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if your base speed is 50, how much does medium armor encumber you ?
Speed: Medium or heavy armor slows the wearer down. The number on Table: Armor and Shields is the character's speed while wearing the armor. Humans, elves, half-elves, and half-orcs have an unencumbered speed of 30 feet. They use the first column. Dwarves, gnomes, and halflings have an unencumbered speed of 20 feet. They use the second column. Remember, however, that a dwarf's land speed remains 20 feet even in medium or heavy armor or when carrying a medium or heavy load.
does it just slow you down 10 ft? or does that 10 ft. represent the armor slowing you down by 1/3 of your speed.
I've heard barbarians in medium armor ( base speed 40 ) , only move 30 ft. but i haven't thought much about it till i've got my character with a base 40, in boots of striding and springing which brings her up to 50.
so i'm not sure if, in armor, she'd now move 40 ft, or 2/3 of 50: aka 30 ft.
2/3 of 40 ft. is 26.64, which i guess is rounded up to 30 ft by most people for barbarians in medium armor ? since i've never seen a barbarian with a speed of 25 ft.
Fast Movement (Ex): A barbarian's land speed is faster than the norm for her race by +10 feet. This benefit applies only when she is wearing no armor, light armor, or medium armor, and not carrying a heavy load. Apply this bonus before modifying the barbarian's speed because of any load carried or armor worn. This bonus stacks with any other bonuses to the barbarian's land speed.
( my character is a human barbarian w/ boots of striding n springing ).
for Haste, is her barbarian bonus an enhancement bonus but it stacks with everything, so it stacks with haste, and she would move at +30 ft. with haste

Charender |

A move of 50 is reduced to 35. The movement penalty for medium and heavy armors is 25% of your movement, then round down to the nearest multiple of 5. I believe there is a footnote somewhere in the equipment section, but I can't find it in the SRD.
20 -> 15
30 -> 20
40 -> 30
50 -> 35
60 -> 45
70 -> 50
80 -> 60
Also note that the chart for barding extends to armor encumberance for higher movement rates.

David Thomassen |

Barding Modifier
(40 ft) (50 ft.) (60 ft.)
Medium 30 ft. 35 ft. 40 ft.
Heavy 30 ft.* 35 ft.* 40 ft.*
* A mount wearing heavy armor moves at only triple its normal speed when running instead of quadruple.
Due to Ninjaing Up a bit from here