula requires radius
• Using the wrong angle reference
• Ignoring unit conversion before calculating
• Assuming a force through the pivot creates torque when it actually creates none
• Confusing torque with power; power depends on both torque and rotational speed

Sign Convention and Direction

In many introductory problems, the calculator is used to find torque magnitude only. In a more complete statics or dynamics analysis, torque can be assigned a sign based on rotation direction:

• Counterclockwise torque is often treated as positive
• Clockwise torque is often treated as negative

When multiple forces act on the same object, the net torque determines whether the object tends to rotate and how strongly it rotates.

\tau_{\text{net}} = \sum \tau

For rotational dynamics, net torque is related to angular acceleration by:

\tau_{\text{net}} = I\alpha

Here, I is moment of inertia and α is angular acceleration.

Torque Calculator FAQ

Is torque highest at 90 degrees?

Yes. A force applied perpendicular to the radius produces the maximum possible torque for that force and radius.

What happens at 0 degrees or 180 degrees?

The line of action passes directly toward or away from the pivot, so the perpendicular component is zero and the torque is zero.

Can increasing the radius increase torque?

Yes. For the same force and angle, a larger radius produces more torque because the turning leverage is greater.

Should I use radius or lever arm?

If the force is not perpendicular, the most exact approach is to use the perpendicular distance to the force line of action. Using radius with the sine term accounts for that automatically.

Why does the calculator allow degrees or radians?

Angles may be supplied in either form. The important part is matching the calculator setting to the way your angle is expressed.