I always found it strange that a fighter in full plate armour could jump much further than a monk, so I wrote something to improve dex based jumping that hopefully doesn't nerf str based characters too much!

Jumping

Your Strength and Dexterity determine how far you can jump.

Long Jump. When you make a long jump, you cover a number of feet up to your Strength score plus your Dexterity modifier (capped by your armor's max Dex Bonus) 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 DM'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 + half of the total of your Strength and Dexterity modifiers (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 DM might allow you to make a Strength (Athletics) or Dexterity (Acrobatics) 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 1 1/2 times your height.

Would love to hear peoples' thoughts/constructive criticism!