Bolt Torque Calculator (metric bolts, T = K·F·d)

Understanding the bolt torque calculator — concept and principle

This calculator estimates the tightening torque needed to give a metric bolt a target clamp force (preload). It uses the short-form torque–tension relation, the bolt's tensile stress area and the proof stress of its ISO property class.

0.2 × 0.010 m × 25.23 kN ≈ 50.5 N·m clamps the joint at 75% of the bolt’s proof load.

How it is calculated

Tensile stress area As = π ÷ 4 × (d − 0.9382 P)², for nominal diameter d and pitch P.
Proof load Fp = Sp × As, with proof stress Sp from ISO 898-1 (4.6: 225 MPa, 5.8: 380 MPa, 8.8: 580 MPa up to M16 and 600 MPa above, 10.9: 830 MPa, 12.9: 970 MPa).
Target preload F = chosen % × Fp.
Torque T = K × F × d (d in metres), where K is the nut factor.

The principle

Tightening a nut stretches the bolt like a stiff spring, which clamps the joint. Most of the torque you apply is spent overcoming friction in the threads and under the head; only a small share actually stretches the bolt. The nut factor K lumps all that friction into one number, typically around 0.2 for dry steel and lower for lubricated threads. Because friction varies, the same torque can produce quite different clamp forces from bolt to bolt.

Worked example

Default inputs: M10 × 1.5, class 8.8, K = 0.2, preload 75% of proof load.

As = π ÷ 4 × (10 − 0.9382 × 1.5)² ≈ 58 mm².
Proof load = 580 MPa × 58 mm² ≈ 33.63 kN.
Preload = 0.75 × 33.63 ≈ 25.23 kN; stress ≈ 435 MPa.
Torque = 0.2 × 25,226 N × 0.010 m ≈ 50.5 N·m.
In other units: ≈ 37.2 ft·lbf or 5.14 kgf·m.

Each point is the calculator re-run with only “Nut factor K” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Nut factor K	Tightening torque (N·m)
0.05	12.6
0.1	25.2
0.15	37.8
0.2	50.5
0.25	63.1
0.3	75.7
0.4	100.9

How to read the result

If threads are oiled or coated, K is lower and the same torque gives much more preload, which can overstress the bolt; reduce the torque accordingly. Critical joints use torque-angle methods, direct tension indicators or ultrasonic measurement for better accuracy. Always follow the equipment maker's torque specification when one exists.

Common mistakes

Using a dry K for lubricated threads.
Confusing proof stress with tensile strength.
Using the nominal diameter area instead of the tensile stress area.
Reusing yielded bolts in critical joints.

Keep in mind: Torque values are estimates; friction scatter is large. For safety-critical joints follow the manufacturer's specifications and applicable standards, and consult a qualified engineer.

Frequently asked questions

What torque should an M10 8.8 bolt have?

With K = 0.2 and 75% of proof load, about 50 N·m; lubricated threads need less.

What is the nut factor K?

An empirical factor combining thread and under-head friction; about 0.2 for dry steel is a common assumption.

Why not tighten to 100% of proof load?

It leaves no margin for friction scatter and service loads, risking permanent stretching.

Sources: ISO 898-1:2013, Mechanical properties of fasteners made of carbon steel and alloy steel — Part 1: Bolts, screws and studs · Bickford, J. H., An Introduction to the Design and Behavior of Bolted Joints, 4th ed. CRC Press

Checked 9 Nov 2026. NASA Reference Publication 1228, Fastener Design Manual (R. T. Barrett, 1990), section “Fastener Torque” (T = K·F·d; K commonly 0.2, about 0.15 typical for steel on steel; Table VI of K versus friction). Proof stresses and the stress-area formula: ISO 898-1:2013 (values as tabulated by TR Fastenings); coarse pitches: ISO 261.

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