Calculate torque, force, or lever arm distance using τ = F × r. Free online mechanics calculator for physics and engineering with multiple unit support (N·m, lb·ft, etc.).
Calculate torque, force, or distance using the formula: τ = F × r
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Torque is one of the most fundamental concepts in mechanics and rotational physics. It describes the rotational force that causes objects to rotate around an axis or pivot point. Whether you're studying physics, engineering, working on mechanical systems, or designing machinery, understanding torque is essential. Our Torque Calculator makes it easy to calculate torque, force, or lever arm distance using the fundamental formula: τ = F × r (torque equals force times distance).
Torque is what makes wheels turn, doors open, wrenches tighten bolts, and engines power vehicles. It's the rotational equivalent of linear force, and understanding it is crucial for analyzing rotational motion, designing mechanical systems, and solving engineering problems involving rotation.
Our Torque Calculator is designed for simplicity and accuracy. Follow these steps to get your calculation:
The calculator uses the fundamental torque formula: Torque = Force × Distance (τ = F × r)
You can rearrange this formula to solve for any variable:
The torque formula is one of the most important equations in rotational mechanics:
τ = F × r
Where: τ = torque, F = force, r = distance from pivot (lever arm)
Torque (τ) is a measure of the rotational force applied to an object. It depends on two factors:
The key insight is that the same force produces more torque when applied farther from the pivot point. This is why longer wrenches make it easier to turn bolts, and why door handles are placed far from the hinges.
Torque calculations are used in countless real-world scenarios across various fields:
It's crucial to use consistent units in your calculations. Our calculator supports multiple unit systems and automatically converts between them:
Note: 1 N·m = 0.737562 lb·ft, 1 lb·ft = 1.35582 N·m
Note: 1 N = 0.224809 lb, 1 kgf = 9.80665 N
Tip: The calculator automatically handles unit conversions, so you can mix different unit systems. For example, you can input force in Newtons, distance in centimeters, and get torque in N·m.
A force of 50 N is applied perpendicular to a wrench at a distance of 0.3 m from the bolt. What is the torque?
τ = F × r = 50 N × 0.3 m = 15 N·m
You need to apply 20 N·m of torque to tighten a bolt. If your wrench is 0.25 m long, what force must you apply?
F = τ / r = 20 N·m / 0.25 m = 80 N
You can apply a maximum force of 200 N. How long must your wrench be to produce 50 N·m of torque?
r = τ / F = 50 N·m / 200 N = 0.25 m = 25 cm
An engine produces 300 N·m of torque. If this torque is applied at a wheel radius of 0.35 m, what force is exerted on the road?
F = τ / r = 300 N·m / 0.35 m = 857.1 N
This is the force that propels the vehicle forward
Calculate the torque when a force of 50 lb is applied at a distance of 2 ft from the pivot.
τ = F × r = 50 lb × 2 ft = 100 lb·ft
Which equals approximately 135.6 N·m
The lever arm (r) in the torque formula is the perpendicular distance from the pivot point to the line of action of the force. This is crucial to understand:
Our calculator assumes the force is applied perpendicular to the lever arm, which is the most common case. For angled forces, you would need to account for the angle using the sine function.
Torque plays a fundamental role in rotational motion, similar to how force affects linear motion:
Understanding torque is essential for analyzing rotating systems, from simple wheels to complex machinery.
Understanding torque has practical applications in daily life:
It's important to distinguish between torque and force:
The same force can produce different torques depending on where it's applied. A small force applied far from the pivot can produce more torque than a large force applied close to the pivot.
Torque (τ) equals force (F) times the lever arm distance (r): τ = F × r. This means torque increases with both force and distance. The same force produces more torque when applied farther from the pivot point. You can rearrange this to solve for force (F = τ/r) or distance (r = τ/F).
In the metric system, N·m (Newton-meters) is most common, along with kgf·m (kilogram-force meters). In the imperial system, lb·ft (pound-feet) and lb·in (pound-inches) are standard. Automotive applications often use lb·ft, while engineering typically uses N·m.
The lever arm (r) is the perpendicular distance from the pivot point to the line of action of the force. It's the shortest distance between the pivot and the force line. Maximum torque occurs when the force is perpendicular to the lever arm. For angled forces, only the perpendicular component contributes to torque.
Torque is directly proportional to distance from the pivot. Doubling the lever arm doubles the torque for the same force. This is why longer wrenches make it easier to turn bolts - they provide more torque with the same applied force. The relationship is linear: τ ∝ r.
Yes, torque can be negative, which indicates rotation in the opposite direction. Torque is a vector quantity with both magnitude and direction. Positive torque causes counterclockwise rotation (by convention), while negative torque causes clockwise rotation. Our calculator focuses on magnitude.
Torque and moment are often used interchangeably, but there are subtle differences. Torque typically refers to rotational force in dynamic situations (causing rotation), while moment often refers to static situations (bending, twisting). Both use the same formula τ = F × r and have the same units.
Engine torque determines a vehicle's ability to accelerate and pull loads. Higher torque at lower RPMs provides better towing capacity and acceleration. Torque is measured at the engine crankshaft and transmitted through the transmission to the wheels. Wheel torque = engine torque × gear ratio.
When force is not perpendicular to the lever arm, only the perpendicular component contributes to torque. The formula becomes τ = F × r × sin(θ), where θ is the angle between the force and lever arm. Maximum torque occurs at 90° (perpendicular), and zero torque occurs when force is parallel to the lever arm (0° or 180°).
Understanding torque and the relationship τ = F × r is fundamental to mechanics, rotational physics, and many practical applications. Our Torque Calculator simplifies these calculations, making it easy to solve problems involving rotational forces, lever systems, and mechanical design.
Whether you're calculating torque for engineering projects, understanding mechanical systems, or solving physics problems, this calculator provides accurate results with support for multiple unit systems. Ready to explore more physics concepts? Check out our other calculators like the Velocity Calculator for motion calculations, or use our Acceleration Calculator for acceleration problems that often complement torque analysis in rotational dynamics.
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