Torque Calculator

Torque Guide

What do I need to know about Torque Formula?

Torque (τ) = Force (F) × perpendicular distance (d) × sin(θ), where θ is the angle between the force vector and the lever arm. When force is applied at 90° (perpendicular), sin(90°) = 1 and τ = F × d. Torque is measured in Newton-metres (N⋅m) in SI units, or foot-pounds (ft⋅lb) in imperial. 1 N⋅m = 0.7376 ft⋅lb. Torque is a vector quantity — the direction (clockwise or anticlockwise) matters for equilibrium problems.

What's the key thing to understand about Common Torque Values?

Tightening bolts: M6 bolt ~10 N⋅m, M10 bolt ~45 N⋅m, M14 bolt ~120 N⋅m, car wheel nuts 80–130 N⋅m. Bicycle components: stem bolts 4–6 N⋅m, bottom bracket 35–50 N⋅m. Car engine output: a 1.0 litre petrol engine ~150 N⋅m, 2.0 litre diesel ~350 N⋅m, performance V8 ~700+ N⋅m. Electric motors can deliver full torque from standstill — a Tesla Model S produces ~660 N⋅m instantly. A human hand grip applies approximately 3–5 N⋅m on a standard screwdriver.

What should I know about Torque Wrenches?

A torque wrench ensures bolts are tightened to a specific torque, preventing over-tightening (which can strip threads or warp components) or under-tightening (which can cause fasteners to loosen). Critical applications: cylinder head bolts (often tightened in multiple stages), wheel nuts (critical for road safety), suspension components, and brake caliper bolts. Most torque wrenches specify the bolt torque in N⋅m; car manufacturer specifications are given in the service manual.

What do I need to know about Torque and Power?

Power (W) = Torque (N⋅m) × Angular velocity (rad/s). Angular velocity in rad/s = RPM × 2π/60. So Power (kW) = Torque × RPM / 9549. An engine producing 200 N⋅m at 3000 RPM generates: 200 × 3000 / 9549 = 62.8 kW (84 hp). This is why car manufacturers specify torque at a particular RPM rather than just giving a single number — torque varies across the rev range, peaking at different RPMs for petrol vs diesel engines.

What's the key thing to understand about Torque as a Vector?

Torque, like force, is a vector quantity with both a magnitude and a direction, calculated as τ = F × r × sin(θ), where F is the applied force, r is the distance from the pivot (lever arm), and θ is the angle between the force and the lever arm. The direction of torque is found using the right-hand rule: curl the fingers of your right hand in the direction of the applied rotation, and your extended thumb points in the direction of the torque vector, which is always perpendicular to the plane of rotation. By convention, a torque that would rotate an object counterclockwise (when viewed from the direction the torque vector points) is considered positive, and a torque producing clockwise rotation is considered negative. This matters whenever multiple torques act on the same object simultaneously — like several forces applied to different points of a wrench, a steering wheel, or a rotating machine shaft — because the torques must be added as vectors (accounting for direction) to find the net torque, exactly as multiple forces must be summed as vectors to find net force in F = ma.

What should I know about Torque and Rotational Equilibrium?

An object is in rotational equilibrium when the net torque acting on it is zero, meaning it has no tendency to start or change its rotation — this is the rotational analogue of Newton's first law. The principle of moments formalises this: for an object in rotational equilibrium, the sum of clockwise torques must exactly equal the sum of counterclockwise torques around any chosen pivot point. This principle is the basis of the simple lever: a seesaw balances when the product of weight and distance from the pivot is equal on both sides (a 40 kg child sitting 1.5 m from the pivot balances a 60 kg child sitting 1 m from the pivot, since both sides give a torque of 60 kg·m). This same principle governs the design of cranes (counterweights balancing a lifted load's torque), bridges (calculating support reaction forces), and the human body (muscles exerting large forces over short lever arms to balance loads held at a greater distance from a joint, such as the elbow), making the principle of moments one of the most widely applied results in both engineering and biomechanics.

What do I need to know about Torque and Angular Acceleration?

Just as Newton's second law F = ma relates force to linear acceleration, its rotational analogue τ = Iα relates net torque to angular acceleration, where I is the moment of inertia (how a body's mass is distributed relative to the rotation axis) and α is angular acceleration. A larger moment of inertia — mass spread farther from the axis — means the same torque produces less angular acceleration, which is exactly why a figure skater or diver pulls their limbs in tight to spin faster for a given amount of applied torque, and why flywheels are deliberately built with mass concentrated at the rim to resist speed changes.

Torque Reference Table for Bolts and Fasteners

Most torque specs you'll look up fall into predictable ranges depending on bolt size, material, and application. The table below gives typical dry (unlubricated) torque figures for common metric bolts in steel, useful as a sanity check against a torque wrench reading or a calculator result.

These are starting points only — always follow the manufacturer's torque specification where one exists, since bolt grade, thread lubrication, and the material being clamped all shift the correct value. A lubricated or anti-seize-coated thread typically needs 10-20% less torque to achieve the same clamping force as a dry thread, because friction (not torque) is what actually resists loosening.

Worked Example: Torque on a Breaker Bar

Suppose you're loosening a seized wheel nut with a 0.5 m breaker bar and need to know how much force you're actually applying. You push down on the end of the bar with 80 N of force, perpendicular to the bar (θ = 90°). Using τ = F × d × sin(θ): τ = 80 N × 0.5 m × sin(90°) = 80 × 0.5 × 1 = 40 N⋅m Now suppose the nut is specified to loosen at 110 N⋅m and your hands can comfortably apply at most 80 N. Rearranging for distance: d = τ / F = 110 / 80 = 1.375 m You'd need a bar roughly 1.4 m long to break the nut loose with the same 80 N push — which is why mechanics switch to a longer bar (or a length of pipe as a 'cheater bar') rather than pushing harder. If the force is applied at an angle instead of perpendicular — say 80 N at 45° to the bar — the effective torque drops: τ = 80 × 0.5 × sin(45°) = 80 × 0.5 × 0.7071 ≈ 28.3 N⋅m, nearly 30% less than pushing straight-on. This is exactly why torque wrenches and breaker bars work best when you pull or push perpendicular to the handle.

Torque, Work, and Energy in Rotating Systems

When a torque rotates an object through an angle, it does work just as a linear force does when pushing something through a distance: W = τ × θ, where θ is measured in radians. If a 40 N⋅m torque rotates a wheel through 3 full revolutions (θ = 3 × 2π ≈ 18.85 rad), the work done is W = 40 × 18.85 ≈ 754 J. This is the rotational analogue of W = F × d in linear motion, and it's why a wrench applying the same torque over more turns (a longer bolt thread, for example) does more total work even though the torque itself hasn't changed. Power delivered by a rotating shaft follows the same pairing: P = τ × ω, where ω is angular velocity in rad/s — this is exactly how an engine's torque curve and power curve are related, and why peak power typically occurs at higher RPM than peak torque, since power keeps climbing with RPM even as torque itself starts to fall, until the drop in torque finally outpaces the rise in RPM.