Movement through dangerous dungeons or wilderness areas often involves more than simply walking. Adventurers might have to climb, crawl, swim, or jump to get where they need to go.
Climbing, Swimming, and Crawling
Each foot of movement costs 1 extra foot (2 extra feet in difficult terrain) when you're climbing, swimming, or crawling. You ignore this extra cost if you have a climbing speed and use it to climb, or a swimming speed and use it to swim. If you don't have a climbing speed or are climbing a slippery vertical surface or one with few handholds, the GM will often require a successful Strength (Athletics) check. Similarly, gaining any distance in rough water might require a successful Strength (Athletics) check.
Jumping
Your Strength determines how far you can jump.
Long Jump
When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.
This rule assumes that the height of your jump doesn't matter, such as a jump across a stream or chasm. At your GM's option, you must succeed on a DC 10 Strength (Athletics) check to clear a low obstacle (no taller than a quarter of the jump's distance), such as a hedge or low wall. Otherwise, you hit it.
When you land in difficult terrain, you must succeed on a DC 10 Dexterity (Acrobatics) check to land on your feet. Otherwise, you land prone.
High Jump
When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier (minimum of 0 feet) if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your GM might allow you to make a Strength (Athletics) check to jump higher than you normally can.
You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1½ times your height.
Flying
Flying creatures enjoy many benefits of mobility, but they must also deal with the danger of falling. If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
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