How does a moisture meter work?

Damp meters don’t actually measure damp. What they are doing, however, is measuring electrical resistance created in a material by the presence of moisture.
Most moisture meters achieve this by using pins. The meter features two metal pins which are either pressed gently against or inserted into the material to be tested. The meter measures the resistance of electricity between the pins and generates a numerical result which represents the percentage moisture content of wood (%MC) which can also be translated into a reading for wood moisture equivalent (WME) when measuring a different material, such as brick or concrete.  
Average readings on the %MC and WME scales (figures provided as a guide only):
Wood 0-40% maximum
Masonry - 0-5% maximum
In wood rot sets in above 20% but doesn’t feel wet to the touch below 30%. As an example a softwood like pine, from which most of the world’s timber is manufactured, would be classed as ‘saturated’ if a reading of between 28-32% was returned.
The WME percentage for masonry is so much lower because heavy materials have a lower capacity to hold moisture than lighter materials, like wood.
More sophisticated models may also feature a totally non-invasive function which uses scanning technology to measure the electrical capacitance of a material a certain distance beneath the surface. By placing the meter against the material a reading will be returned; the higher the reading, generally the higher the moisture content.
It can also be useful to a use a combination of pin and scanning testing if using a moisture meter with dual functionality. By starting an investigation with the non-invasive method a tester will be alerted to the presence of water or not. The tester can then apply the pin method to confirm whether the moisture is sub-surface (deep inside the material) or at the surface.
As well as numerical readings most moisture meters also feature an easy-to-read coloured scale which moves up or down through the warning colours depending on the level of moisture present. This is a handy function for quick reference or to narrow down a large area for further investigation.
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