Sometimes an offset adapter is necessary or convenient on a torque wrench. This calculator calculates the correct torque wrench settings to achieve the desired fastener torque.

The torque wrench is designed to provide a torque indication based on a force applied to the handle and the length about which that force acts to turn a fastener. The calibration may not hold if that geometry is changed by some form of adapter.

An oft cited solution is to set the adapter up at exactly 90° to the long axis of the torque wrench, but that is not always possible or convenient.

For the purposes of this explanation, let's use the Facom S.234 adapter (above).

The solution of the problem requires no more than a bit of high school geometry, the Law of Cosines is key to the solution.

The diagram above shows the geometry and guides the solution.

Points:

- x is the point on the torque wrench handle where the force is applied (it is NOT the end of the handle);
- y is the centre of the torque wrench square where the torque is normally applied to a fastener; and
- z is the centre of the fastener with the offset extension applied.

Dimensions:

- a is the length from the point x to point y;
- b is the centre to centre length of the extension; and
- angle is the offset angle of the extension.

In normal use (ie without the extension), force f is applied normal to the handle of the torque wrench, and the force acts through distance a on the fastener. The torque wrench is calibrated for this scenario.

With the extension, two factors come into play at the point where the torque wrench indicates some given torque:

- the length c through which the turning force acts on the fastener my be different; and
- the component of force normal to line c may be different.

The length c can be found using the Law of cosines. \(c=\sqrt {a^2+b^2-2ab \cos C}=\sqrt {a^2+b^2-2ab \cos (180-angle)}\).

The force normal to c \(f^\prime=f \cos B\) and cos B is found using the Law of Cosines, \( \cos B=\frac{a^2+c^2-b^2}{2ac}\).

So, the needed setting t' for torque t is \(t^\prime= \frac{t}{ \cos B} \frac{a}{c}\).

Above is a calculation using Calculate torque setting when using an offset adapter.

There are lots of calculators on the net that purport to make this calculation, if they give different answers, it is probably because they are flawed. I wrote this one because I could not find one that was correct.

## Hydraulic gland nut adapter example

The adapter above is often used to tighten the gland nut on hydraulic cylinders. To use the calculator for this configuration, you need to use the distance from the centre of the square hole to the centre of the adapter pins spread to suit the gland nut, and the angle from the torque wrench axis to a line from the centre of the square adapter to the centre of the spread pins.

Above is a sample calculation.

## The 90° case

The case of an offset adapter at 90° is an interesting one. In that case, a right triangle is formed by sides abc and the ratio \(\frac{a}{c}=\cos B\) so the needed setting t' for torque t is \(t^\prime= \frac{t}{ \cos B} \cos B=t\)