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Jim is a halfling rogue with two levels of exhaustion. This means that their base speed is 25 ft., and that their current speed is halved to 12.5 ft.

Now imagine that Jim uses their movement to move, their action to Dash and their Cunning Action to Dash, all in a straight line.

How far can Jim run? Is it 12.5 ft. rounded down to 10 ft. times 3 = 30 ft.? Or is it 3 times 12.5 = 37.5, rounded down to 35 ft.?

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Jim can move 36 feet, or 35 feet (7 squares) if using the variant grid rules.

First, the rounding rule:

There’s one more general rule you need to know at the outset. Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.

So half-speed for Jim is 12.5 feet, rounded down, giving a speed of 12 feet. The rules for movement state:

On your turn, you can move a distance up to your speed.

Jim's speed is 12, so he can move 12 feet with his usual move, and an additional 12 feet for each Dash, resulting in a total of 36 feet with his two available Dashes.

Using a grid is a variant rule.

Moving 5 feet at a time is not the standard rule for D&D, it is actually an optional rule, under the heading "VARIANT: PLAYING ON A GRID". When playing on a grid, you use your movement in 5 foot blocks:

Rather than moving foot by foot, move square by square on the grid. This means you use your speed in 5-foot segments.

So with his usual move, having a speed of 12 translates to 10 feet of movement:

To enter a square, you must have at least 1 square of movement left

After using 10 feet (2 squares), Jim has 2 feet of movement left. You do not round a 12 feet speed down to 10 feet. You just have 2 feet of movement remaining after moving 10, which is not enough to enter a new square. Dashing twice adds 24 feet to his available movement, so he would have 26 feet of movement remaining, or 5 squares, which gives a total movement on the turn of 35 feet (7 squares.

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    \$\begingroup\$ +1. I especially love how this answer is fine for the game "as it was created" and yet completely wrong/different for all european translations using the metric system (or the 5 ft = 1,5 m) \$\endgroup\$ Sep 11, 2021 at 9:07
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36 feet (or 7 squares on a grid)

First, your halved speed is 12 feet, not 12.5, because of the Round Down rule (PHB p.7):

Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.

Second, there's no basic rule about rounding your speed to the nearest 5 feet. Your reduced speed is 12, and you multiply that by 2 or 3 depending on your Dash actions.

If you're using the "Playing on a Grid" variant (PHB p.192, sidebar), here's what it says:

If you play out a combat using a square grid and miniatures or other tokens, follow these rules.[...]

Speed. Rather than moving foot by foot, move square by square on the grid. This means you use your speed in 5-foot segments. This is particularly easy if you translate your speed into squares by dividing the speed by 5. For example, a speed of 30 feet translates into a speed of 6 squares. If you use a grid often, consider writing your speed in squares on your character sheet.

Entering a Square. To enter a square, you must have at least 1 square of movement left[...] If a square costs extra movement, as a square of difficult terrain does, you must have enough movement left to pay for entering it.

Your speed is what your speed is; you use your speed in 5-foot segments, but your speed isn't "two squares", it's 12 feet. You convert it to squares only when you're actually using it to move. Writing it down in squares is merely a simplification for ease of use.

So the answer is you can move 36 feet in freeform, or 7 squares (35 feet) in grid-based movement, because the extra foot you have left isn't enough to enter the next square, and thus doesn't do anything.

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