Calculate torque from force, lever arm length and angle in N·m or ft·lbs, or solve for the force, lever arm or angle needed for a target torque.
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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.
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.
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.
What Each Calculator Input Means
| Input | Meaning | Typical Units |
|---|---|---|
| Radius | Distance from the pivot or axis to the point where the force is applied | m, cm, in, ft |
| Force | Magnitude of the push or pull creating rotation | N, lbf |
| Angle | Angle between the radius line and the force vector | degrees, radians |
| Torque | Rotational effect produced by the force | N·m, kN·m, ft·lbf, in·lbf |
Rearranged Torque Equations
Choose the quantity to solve for and enter the required magnitudes. Inverse force and radius require a nonzero sine; at 0° or 180° they are impossible for nonzero torque and indeterminate for zero torque.
For the angle task, torque magnitude/(radius × force) must lie from 0 through 1. The calculator reports the principal angle and its supplement within 0–180°; both yield the same magnitude, and they coincide at 90°. A ratio above 1 is physically inconsistent, apart from floating point roundoff at the boundary.
How the Angle Changes Torque
The angle matters because only the component of force that acts perpendicular to the radius produces rotation.
| Angle | Torque Factor | Interpretation |
|---|---|---|
| 0° | sin(0^°) = 0 |
No torque |
| 30° | sin(30^°) = 0.5 |
Half of the perpendicular-case torque |
| 45° | sin(45^°) ≈ 0.707 |
About 70.7% of maximum |
| 60° | sin(60^°) ≈ 0.866 |
About 86.6% of maximum |
| 90° | sin(90^°) = 1 |
Maximum torque |
How to Use the Torque Calculator Correctly
- Enter any three known values: radius, force, angle, or torque.
- Choose the correct unit system before calculating.
- Use the radius, not the diameter.
- Make sure the angle is measured between the radius and the force direction.
- If your angle is given in radians, select radians instead of degrees.
- Select the unit beside each value. The calculator converts mixed input units to SI before calculating, then converts the result to your selected output unit.
Examples
If a force of 120 N is applied 0.35 m from the pivot at an angle of 60°, the torque is:
If you need 250 N·m of torque with a 0.5 m lever arm and a 90° force angle, the required force is:
For 40 N·m, a 0.25 m radius and a 200 N force, the principal angle is 53.13°; the supplementary 126.87° produces the same magnitude:
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.
| Conversion | Meaning |
|---|---|
1 lb × ft ≈ 1.35582 N × m |
Convert pound-feet to newton-meters |
1 N × m ≈ 0.73756 lb × ft |
Convert newton-meters to pound-feet |
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
- Confusing radius r with perpendicular moment arm d: enter r with the included angle; d = r sin(θ). Do not apply the sine factor twice.
- 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.
For rotational dynamics, net torque is related to angular acceleration by:
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. This calculator takes radius r and the angle, then computes d = r sin(θ). If entering a known perpendicular moment arm as the distance, use 90° so the sine factor is not applied twice.
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.
