Torque Calculator
Calculate torque, force, or lever arm distance using the formula τ = r × F × sin(θ). Perfect for torque wrench settings, automotive work, engineering calculations, and physics homework. Includes unit conversions for N·m, lb·ft, and lb·in.
📊 Common Torque Unit Conversions
| Unit | Equivalent |
|---|---|
| 1 N·m | 0.7376 lb·ft |
| 1 N·m | 8.8507 lb·in |
| 1 lb·ft | 1.3558 N·m |
| 1 lb·in | 0.1130 N·m |
| 1 kg·m | 9.8067 N·m |
| 1 oz·in | 0.00706 N·m |
Understanding Torque
Torque (also called moment or moment of force) is the measure of the rotational force that causes an object to rotate about an axis. Just as force causes linear acceleration, torque causes angular acceleration. The magnitude of torque depends on three factors:
- Force (F): The applied force — greater force produces greater torque.
- Lever Arm (r): The perpendicular distance from the pivot point to the line of action of the force — a longer lever arm produces greater torque.
- Angle (θ): The angle between the lever arm and the force vector — torque is maximum at 90° (perpendicular) and zero at 0° or 180°.
Torque Formula: τ = r × F × sin(θ)
Where:
τ = Torque (N·m or lb·ft)
r = Lever arm distance (m or ft)
F = Applied force (N or lbf)
θ = Angle between r and F (degrees)
How the Torque Calculator Works
This calculator supports three modes:
- Solve for Torque (τ): Enter force, lever arm, and angle to calculate the resulting torque.
- Solve for Force (F): Enter torque, lever arm, and angle to find the required force.
- Solve for Lever Arm (r): Enter torque, force, and angle to find the required distance.
The calculator uses the formula τ = r × F × sin(θ), rearranged as needed. It also converts torque values to N·m, lb·ft, and lb·in for your convenience.
Why Use This Torque Calculator?
- Three Modes: Solve for torque, force, or lever arm distance.
- Unit Flexibility: Switch between metric and imperial units.
- Visual Understanding: A diagram shows the relationship between force, lever arm, and angle.
- Educational: See step-by-step calculations and the formula in action.
- Free & Private: No registration, no data storage.
Real-World Applications of Torque
- Automotive: Torque wrench settings for bolts and lug nuts.
- Engineering: Designing levers, gears, and rotating machinery.
- Construction: Determining force needed to turn valves and handles.
- Sports: Golf swings, baseball bats, and tennis rackets.
- Everyday Life: Opening doors, using wrenches, and seesaws.
❓ Torque Calculator FAQ
What is torque?
Torque is the measure of the rotational force that causes an object to rotate about an axis. It is calculated as the product of force and the perpendicular distance from the pivot point to the line of action of the force.
What is the formula for torque?
The torque formula is τ = r × F × sin(θ), where τ is torque, r is the lever arm distance, F is the applied force, and θ is the angle between the lever arm and the force.
When is torque maximum?
Torque is maximum when the force is applied perpendicular to the lever arm, which is when θ = 90° and sin(θ) = 1.
When is torque zero?
Torque is zero when the force is applied directly toward or away from the pivot point (θ = 0° or 180°), or when the lever arm distance is zero.
What are the most common torque units?
N·m (Newton-meter) is the standard SI unit of torque. lb·ft (pound-foot) is common in automotive and mechanical work in the US, while lb·in (pound-inch) is used for smaller fasteners and tools.
How do I convert N·m to lb·ft?
Multiply N·m by 0.7376 to get lb·ft. For example, 10 N·m × 0.7376 = 7.376 lb·ft.
How do I convert lb·ft to N·m?
Multiply lb·ft by 1.3558 to get N·m. For example, 10 lb·ft × 1.3558 = 13.558 N·m.
What is the difference between torque and force?
Force is a push or pull that causes linear motion. Torque is a rotational force that causes angular motion. Force is measured in newtons (N) or pounds (lbf), while torque is measured in newton-meters (N·m) or pound-feet (lb·ft).
How does the angle affect torque?
Torque depends on sin(θ), where θ is the angle between the lever arm and the force. The torque is maximum at 90° (sin(90°) = 1) and decreases as the angle approaches 0° or 180° (sin(0°) = 0).
What is a torque wrench?
A torque wrench is a tool used to apply a specific amount of torque to a fastener, such as a bolt or nut. It is essential in automotive and mechanical work to ensure bolts are tightened to the correct specification.
How do I calculate the force needed for a given torque?
Rearrange the torque formula: F = τ / (r × sin(θ)). This calculator's "Solve for Force" mode does this for you.
How do I calculate the lever arm needed for a given torque?
Rearrange the torque formula: r = τ / (F × sin(θ)). This calculator's "Solve for Lever Arm" mode does this for you.
What is the difference between torque and work?
Torque is a rotational force (N·m or lb·ft), while work is energy (joules or foot-pounds). Although they share the same units in some systems, they represent different physical quantities. One newton-meter of torque is not the same as one joule of work.
What is the relationship between torque and angular acceleration?
According to Newton's second law for rotation, τ = I × α, where τ is torque, I is the moment of inertia, and α is the angular acceleration. This is the rotational equivalent of F = m × a.
What is the lever arm?
The lever arm is the perpendicular distance from the axis of rotation (pivot point) to the line of action of the force. It determines how effectively a force can produce rotation.
How does a longer wrench create more torque?
A longer wrench increases the lever arm distance (r). Since torque = r × F × sin(θ), a longer lever arm produces more torque for the same applied force, making it easier to turn bolts.
What is the torque of a 100 N force at 0.5 m from the pivot at 90°?
Using τ = r × F × sin(θ) = 0.5 × 100 × sin(90°) = 0.5 × 100 × 1 = 50 N·m.
Is this torque calculator accurate for real-world applications?
This calculator provides accurate results based on the standard torque formula. It is suitable for engineering calculations, automotive work, and physics homework. Always verify critical specifications with professional tools and standards.