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Torque calculator with bolt torque mode: reverse-solve force or lever arm, and get bolt clamp load (preload) from T = K × D × F. N·m, lb·ft, kN.
The Torque Calculator helps you calculate torque (rotational force) from applied force and lever arm distance. It supports various units and includes angle calculations for non-perpendicular forces. Essential for mechanical engineering, automotive work, and physics problems.
Have feedback? Report bugs, suggest features, or share your thoughts — we read them allWhat is Torque?
Torque (also called moment) is a measure of the rotational force applied to an object. It describes the tendency of a force to rotate an object around an axis or pivot point. Torque is calculated by multiplying the applied force by the perpendicular distance from the axis of rotation (lever arm). The SI unit is Newton-meter (N·m), while imperial units include pound-foot (lb·ft) and pound-inch (lb·in). Understanding torque is crucial in mechanical engineering, automotive work, construction, and physics.
How to Use the Torque Calculator
- Select calculation mode: calculate torque from force, force from torque, or distance from torque
- Enter the applied force in your preferred unit (N, kN, lb, kgf)
- Enter the lever arm distance (perpendicular distance from pivot to force application)
- Optionally adjust the angle if force is not perpendicular to the lever arm
- Click Calculate to see the torque in multiple units
- Results show torque in N·m, lb·ft, and lb·in for easy conversion
Torque Formulas
1. Torque = Force × Distance (perpendicular)
2. Torque = Force × Distance × sin(Angle)
3. 1 N·m = 0.7376 lb·ft = 8.851 lb·in
Common Torque Examples
Car wheel lug nuts: 80-140 N·m (60-100 lb·ft)
Bicycle crank torque (strong rider): 100-150 N·m (74-111 lb·ft)
M10 bolt: 40-50 N·m (30-37 lb·ft)
Hand wrench: 20 lb force × 1 ft = 20 lb·ft torque
Applications of Torque
- Automotive: Tightening bolts, lug nuts, engine components to specification
- Construction: Fastener installation, structural connections, anchor bolts
- Manufacturing: Assembly processes, quality control, torque specifications
- Bicycles: Proper tightening of components, preventing over-tightening
- Machinery: Motor selection, gear calculations, shaft design
- Physics: Understanding rotational dynamics, angular momentum
- Tool design: Wrench length, mechanical advantage calculations
Tips for Torque Applications
- Always use a torque wrench for critical fasteners - never estimate
- Torque specifications are typically for clean, dry threads unless noted otherwise
- Maximum torque occurs at 90° - angle reduces effective torque
- Longer wrench = more leverage = same torque with less force
- Over-torquing can strip threads or break fasteners
- Under-torquing can lead to loosening and joint failure
- Check manufacturer specifications for proper torque values
Torque Direction & Sign Convention
Torque is a vector quantity with both magnitude and direction. By convention, counterclockwise rotation is considered positive torque, while clockwise rotation is negative. The right-hand rule determines direction: point your right thumb along the axis of rotation, and your fingers curl in the direction of positive torque. In calculations, we typically work with torque magnitude, but direction becomes important when analyzing systems with multiple torques or rotational equilibrium.
Frequently Asked Questions
Torque equals force times the perpendicular distance from the axis of rotation: τ = F × d. If you push with 50 N on the end of a 0.3 m wrench, you apply 50 × 0.3 = 15 N·m of torque on the bolt. If the force is not perpendicular to the lever arm, include the angle: τ = F × d × sin(θ). For a typical wrench, your hand pulls perpendicular to the handle, so θ = 90° and sin(θ) = 1, which is why the simple formula usually works. Always measure d from the center of the rotating shaft to where the force is applied, not from the head of the bolt to the end of the wrench handle in general.
The full formula is τ = r × F × sin(θ), where r is the distance from the axis to the point of force application (the lever arm), F is the magnitude of the applied force, and θ is the angle between the force vector and the lever arm. When the force is perpendicular to the lever arm (the most efficient orientation), sin(θ) = 1 and τ = r × F. In vector form, torque is the cross product τ = r × F, which also defines the direction of rotation by the right-hand rule. The SI unit is the newton-meter (N·m); imperial units are pound-foot (lb·ft) and pound-inch (lb·in).
