Bolt Torque Calculator - ISO 898-1 Fastener Torque

A bolt torque calculator estimates the tightening torque a bolt needs to reach a target clamping force. It uses the bolt's diameter, thread pitch, material, and strength class to work out a torque value in newton-metres (Nm).

How bolt torque works

Turning a bolt with a wrench applies torque, a rotational force. Most of that torque overcomes friction: some in the threads, more under the bolt head. Only a small part of it stretches the bolt slightly, like a spring, and creates the clamping force that holds a joint together. That clamping force is called preload, or tension. Because friction eats up most of the torque, the surface condition of the bolt, and whether it is lubricated, changes how much clamping force a given torque produces.

How to calculate bolt torque

The standard torque-tension formula is:

T = K × D × F

• T — torque, in newton-metres (Nm)
• K — torque coefficient, a friction factor set by the material and lubrication
• D — nominal bolt diameter, in metres
• F — clamp load (preload), in newtons (N)

The diameter must be in metres, not millimetres. A 10 mm bolt is entered as 0.01 m in this formula. Using millimetres directly makes the torque come out 1,000 times too large.

Torque coefficient (K)

The torque coefficient stands in for friction. A lower K means less torque is lost to friction, so more of it becomes clamping force. This calculator uses these values:

Clamp load (F)

Clamp load is the axial force a tightened bolt exerts on the joint. This calculator sets the target clamp load to 75% of the bolt's proof load, a common target for a joint that may be taken apart and reassembled:

F = 0.75 × Sp × As

Sp is the minimum proof stress of the bolt's property class, defined by the ISO 898-1 standard. As is the tensile stress area, the effective cross-section of the threaded shank that carries the load:

As = (π/4) × (d − 0.9382 × P)²

Here d is the nominal diameter and P is the thread pitch, both in millimetres. As is smaller than the plain shank area, because the threads cut material away.

Proof stress by property class:

Material and property class are set separately in this calculator. Choosing "Stainless Steel" does not change or restrict which property class is available; the five classes above apply regardless of material.

Worked example

Take a steel M10 bolt, 10 mm nominal diameter, 1.5 mm thread pitch, property class 8.8, tightened dry.

1. Tensile stress area: As = (π/4) × (10 − 0.9382 × 1.5)² ≈ 57.99 mm²
2. Proof stress: Sp = 580 MPa, since the diameter is 16 mm or less
3. Clamp load: F = 0.75 × 580 × 57.99 ≈ 25,225 N
4. Torque: T = 0.20 × 0.01 × 25,225 ≈ 50.45 Nm

The same bolt, lubricated instead of dry (K = 0.15), needs about 37.84 Nm — roughly a quarter less. Lubrication lowers friction, so less torque is wasted and more of it becomes clamping force.

Quick reference: steel bolts, property class 8.8

Approximate torque at standard coarse thread pitch, 75% preload:

These figures assume property class 8.8 and a 75% preload target. A different class, material, or preload changes the result, so use the calculator above for an exact figure.

Calculating torque in code

1def bolt_torque(diameter_mm, torque_coefficient, tension_n):
2    diameter_m = diameter_mm / 1000  # convert mm to m
3    return round(torque_coefficient * diameter_m * tension_n, 2)
4
5torque = bolt_torque(10, 0.20, 25225)
6# 50.45
7

The diameter must be divided by 1000 before it is multiplied by K and F. Skipping that step gives a torque 1,000 times too large.

What the calculator assumes

• Room temperature, roughly 20-25°C
• Clean, undamaged threads with proper engagement
• A preload target of 75% of the bolt's proof load
• A static joint, not exposed to heavy vibration or thermal cycling

This calculator supports nominal diameters from 3 mm to 36 mm. For joints where failure could cause injury or major damage — pressure vessels, structural steel, aerospace parts — use the manufacturer's torque specification or a relevant engineering standard instead. Real joints add factors, such as gasket compression, thermal expansion, and friction variance between individual fasteners, that a general formula cannot capture.

Frequently asked questions

What is a bolt torque calculator?

A tool that estimates the tightening torque, in newton-metres, needed for a bolt to reach a target clamping force. It takes the bolt's diameter, thread pitch, material, and property class as inputs.

How do I calculate bolt torque by hand?

Use T = K × D × F, with D in metres. K comes from a torque coefficient table for the bolt's material and lubrication condition. F comes from the bolt's property class and tensile stress area, usually set to 75% of the proof load for a joint that will be reused.

What happens if a bolt is over-torqued?

It can stretch past its elastic limit, strip its threads, or snap. Aluminum threads strip especially easily. Over-torquing also shortens a bolt's fatigue life, because it then operates closer to its yield point, leaving less margin for extra load during use.

What happens if a bolt is under-torqued?

The joint can loosen under vibration, leak if it compresses a gasket, or let parts shift under sideways load. Under-torqued bolts are also more likely to crack from repeated stress cycling, since the clamping force that normally absorbs that stress is too low.

Does lubrication change how much torque a bolt needs?

Yes. Lubrication lowers the torque coefficient by cutting friction, so less applied torque is lost and more converts into clamping force. A lubricated steel bolt typically needs about 25% less torque than the same bolt dry, to reach the same clamp load.

What is the difference between torque and tension in a bolt?

Torque is the twisting force applied with a wrench. Tension, also called preload, is the resulting stretch inside the bolt, which produces the clamping force. The two are linked by friction, so the same torque value can produce different tension depending on lubrication and surface condition.

Can this calculator be used for stainless steel bolts?

Yes. Stainless steel has its own coefficients in this calculator: 0.22 dry and 0.17 lubricated, both higher than plain steel, because stainless resists sliding more and is prone to galling, a form of thread seizure under friction. Anti-seize compound is commonly used on stainless-to-stainless joints to prevent it.

References

1. International Organization for Standardization. ISO 898-1:2013 — Mechanical properties of fasteners made of carbon steel and alloy steel, Part 1: Bolts, screws and studs with specified property classes.
2. Fastenal Engineering. Torque-Tension Relationship, ISO 898-1 Property Classes 4.6, 8.8, 10.9 and 12.9, Metric Coarse Thread.
3. Motosh, N. (1976). "Development of Design Charts for Bolts Preloaded up to the Plastic Range." Journal of Engineering for Industry, 98(3), 849–851.