Tactical Movement
When moving diagonally, the first diagonal move in a turn is treated as a 5-foot distance, then the second is treated as 10 feet. The third diagonal move in that same turn is then 5 feet, the 4th is 10 feet, and so on.
To save on awkward calculation for fractions of grids, moving through difficult terrain, stealthy movement, swimming, climbing, or crawling are movements made at half-speed. If a creature has a climb or swim speed, their normal movement speed applies unless other difficult conditions—treacherous rocks or strong currents, for example—apply. A creature without a climb speed attempting to climb difficult terrain has their movement speed reduced by half again.
A creature cannot move into a space if it does not have sufficient movement remaining.
A tabaxi who climbs a normal tree can easily climb 30 ft in a round and still take an action, as their heritage grants a climb speed of 30 ft. A human climbing that same tree can move at only half-speed, so could climb only 15 ft in a round while also taking an action. That same tabaxi might have a much harder time climbing a sheer cliff with few natural handholds, so could move at half-speed, or 15 ft. Meanwhile, the human is reduced to one-quarter their base speed, and since the default in D&D is to round down, the human can climb only 5 ft per round unless they use the Dash action to move another 5 feet. A dwarf with a base speed of 25 ft can move up to 3 squares diagonally, but cannot move into a fourth diagonal square because that move requires 10 ft of movement, and the dwarf has only 5 ft of movement remaining after moving 5 ft, 10 ft, then 5 ft again.
Added to House Rules in 2023.