Torque Calculator

Torque calculator: lever arm, power and bolt tightening

This torque calculator covers three torque questions from physics class, the workshop and machine design. It solves τ = F · r · sin θ for whichever variable you are missing — torque, force, lever arm or angle — with N·m, lb·ft, kgf·m, lbf and inches handled automatically; converts between power, torque and rotational speed with P = τ · ω; and works as a bolt torque calculator, estimating the tightening torque from thread size, property class, nut factor and target preload, with a metric and UNC torque chart for every size.

How to use the Torque Calculator

1. Choose the mode: Torque from a force, Power ↔ torque ↔ speed or Bolt tightening torque.
2. In the lever mode pick what to Solve for, then enter the other three values with their units. θ is the angle between the force and the arm (90° for a force at right angles).
3. In the power mode pick the unknown and enter the other two — for example 3.14 kW and 3,000 rpm to get 10 N·m.
4. In the bolt mode select the thread (M3–M30, #4 to 1″ UNC or a custom metric d × pitch), the property class or SAE grade, a nut factor K and the preload as a percentage of proof load, or type a clamp load; open the torque chart to see every size.
5. Read the result, the worked formula in the caption and the conversions in the detail rows; copy the text or download the diagram.

Torque Calculator features

Torque formula and worked example

Torque (or moment) is force times the perpendicular distance from the pivot: τ = F · r · sin θ, where θ is the angle between the force and the lever arm. Only the component of the force at right angles to the arm turns it; a force along the arm (θ = 0°) produces no torque, and the maximum for a given force and arm occurs at θ = 90°.

Example: pushing a 0.2 m spanner with 50 N at right angles gives τ = 50 × 0.2 × sin 90° = 10 N·m (7.38 lb·ft). Pulling at 30° to the handle halves it to 5 N·m.

Power, torque and rpm

Mechanical power is torque times angular speed: P = τ · ω with ω in radians per second, and ω = 2π·N/60 for N in rpm. Rearranged, τ = 9549 · P(kW) / N(rpm), or in imperial units τ(lb·ft) = 5252 · hp / rpm — which is why a petrol engine’s horsepower and torque curves always cross at 5,252 rpm. A 3.14 kW motor at 3,000 rpm produces 10 N·m; the gear ratio calculator follows it through a reduction, and the horsepower calculator adds quarter-mile estimates and crank vs wheel power.

Bolt torque: how the estimate works

The tightening torque needed to stretch a bolt to a chosen preload is approximated by the short-form equation T = K · F · d, where F is the clamp load, d the nominal diameter and K the “nut factor”, an empirical number that bundles thread friction, under-head friction and thread geometry. Shigley’s Mechanical Engineering Design (table 8-15) gives K ≈ 0.30 for non-plated black finish, 0.20 zinc-plated, 0.18 lubricated, 0.16 cadmium-plated and 0.12 with anti-seize; Fastenal’s published charts use 0.20 dry and 0.15 lubricated. K is the biggest source of error, which is why critical joints use torque-angle or bolt stretch instead, and why full VDI 2230 joint analysis is beyond this tool.

Shigley recommends a preload of 75% of the proof load for reusable connections and 90% for permanent ones. Proof load is the proof stress of the class (ISO 898-1: 580 MPa for 8.8 up to M16, 600 MPa above, 830 MPa for 10.9, 970 MPa for 12.9; SAE J429: 55, 85 and 120 ksi for grades 2, 5 and 8 in the smaller sizes) times the tensile stress area, A_s = π/4 · (d − 0.9382 P)² for metric threads — 58.0 mm² for M10 × 1.5. An M10 8.8 bolt at 75% with K = 0.2 needs about 50 N·m, matching Fastenal’s dry chart. Values checked October 2026 against TR Fastenings’ ISO 898-1 table, Portland Bolt’s SAE J429 table and Fastenal’s torque-tension chart. For safety-critical joints, follow the manufacturer’s specified torque.