Torque Calculator
Formula
τ = F × r × sin(θ)
Where: τ = Torque, F = Force, r = Distance (lever arm), θ = Angle
About This Calculator
Torque Calculator is designed to reduce manual errors and give repeatable outputs when you need quick, reliable answers.
Calculate rotational force (torque) from applied force, lever arm length, and angle. Used in engineering, automotive, and mechanical design to verify bolt tightening specs, motor output, and structural loads.
If your workflow expands, pair this calculator with Projectile Motion Calculator and Newton's Second Law Calculator to cross-check assumptions and build a stronger analysis chain.
Formula
τ = F × d × sin(θ), where τ is torque (N·m), F is applied force (N), d is moment arm distance (m), and θ is the angle between force vector and lever arm.
Example Calculation
The worked example below demonstrates how the input fields translate into the final output. Use it as a quick validation pass before entering your own numbers.
- force (N): 50
- distance (m): 0.3
- angle (degrees): 90
Explanation of Results
Result Interpretation
When force is applied perpendicular (90°), sin(90°) = 1, so torque = 50 × 0.3 × 1 = 15 N·m. If the angle were 30°, torque would drop to 50 × 0.3 × 0.5 = 7.5 N·m — half the value.
FAQ
What is the torque formula?
Torque (τ) = Force (F) × Distance (d) × sin(angle θ). The angle is between the force vector and the lever arm. Maximum torque occurs when force is perpendicular to the arm (θ = 90°), giving sin(90°) = 1.
What units does torque use?
Torque is measured in Newton-meters (N·m) in SI units, or foot-pounds (ft·lb) in imperial. 1 N·m = 0.7376 ft·lb. Automotive torque specs are usually in N·m or ft·lb depending on region.
Why does angle matter in torque calculations?
Only the perpendicular component of force creates rotation. The sin(θ) factor accounts for this — a force applied at 45° produces only 70.7% of the torque that the same force perpendicular to the arm would produce. Always apply force as close to 90° as possible for maximum efficiency.
How do I calculate torque for tightening bolts?
Use the wrench length as the moment arm (d), the force you apply as F, and 90° as the angle (you push perpendicular to the wrench handle). A 0.25 m wrench with 80 N of force gives 20 N·m — always check against the manufacturer's torque spec for that fastener.
Related Calculators
Continue exploring tools in this topic cluster to improve internal discoverability and reduce orphaned workflows.
See Also
Other calculators in Mechanics