A folding wheelchair is easily convertible between a folding wheelchair of a first type and a folding wheelchair of a second type through the use of conversion components, some of which are mounted permanently to the wheelchair and some of which are received by the mounted conversion components. In one form, the first type is a folding beach wheelchair while the second type is a folding all-terrain or trail wheelchair. Conversion is achieved through changeable front and back wheels. For instance, the folding beach wheelchair includes right and left rear wheels having oversized, low pressure tires. Right and left front brackets are mounted to the existing frame and are configured to receive right and left wheel assemblies, having smaller, low pressure tires mounted for pivoting movement. The folding all-terrain wheels have solid, high pressure or the like tires.