Three conversions cover almost all wrench and torque-spec datasheets. 1 N·m = 0.7376 lb·ft, so divide N·m by 1.3558 to get lb·ft. 1 N·m = 8.851 lb·in, so multiply N·m by 8.851 to get lb·in. 1 lb·ft = 12 lb·in (always — by definition of the foot). For example, a 100 N·m torque spec is 73.76 lb·ft or 885.1 lb·in. Mixing inches and feet is the most common error: many automotive manuals state spec in lb·ft for big bolts and lb·in for small fasteners. This calculator shows all three units side by side so you can match any service manual instantly.
Torque equals force times lever arm length, so doubling the lever arm doubles the torque you can apply with the same effort. A standard 25 cm wrench at 200 N of hand force produces 50 N·m; slip a 50 cm cheater pipe over it and the same 200 N now delivers 100 N·m. This is the reason mechanics keep breaker bars (24-36 in / 60-90 cm) for stubborn fasteners. The trade-off is bolt safety: doubling the wrench length doubles the chance you exceed the bolt's yield torque and snap it. For critical fasteners, use a torque wrench set to spec rather than a long lever, especially on aluminum or stainless threads that strip easily.
Torque is the rotational force at a moment in time (N·m or lb·ft); horsepower is the rate at which torque does work over time (work ÷ time). They are linked by the equation HP = (Torque × RPM) ÷ 5,252 in imperial units, or kW = (Torque [N·m] × RPM) ÷ 9,549 in SI. A V8 engine and an electric motor can produce the same peak horsepower with very different torque curves: diesel and electric motors deliver near-maximum torque from zero RPM (great for towing), while gas engines need to spin up to peak. At 5,252 RPM, horsepower and lb·ft torque always have the same numerical value — that's where the two curves cross on any dyno chart.
Always follow the manufacturer's spec from the service manual; it accounts for material, thread pitch, and joint friction. As a rule of thumb for clean, dry steel bolts: M6 (1/4") takes 9-12 N·m, M8 (5/16") takes 22-30 N·m, M10 (3/8") takes 45-60 N·m, M12 (1/2") takes 80-105 N·m, M14 (9/16") takes 130-170 N·m, M16 (5/8") takes 200-260 N·m. Cut these by 25% for oiled threads and by 50% for aluminum threads. Multi-bolt patterns (cylinder heads, wheel hubs) require tightening in a star or cross sequence in 2-3 passes, with the final pass at full torque, to seat the joint evenly. Re-torque after the first heat cycle on critical joints.
Use the nut-factor relation T = K × D × F, where T is the applied torque, K is the nut factor (≈0.20 dry steel, ≈0.15 lubricated, ≈0.10 moly/anti-seize), D is the nominal bolt diameter, and F is the resulting clamp load (preload). Back-solve for the clamp force: F = T / (K × D). For example, 50 N·m on a dry M10 bolt (D = 0.010 m, K = 0.20) gives F = 50 / (0.20 × 0.010) = 25,000 N = 25 kN (about 5,600 lbf). Switch the bolt to lubricated threads (K = 0.15) and the same 50 N·m now produces 33.3 kN — a 33% jump in tension that can over-stress the joint. Enable the 'bolt joint' option in this calculator to compute the clamp load automatically in kN and lbf for any torque, diameter, and lubrication condition.
Roughly 90% of the torque you apply to a bolt is lost to friction — about 50% under the bolt head and 40% in the threads — leaving only 10% as the useful tension that clamps the joint together. The standard formula is T = K × D × F, where T is applied torque, K is the nut factor (~0.20 for dry steel, ~0.15 for oiled, ~0.10 for moly grease), D is the nominal bolt diameter, and F is the desired clamp load. This is why oiling or lubricating threads without adjusting the torque spec can over-tension and snap bolts: same torque now delivers 50% more clamp load. For ultra-critical joints (engine head bolts, structural splices), engineers use torque-to-yield or stretch measurement rather than torque alone.
Torque is a vector pointing along the axis of rotation, and the right-hand rule sets its direction: curl the fingers of your right hand in the direction the object rotates, and the thumb points along the torque vector. For a standard right-hand-threaded bolt viewed from the head, tightening rotates clockwise — by the right-hand rule, the torque vector points into the bolt (away from you). Loosening rotates counter-clockwise — torque vector points toward you. This convention matters when summing torques on a free-body diagram, when working with gyroscopic effects on bicycles and aircraft, and when programming robot manipulators. In 2D problems most engineers simplify to a signed scalar: positive for counter-clockwise, negative for clockwise.
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