Torque Calculator
torque calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Torque Calculator
Calculator
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Formula: τ = r × F × sin(θ)
Worked example — 25 N·m
Formula
τ = r × F × sin(θ)
Rotational force. Torque equals the cross product of position vector and force.
Worked Examples
Example 1: Wrench
Problem:50 N force, 0.5 m handle, 90°
Solution:τ=0.5×50×sin(90°)=25 N·m
Result:25 N·m
Frequently Asked Questions
What is torque in physics?
Torque (τ) is the rotational equivalent of force. It measures how effectively a force causes an object to rotate about an axis: τ = r × F × sin(θ), where r is the lever arm length, F is the applied force, and θ is the angle between r and F. The SI unit is Newton-metres (N·m).
How do you calculate torque with an angle?
Use τ = r × F × sin(θ). Maximum torque occurs at θ = 90° (sin 90° = 1). Example: a 50 N force applied at 0.4 m from the pivot at 60°: τ = 0.4 × 50 × sin(60°) = 0.4 × 50 × 0.866 ≈ 17.3 N·m.
What units are used for torque calculations?
Force F is in Newtons (N), lever arm r in metres (m), and angle θ in degrees (converted internally to radians). Torque τ is in Newton-metres (N·m). In imperial units, 1 N·m = 0.7376 ft·lbf. Automotive specs often use N·m or lb·ft.
What is the relationship between torque and power?
Power equals torque multiplied by angular velocity: P = τω, where ω is in radians per second. In practical terms: Power (W) = Torque (N·m) × 2π × RPM / 60. For cars: HP ≈ Torque (lb·ft) × RPM / 5252. A 300 lb·ft engine at 4000 RPM produces about 228 HP.
What is the difference between horsepower and torque?
Horsepower measures how quickly work is done (sustained speed and acceleration at higher RPMs). Torque measures rotational force (pulling power and low-end acceleration). Diesel trucks emphasize torque for towing. Sports cars emphasize horsepower for top speed. HP = torque x RPM / 5,252.
Background & Theory
Torque at a Glance: Typical Values
Torque (τ) measures a force's tendency to rotate an object about a pivot. Because it depends on both the magnitude of the force and the angle at which it's applied, the same push can produce very different torque depending on where and how it's applied — pushing a door near its hinge takes much more force than pushing near the handle for the same rotating effect.
| Application | Typical torque |
|---|---|
| Car wheel lug nut | 80-140 N·m (varies by vehicle, check manufacturer spec) |
| Spark plug | 20-30 N·m |
| Small electronics screw (M2-M3) | 0.2-0.6 N·m |
| Passenger car engine (peak) | 150-400 N·m |
| Large diesel truck engine (peak) | 1,000-2,500 N·m |
Always torque fasteners to the manufacturer's exact specification with a calibrated torque wrench — over-tightening can strip threads or warp components, while under-tightening risks parts working loose.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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