Torque Calculator
Calculate torque (τ = F × r), force, or lever arm. Includes power-RPM-torque conversion for engine and motor calculations — results in N·m and ft·lb.
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Enter your values above to see the results.
Tips & Notes
- ✓Torque = Force × perpendicular distance. A 20 N force applied 0.5 m from a pivot produces 10 N·m. Doubling the wrench length doubles the torque — this is why breaker bars are longer than standard ratchets.
- ✓Power-torque-RPM relationship: Power (W) = Torque (N·m) × Angular velocity (rad/s) = Torque × 2π × RPM / 60. A 100 kW engine at 3,000 RPM produces: Torque = 100,000 × 60 / (2π × 3,000) = 318.3 N·m.
- ✓Unit conversions: 1 N·m = 0.7376 ft·lb = 8.851 in·lb. Engine torque is often in N·m or ft·lb; fastener torque specs are often in N·m or in·lb. Always verify units before tightening.
- ✓Torque wrenches measure and limit applied torque to protect threaded connections. Under-torquing causes loosening; over-torquing strips threads or stretches bolts past their elastic limit.
- ✓Moment of a couple: two equal opposite forces separated by distance d create a pure torque (couple) = F × d, with no net force. Steering wheels and screwdrivers apply couples, not single forces.
Common Mistakes
- ✗Using total arm length instead of perpendicular distance — torque uses the perpendicular component of the force times the arm length. If force is at angle θ: τ = F × r × sin(θ). A force parallel to the lever arm creates zero torque.
- ✗Forgetting to convert RPM to rad/s in power calculations — Power = τ × ω requires ω in rad/s. ω = 2π × RPM / 60. At 1,500 RPM: ω = 2π × 1,500 / 60 = 157.08 rad/s, not 1,500.
- ✗Confusing torque (N·m) with energy (J = N·m) — both have the same units but different meanings. Torque is a rotational force about an axis; energy is work done. Never add or equate them.
- ✗Applying torque spec in wrong units — a bolt spec of 25 ft·lb is not the same as 25 N·m (25 ft·lb = 33.9 N·m). Using the wrong unit can over- or under-torque by 36%, risking joint failure.
- ✗Ignoring friction in torque transmission — threaded fasteners lose 70-90% of applied torque to thread and bearing friction. Only 10-30% actually becomes bolt clamping force. Use proper lubrication and torque specs.
Torque Calculator Overview
Torque is the rotational equivalent of force — every rotating machine, threaded fastener, and lever system involves torque. The principle that τ = F × r allows engineers to trade force for distance: a small force over a long arm can produce the same torque as a large force over a short arm.
Torque formula:
τ = F × r × sin(θ) | For perpendicular force: τ = F × r | Units: N·m (SI), ft·lb (imperial)
EX: Tighten an M12 bolt with target 86 N·m. Using a 0.25 m wrench: F = 86 / 0.25 = 344 N (about 35 kg of hand force). Extend to 0.4 m breaker bar: F = 86 / 0.4 = 215 N (22 kg). Longer wrench = less force required.Power-Torque-RPM relationship:
Power (W) = τ (N·m) × 2π × RPM / 60 | Torque = Power × 60 / (2π × RPM) = Power (kW) × 9,549 / RPM
EX: 200 kW engine at 5,500 RPM → Torque = 200,000 × 60 / (2π × 5,500) = 347 N·m. Same engine at 2,500 RPM peak torque of 420 N·m → Power at that point = 420 × 2π × 2,500 / 60 = 109.9 kWTorque specifications — common fasteners:
| Bolt Size | Grade 8.8 (Dry) | Grade 8.8 (Lubricated) | Grade 10.9 (Dry) |
|---|---|---|---|
| M6 | 10 N·m | 8 N·m | 14 N·m |
| M8 | 25 N·m | 20 N·m | 35 N·m |
| M10 | 49 N·m | 39 N·m | 69 N·m |
