The dominant motherboard form factor is ATX.
A form factor is an industry standard for how components work together to make a system from parts. The three commonly used motherboard form factors regulate how motherboards connect to cases, power supplies and backplanes with elements such as microphone jacks and USB connectors.
ATX Form Factor
The ATX form factor grew out of the Baby-AT form factor that dominated systems construction in the 1990s. Functionally, it's a Baby-AT motherboard rotated 90 degrees, with the CPU shifted away from the expansion slots, so that the board can hold full height expansion cards in all sockets. ATX motherboards also integrate many components that used to be separate cards onto the motherboard, like Ethernet cards, and basic integrated video cards. ATX motherboards are 12-by-9.6 inches.
MicroATX Form Factor
The MicroATX form factor is a reduced-size ATX motherboard with fewer expansion slots. It is primarily used as a cost-reduction component for small form factor computers, using half-sized cases. It uses the standard ATX backplane configuration, meaning that the ATX backplane shield can work with MicroATX motherboards. Using the alternate mounting holes, a MicroATX motherboard can be mounted in a full-sized ATX case. The MicroATX motherboard is typically 9.6-by-9.6 inches.
FlexATX Form Factor
FlexATX is a variation on the MicroATX form factor; a FlexATX motherboard uses the same I/O panel and configurations as the MicroATX board. It has a slightly smaller motherboard size, and uses the same mounting holes as MicroATX. It does compromise on using socket-only CPUs to encourage use in smaller computers. Most "all-in-one" small desktop computers, like nettops, use FlexATX motherboards to reduce component costs and overall system size. FlexATX motherboards are 9.6-by-7.5 inches.
BTX Form Factor
The BTX form factor is an emerging standard, meant to address thermal and mechanical and electrical issues with desktop computer systems. It is intended is to make cases that are better engineered for airflow-based cooling. It is meant to be used in small, thin computers, and has several candidate motherboard dimensions, most of which match the existing spectrum of ATX motherboards.
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