# How do you calculate the range of an attack when attacking diagonally?

I was recently in a situation where I had to make a crossbow attack on an enemy that is in the opposite corner of the room from where I was.

It looked a bit like this:

For the sake of simplicity, let's assume my weapon has a range of 25 feet, and that each square is 5 feet wide.

If I count the diagonal squares, the enemy would just be in range. But if I calculate it mathematically with Pythagoras' theorem, the enemy would be 35 feet away, and thus not be in range.

The PHB only states about the Range weapon property:

Range. A weapon that can be used to make a ranged attack has a range shown in parentheses after the ammunition or thrown property. The range lists two numbers. The first is the weapon's normal range in feet, and the second indicates the weapon's long range. When attacking a target beyond normal range, you have disadvantage on the attack roll. You can't attack a target beyond the weapon's long range.

I know there is a rule for diagonal movement where your first diagonal square costs 5 feet, the second 10 feet, and so on... I don't know where this rule is written, I just heard it somewhere.

How is the range of an attack determined, by RAW?

• Just count the squares?
• Calculate the diagonal, which would amount to 7 feet for each square?
• Use the movement rules?
• A retractable, ribbon measuring-tape is a godsend. Every inch is usually 5ft. This can certainly be tweaked depending on the size of your miniatures/scenery. Sep 5, 2019 at 2:47
• Pathfinder uses 5 ft and 10 ft alternating. For diagonals like this, that is slightly more permissive than pure Pythagoras, Given a tile side of length X, Pythagoras would use 1.41*X instead of the 1.5*X the pathfinder rule results in. If you're a DM, you can choose to rule it in, if you're not, ask your DM. Sep 5, 2019 at 9:33

Let's get one thing out of the way first: Playing on a grid is a variant to the normal rules. These variant rules can be found in the green insert/sidebar on page 192 of the Player's Handbook. To calculate range using these rules you count squares as though you were moving:

To determine the range on a grid between two things—whether creatures or objects—start counting squares from a square adjacent to one of them and stop counting in the space of the other one. Count by the shortest route.

In these rules diagonal squares are treated as 5 ft. apart.

To enter a square, you must have at least [5 feet] of movement left, even if the square is diagonally adjacent to the square you're in.

This rule "sacrifices realism for the sake of smooth play." The Dungeon Master's Guide (p. 252) includes the additional variant rule1 that every second diagonal counts as 5 additional feet.

When measuring range or moving diagonally on a grid, the first diagonal square counts as 5 feet, but the second diagonal square counts as 10 feet.

1: Yo dawg, I heard you liked variant rules...

• "All these squares make a circle..." Sep 4, 2019 at 21:46
• I'll add that my group has used the "diagonals alternate between 5 and 10 feet" rule for several years, on 3.5 and 5e, and it's hit a good balance between accuracy and ease of calculation. Sep 4, 2019 at 21:49
• @MarkWells that was RAW for 3.x Sep 27, 2019 at 2:53