| M12 | 86 N·m | 69 N·m | 120 N·m |
| M16 | 210 N·m | 168 N·m | 295 N·m |
| M20 | 410 N·m | 328 N·m | 580 N·m |
| Vehicle Type | Peak Torque | RPM at Peak Torque | Peak Power |
|---|---|---|---|
| Small economy car (1.0L turbo) | 170–200 N·m | 1,500–3,000 | 85–100 kW |
| Family sedan (2.0L) | 250–320 N·m | 1,800–3,500 | 130–160 kW |
| Performance car (3.0L turbo) | 450–600 N·m | 2,000–4,000 | 280–400 kW |
| Heavy truck diesel | 2,000–3,000 N·m | 1,000–1,500 | 300–450 kW |
| Electric motor (Tesla Model 3) | 420 N·m | 0–5,000 | 283 kW |
Frequently Asked Questions
Torque τ = F × r × sin(θ), where F is force in Newtons, r is the distance from the pivot to where force is applied (meters), and θ is the angle between force and lever arm. For a force perpendicular to the arm (θ = 90°, sin = 1): τ = F × r. Example: a 50 N force applied at the end of a 0.4 m wrench perpendicular to the handle → τ = 50 × 0.4 = 20 N·m. Extending the wrench to 0.6 m: τ = 50 × 0.6 = 30 N·m — 50% more torque with 50% longer wrench.
Torque (N·m) = Power (W) × 60 / (2π × RPM) = Power (kW) × 9,549 / RPM. Example: 150 kW engine at 4,000 RPM → Torque = 150,000 × 60 / (2π × 4,000) = 9,000,000 / 25,133 = 358 N·m. At peak power RPM, torque can be calculated from power. Peak torque occurs at a different (lower) RPM than peak power for most engines — this is why towing vehicles need high low-RPM torque, not high peak power.
1 N·m = 0.7376 ft·lb. 1 ft·lb = 1.3558 N·m. 1 in·lb = 0.1130 N·m. Quick reference: 10 N·m = 7.4 ft·lb; 25 N·m = 18.4 ft·lb; 50 N·m = 36.9 ft·lb; 100 N·m = 73.8 ft·lb; 200 N·m = 147.5 ft·lb. Automotive lug nuts in the US are often specified in ft·lb (80-120 ft·lb for most passenger cars = 108-163 N·m). Always use a calibrated torque wrench and the manufacturer specification for critical fasteners.
Bolt torque spec depends on bolt size, grade, and lubrication state. General guideline for steel bolts, dry conditions: M8 Grade 8.8: 25 N·m; M10 Grade 8.8: 49 N·m; M12 Grade 8.8: 86 N·m; M16 Grade 8.8: 210 N·m. Lubricated (engine oil or thread lubricant) reduces required torque by 20-30%. A commonly cited rule of thumb for dry steel fasteners: T ≈ 0.2 × F_clamp × d, where F_clamp is desired clamping force and d is bolt diameter. Always use manufacturer torque specifications when available — they account for joint stiffness, gasket compression, and safety factors.
Torque produces angular acceleration in rotating systems: τ = I × α, the rotational analog of F = ma. Here I is moment of inertia (kg·m²) and α is angular acceleration (rad/s²). For a solid disk: I = ½mr². Example: a 10 kg flywheel with 0.3 m radius (I = ½ × 10 × 0.09 = 0.45 kg·m²), accelerated from 0 to 1,500 RPM (157 rad/s) in 5 seconds → α = 157/5 = 31.4 rad/s² → τ = 0.45 × 31.4 = 14.1 N·m required to accelerate the flywheel.
In everyday engineering usage, torque and moment are often used interchangeably, but there is a subtle distinction. Torque typically refers to a twisting force along an axis — what a motor delivers or a wrench applies. Moment (bending moment) typically refers to the tendency of a force to rotate a structure about a point — what a beam experiences under transverse loads. Both are calculated as Force × perpendicular distance (N·m), but torque acts about the long axis of a shaft, while bending moment acts about an axis perpendicular to the structural member. In structural engineering, moment is used; in mechanical engineering, torque is more common.