Torque calculator for force, lever arm, and angle using τ = rF sin(θ), with signed torque and moment-of-force context.
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Torque is a turning effect
Torque measures how strongly a force tends to rotate an object around a pivot. The same force produces more torque when it acts farther from the pivot or when the force is closer to perpendicular to the lever arm.
The angle matters
The calculator uses the torque equation τ = rF sin(θ), where θ is the angle between the lever arm and the force. A 90° angle produces the maximum torque for the same force and lever arm.
Solved torque
This torque calculator used τ = rF sin(θ) with a 90° angle between the force and lever arm.
Moment of force
Torque around a pivot
Torque and moment of force describe the same turning effect, which is why the page targets both torque calculator and moment of force calculator intent.
Perpendicular components
r⊥ = r sin(θ)
The calculator converts the lever arm to its perpendicular component before applying the turning-force equation.
Why 90° matters
Maximum torque
When the force is perpendicular to the lever arm, sin(θ) is 1 and the turning effect is strongest.
Formula breakdown
Perpendicular lever arm
r⊥ = r × sin(θ)
Torque from force and distance
τ = F × r⊥
Classic torque equation
τ = rF sin(θ)
Physics
Use this torque calculator to calculate torque from force, lever arm, and angle. It is useful when you need a torque formula calculator, a moment of force calculator, or a quick way to estimate turning effect around a pivot, shaft, or fastener.
This torque calculator solves the turning effect created when a force acts at a distance from a pivot. Enter force in newtons, lever arm in metres, and the angle between them in degrees to calculate torque in newton-metres.
That makes the page useful for searches such as torque calculator, calculate torque from force and distance, and torque calculator with angle, where the real question is not just the formula itself but how the angle changes the result.
Torque is the tendency of a force to rotate an object around an axis. The farther from the pivot the force is applied, and the more perpendicular that force is to the lever arm, the larger the torque becomes.
In practical terms, torque is the moment of force. Mechanics texts often use those phrases interchangeably, so a torque calculator and a moment of force calculator usually describe the same turning-force workflow.
τ = rF sin(θ)
Classic torque equation using lever arm, force, and the angle between them.
r⊥ = r sin(θ)
Perpendicular lever arm used to turn the force into a pure moment.
τ = F × r⊥
Torque as force multiplied by the perpendicular distance from the pivot.
The sine term is what makes the angle important. If the force is applied at 90 degrees to the lever arm, sin(θ) equals 1 and the torque is maximized. If the force is parallel to the lever arm, sin(θ) equals 0 and there is no turning effect.
That is why the same wrench force can produce very different torque values depending on the angle of application. A small change in angle can have a large effect on the final torque.
If a 50 N force acts on a 0.3 m lever arm at 90°, the torque is 15 N·m. If the same force acts at 45°, the torque falls to about 10.61 N·m because only part of the force contributes to rotation.
For a negative force or a sign convention that points the opposite way, the calculator keeps the sign. That is useful when you want to show clockwise versus counterclockwise torque in the same coordinate system.
Force measures push or pull. Torque measures the rotational effect created by that force at some distance from the pivot. A large force applied close to the pivot can create less torque than a smaller force applied farther away.
That is why torque and force are related but not interchangeable. The same motor, wrench, or load can feel very different depending on where the force is applied and how the angle is oriented.
Torque is usually reported in newton-metres in SI work. In some workshop contexts you may also see pound-feet or ounce-inches, but this page keeps the calculation in newton-metres because that is the standard physics expression.
A torque value is a signed quantity when a convention is used. Positive and negative results can help distinguish rotation direction, which is why the calculator preserves signed inputs instead of forcing everything into a positive-only display.
This calculator assumes the force, lever arm, and angle describe a simple static torque problem. It does not solve full rigid-body dynamics, distributed loads, or systems where multiple torques interact and change over time.
For more advanced mechanics problems you may need a statics or rotational-dynamics workflow instead. This calculator is best for quick checks, classroom problems, wrench-force estimates, and simple pivot calculations.
Frequently asked questions
Torque is the turning effect of a force acting around a pivot or axis. It is also called the moment of force.
Use τ = F × r⊥, where r⊥ is the perpendicular distance from the pivot to the line of action of the force. If you know the angle between the force and lever arm, use τ = rF sin(θ).
The lever arm is the distance from the pivot to the point where the force is applied. Only the perpendicular part of that distance contributes to torque.
Only the component of force perpendicular to the lever arm contributes to rotation. The sine term in the torque equation captures that effect, so a 90° angle produces the strongest torque.
Yes. In mechanics, torque and moment of force describe the same turning effect around an axis or pivot.
Use newtons for force, metres for lever arm, degrees for the angle, and newton-metres for the result if you are working in SI units.
Yes. A negative torque usually means the force is acting in the opposite rotational direction under your chosen sign convention.
Torque is maximized when the force is perpendicular to the lever arm, because sin(90°) = 1.
Force measures push or pull, while torque measures the rotational effect of that force about a pivot. A force can be large without creating much torque if it acts close to the pivot or nearly along the lever arm.
Yes, as long as the problem is a simple single-force torque calculation. If multiple forces or changing motion are involved, you may need a more advanced statics or rotational dynamics method.
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