Radius or Diameter?

Circle circumference, diameter, radius

I've been working on refining spell descriptions (again) lately -- for hopefully upcoming expanded releases of the OED Book of Spells and Book of War rules. (E.g., we started testing top-level spells in mass battle play in the BOW livestream sessions the other week.) A couple of recent testbeds brought to mind the question: what's better for expressing the area of a circular spell effect, the radius, or the diameter?

For many years I've been strongly biased towards using the radius, because that's the used in mathematical definition of a circle. Arguably, however, it's easier and more common to measure real-world existing circles via the diameter (given the center is not actually part of the circle or necessarily distinguished; think tires, pizzas, wells, etc.)

Funny observation: Gygax's writing for O/AD&D was amazingly inconsistent on the matter, often flip-flopping for various spells in opposite directions. Starting with the first few spells in the Chainmail list, I see:

  • Chainmail: Catapults/fireballs given by diameter, light by radius, protection from evil by diameter, etc.
  • Original D&D: Fireballs by radius, light by diameter, protection from evil by radius (so, each of example toggles)
  • Swords & Spells: Everything by diameter.
  • Advanced D&D: Everything by radius (as far as I can tell).

I think the Swords & Spells case is interesting, because it gives a big list with all the stats (range, area, duration) for every spell in OD&D in a master list. When I did the same thing for my simulator, I found that things got confusing for a specific reason -- every other shape was being expressed by overall width (squares, lines, cubes, rectangles, etc.), but circles were listed by half-width. So I was getting a bit scrambled comparing entries of "circle-2-in." next to "square-3-in." and remembering that the former is actually bigger (wider). Note this is the case where Gygax gave diameters for everything, and I think this explains why.

The other (and related) case is trying to build templates for area spells in a VTT, specifically Roll20. There's a single pipeline for importing a token image and specifying how big it should be in map-square-units, and that interface asks for the total width (whether the image is of a square, rectangle, circle, etc.). So for my circle areas I was having to do an extra mental step and remember to double the indicated rule dimension for each token. In addition, I'd note that hand-drawing circles, ellipses, etc. in Roll20 and most drawing software I'm familiar with involves drawing and reporting on the bounding box for the shape in question; they don't draw from center to circumference.

Based on these experiences, for consistency with other shapes, I had an urge to switch all the circular specifications from radius over to diameter. But I also thought to ask opinions online, and got feedback like this on the ODD74 forums:

Poll: Radius (17) vs. diameter (0).

Similarly, folks on Twitter were almost unanimously in favor of using the radius. Voting on the Wandering DMs Discord server also went for the radius (with some votes switching from diameter back to radius based on discussion there: esp., targeting and determining casualties for a blasting spell). I didn't bother to ask on an AD&D forum, since those rules do uniformly use radius, so I assume everyone will be habituated to that.

Therefore, I'm taking that as an overwhelming preference among the classic D&D community, and not indulge my momentary instinct to switch things to a Swords & Spells type presentation, but instead keep giving radius like everyone expects.

We're all lucky I didn't find some way to argue for the circumference.


  1. My knee-jerk response was radius, but honestly you make a compelling case for diameter. Can you list both? I.e. 15' radius (30' D.)

    1. Ack, it hurts us. :-) I think my rules' focus on extreme minimalism strikes that out as an option.

  2. I think the evolution maybe comes from the perspective of the player. With miniatures it is more of an open terrain, top-down perspective, while in the RPG it is more from the point of view of a character in a dungeon with lots of potential items or beings in the way.

    When I'm looking at an area in front of me, I don't consider a diameter around a center, I look from side to side from the center point; when I look down at a miniature I have the eagle's eye perspective of everything around the target.

    Though that might be overthinking Gary's thought process.

    1. I think I agree, that's a strong case. Most of the arguments I'm seeing for radius seem to slide in exactly that direction. Also there's some good comments that theater-of-the-mind works better with declared center & radius, vs. a miniatures game where you plop down a physical template (which is exactly what Gary in Swords & Spells and me in Book of War et. al. are are dealing with).

  3. I lean towards radius on this, since you 'center' a spell on an area, and then are thinking of how 'far' it is going to reach. When playing a caster, I think in radius, not diameter.

  4. The coolest kids are out here using circumference

  5. Similar discussions come up in engineering and constriction. The answer that I've worked with now for 28y is that whether to define a circle by radius or diameter comes down to whether you will be standing inside or outside the circle in question. Therefore we speak about crane operating radius but we talk about pipe or pile diameter.

    In D&D terms I'd say that Fireball is defined by diameter but Protection from evil is defined by radius.

    1. Damn, that's a nifty insight. My own instinct echoes that, that from the fireball caster's perspective diameter is better, while from the target's radius is better (but not ever agrees with that).

  6. Thinking now on using diameter, it does seem to have some nice qualities. For big area spells like fireball, it makes a kind of intuitive sense that you create it from a face, like with cube spells. It would also make ranges feel more consistent.

    However, the main case for radii seems to be things which would be centered on the character. Torches and light sources being the obvious one here, but I think this would also be relevant for spells like Silence or Darkness which you could attach to an object. Lots to think on further here

  7. I personally hand a player the wet-erase pen and have them mark the target of the spell. They know the radius, so you would think they could pick a spot that would result in no friendly fire. Alas, when the whole shape is drawn up, the result is sometimes suboptimal. This is partly because I don't want someone to draw a whole circle and then decide they actually want it to be somewhere else; too much time.

    I believe that a caster would need to target a spot from whence the spell blossoms, rather than seeing some hologram of the area that moves around as the caster moves their target point. That would be an amazing UI benefit for a high-level MU! You see this frequently in modern video games like BG3.

    My method also takes into account that Fireballs and a few other spells fill volume, and it's up to the DM to decide on how that goes depending on ceiling height, how many halls leading away there are to accept the pressure, etc. And so indoors it's usual for Fireballs to either be shot too far downrange (down a long hall for example, or into a high-ceilinged room where more of the volume is taken up than the player expected), and miss some of the enemy, or else targeted too close and fry some of the PCs. This uncertainty is a desirable part of the game.

    If I called for the player to drop a template down, it's effectively asking them to select the nearest edge of the diameter, and giving them several chances to adjust to get things perfect. Which is not what I want to see.

    From my perspective, when dealing with circles, I need to know the center point and the radius. For example, if I need to draw out the area of a potential well on the ground, I might want a well of a certain diameter to fit the lid or whatever, but to actually dig the well I need to mark some center point and draw the circle around that using the radius.

    I can definitely see using the diameter to describe the well, though. It's a 3' well, not a 1.5' radius well. Same with a Fireball being a 40' sphere. I guess it's up to the game to convey to the DM that this is how the description works, because otherwise overeager players will be trying to plot out Fireballs with 40' radii. The issue is maintaining an understanding that radius and diameter are inextricably linked, with diameter being the nominal and ideological size but radius being the tool used to accomplish that.

    Interestingly, practical geometry cares about the center point of a square, too. If I want to draw a square on the ground that has 90-degree corners, I'll need to test the draft square by measuring diagonally corner to corner; if these two measurements are equal I know I have achieved an accurate square. This creates a center point of the square at the intersection of the diagonals. So, while drawing a circle requires first creating a center point, and we put great emphasis on it, creating a square requires finally creating a center point and it's given little importance.