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Your speed tells you how far you can move in a round and still do something, such as attack or cast a spell. Your speed depends mostly on your size and your armor.
Dwarves, gnomes, and halflings have a speed of 20 feet (4 squares), or 15 feet (3 squares) when wearing medium or heavy Armor (except for dwarves, who move 20 feet in any armor).
Humans, elves, half-elves, half-orcs, and most Humanoid Monsters have a speed of 30 feet (6 squares), or 20 feet (4 squares) in medium or heavy armor.
If you use two move actions in a round (sometimes called a "double move" action), you can move up to double your speed. If you spend the entire round running, you can move up to quadruple your speed (or triple if you are in heavy armor).