MDF is short for medium density fiberboard. MDF and particleboard are two forms of inexpensive wood-based sheet goods used by home and furniture builders, sometimes as substitutes for plywood.
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Very fine particle waste wood products, much more like layers of paper than wood, make MDF. Particleboard comes from very coarse sawdust mixed with special glues.
MDF is reasonably water-resistant, although you do not want to expose it to water if you can avoid it. Particleboard will soak up water easily, lose its stability and can fall apart.
MDF has a very smooth texture and does not need edge banding; it also takes finishes well. Particleboard simply does not look good—any exposed edges will need to be finished, as will its flat surfaces.
MDF is often used for built-ins. Particleboard is best used for under-flooring. Either material can become shelving and some types of furniture.
Neither MDF nor particleboard is solid wood, so neither is as strong nor holds screws as well as solid wood. Some applications require special fasteners to use with these products. If you build with either material, use recommended glues in addition to any fasteners.