Enter values to see results
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N·m
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ft·lbs
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N
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rad
Enter values to see results
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N·m
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ft·lbs
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N
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rad
The Torque Calculator determines the rotational force (moment of force) produced when a force is applied at a distance from a pivot point. Torque is the rotational equivalent of linear force and is what causes objects to rotate, tighten bolts, open doors, and drive engines. The fundamental formula is:
$$\tau = rF\sin\theta$$
where r is the lever arm (distance from the pivot to the point of force application), F is the magnitude of the applied force, and θ is the angle between the force vector and the lever arm. When the force is applied perpendicular to the lever arm (θ = 90°), torque is maximized since sin(90°) = 1.
This calculator provides results in both Newton-meters (N·m, the SI unit) and foot-pounds (ft·lbs, commonly used in automotive and construction contexts). It also shows the effective perpendicular component of the force, which is the portion that actually contributes to rotation. Understanding torque is essential for mechanical engineering, automotive design, structural analysis, and everyday tasks like using wrenches, levers, and hinged mechanisms.
Torque is the cross product of the position vector and force vector:
$$\vec{\tau} = \vec{r} \times \vec{F}$$
The magnitude is:
$$\tau = rF\sin\theta$$
Only the component of force perpendicular to the lever arm produces torque:
$$F_{\perp} = F\sin\theta$$
The conversion to foot-pounds:
$$\text{ft·lbs} = \text{N·m} \times 0.737562$$
Key special cases: at θ = 90°, sinθ = 1 (maximum torque). At θ = 0° or 180°, sinθ = 0 (zero torque, because the force is along the lever arm and cannot cause rotation).
Higher torque means greater rotational effect. A car engine producing 400 N·m has strong rotational force at the crankshaft. A wrench with a longer handle produces more torque with the same force. When the angle deviates from 90°, torque decreases — this is why you should push perpendicular to a wrench for maximum effectiveness. In static equilibrium, the sum of all torques about any point equals zero.
Inputs
Results
Applying 50 N at the end of a 30 cm wrench at 90° produces 15 N·m (11.06 ft·lbs) of torque.
Inputs
Results
At 45°, only 70.7 N of the 100 N force contributes to torque, producing 35.4 N·m instead of the 50 N·m at 90°.
Force causes linear acceleration (F = ma), while torque causes angular acceleration (τ = Iα). Torque depends on both the force magnitude and how far from the pivot it is applied. A small force at a large distance can produce the same torque as a large force at a small distance.
Only the component of force perpendicular to the lever arm creates rotation. When force is parallel to the lever arm (θ = 0°), it pushes directly toward or away from the pivot without causing any rotation, so torque is zero.
Both measure torque. Newton-meters (N·m) are the SI unit used internationally. Foot-pounds (ft·lbs) are used in the US customary system, particularly in automotive contexts. 1 N·m = 0.7376 ft·lbs.
Power equals torque times angular velocity: P = τω. In automotive terms, horsepower = torque (ft·lbs) × RPM / 5252. This is why high-torque engines feel powerful at low RPM.
A torque wrench measures the torque applied to a fastener. Proper torque ensures bolts are tight enough to hold but not so tight they strip threads or deform parts. Critical in automotive, aerospace, and structural applications.
Yes. The sign indicates the direction of rotation. By convention, counterclockwise torque is positive and clockwise is negative. In equilibrium problems, opposing torques cancel out.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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