Calculate magnetic holding force: this is how the calculation works for raw magnets

The greater the adhesive force, the stronger the effect of a magnet on its surroundings. Especially for reasons of occupational safety in trade and industry, it is important to know how strong magnetic material is when using it. If a magnet is too weak, for example, it may not have the necessary adhesive force to hold steel beams or iron signs in place. That can be dangerous.
On the other hand, if it is too strong, it takes a corresponding amount of force to loosen it again – once it has been attached. This too can lead to accidents.
Finding out about the adhesive force is therefore essential if you work with magnets as a hobby or in a professional environment.
But it is even better if you know how magnetic holding power is calculated.
You can find out more about this below.

What exactly is the adhesive force?

Adhesiveness or adhesion derives from the term "adhaerere", which means nothing other than "to adhere". It is therefore a measure of the force that a magnet can exert on a magnetic adhesive surface. It depends on various factors such as:

• Materials
• Volume
• Geometry
• Arrangement of the magnet components

The strength of a magnet is always given as a weight when calculating the magnetic holding force. 1 kg corresponds to a force of 10 N.

How to calculate magnetic holding power?

Calculating the holding force of raw magnets involves a not inconsiderable amount of mathematical work. There are no such things as simple formulas for arbitrary magnet shapes.
Alternatively, free-to-use software is available that quickly calculates the appropriate results.
For mathematics enthusiasts, however, there are formulas that can be applied to less complex symmetrical geometries - such as blockmagnets and cubemagnets.
A formula to calculate the holding force of magnets is:

B is the flux density in the gap and A is the magnetic area in square meters.

The higher the field line density (induction B), the greater the adhesive force.
The magnetic conductivity of a magnet should therefore be as high as possible for a given magnetic field strength H of a permanent magnet. This in turn requires a high cross-section and a short length of the path - and last but not least, a high relative permeability. In this context, ideal materials for calculating the magnetic holding force are nickel or steel for calculating the attractive force of magnets.
The calculation itself assumes ideal conditions, often in the form of a polished soft iron plate 10mm thick.

Calculate the adhesive force on a current-carrying piece of conductor

With electromagnets, it is much easier to calculate the magnetic holding force.
The prerequisite for this is that there is a magnetic field with a known direction, orientation and known amount B – in addition, there is a piece of conductor of length l at said point through which current of strength I flows.

In order to calculate the direction and orientation of the magnetic holding force F, you first need the so-called three-finger or right-hand rule.
The same bears its catchy name because it is applied with the help of one's own hand:

• Extend your thumb in the direction of the electric current
• Stretch your index finger in the direction of the magnet
• Spread your middle finger

The middle finger now shows you the direction of the magnetic force.

You can then calculate the magnetic holding force.

Calculating magnetic attraction – The formula:

 refers to the width of the angle between your thumb and index finger.