A) Cast Light on a coin. Your effective radius is 20'... or 3.5 squares to either side, because the 5' square the coin is in consumes '0.5 squares' of radius.
B) Cast Light on a 5'x5' block. Your effective radius is 22.5'... or 4 full squares to either side, because you fill the 5' square the block is in.
C) Cast Light on a 10'x10' block. Your effective radius is 25'... or 5 full squares to either side, because you fill two 5' squares across the center.
Right?
But, you cast Fireball on a point, and it explodes 20' in all directions. Do you cast it at an intersection then (never actually at a real target), and it goes 4 squares in all directions? Or at a square ("I fireball the ogre!"), and it goes 4squares in all directions FROM THAT SQUARE (effectively a 45' DIAMETER, not 40')?
Torches shed 20' of bright light. Torches don't occupy space, so they are a "point" in the center of a "square"... so only 3.5 squares to any direction?
Technically, a 10ft x10ft cube is ineligible, because the diagonal would be ~17ft long point to point.
However, yeah, a "grid" is an optional way of representing the world. If you use one, then using corners is the easiest option. However, even with a coin versus a 10ft sphere, radius still means radius. The outer surface of the object wouldn't extend the illumination factor. You could interpret this as larger objects being dimmer per square inch.
A) Cast Light on a coin. Your effective radius is 20'... or 3.5 squares to either side, because the 5' square the coin is in consumes '0.5 squares' of radius.
B) Cast Light on a 5'x5' block. Your effective radius is 22.5'... or 4 full squares to either side, because you fill the 5' square the block is in.
C) Cast Light on a 10'x10' block. Your effective radius is 25'... or 5 full squares to either side, because you fill two 5' squares across the center.
Right?
But, you cast Fireball on a point, and it explodes 20' in all directions. Do you cast it at an intersection then (never actually at a real target), and it goes 4 squares in all directions? Or at a square ("I fireball the ogre!"), and it goes 4squares in all directions FROM THAT SQUARE (effectively a 45' DIAMETER, not 40')?
Torches shed 20' of bright light. Torches don't occupy space, so they are a "point" in the center of a "square"... so only 3.5 squares to any direction?
There are 3 distinct ways you can adjudicate AOEs on a grid, per Xanathar's. I'll go over all of them, and assume you're measuring diagonals the "stock" way, not the variant of 5-10-15-25.... Also, note that Light can't target a point in space, so none of the three ways apply to it - all three are for AOEs emanating from a point in space.
DMG method: spells targeting a point in space, like fireball, are locked to a grid intersection. This means Fireball's footprint on the grid is an 8x8 square, i.e. a 40 foot x 40 foot square.
Xanathar's, alternative 1: tokens. Tokens are method 1 in the case of a sphere, so Fireball has the same footprint as in method 1.
Xanathar's alternative 2: template. This is exactly equivalent to measuring distances accurately from the grid intersection and rounding all fractions up. In the specific case of Fireball, this is a square with the corners missing - i.e. an 8x8 or 40x40 foot square without the corners.
When an AOE like Light comes into play, distances are measured using the Chebyshev distance, like on a chess board. In your example, Light on a coin acts the same way as on a 5x5x5 stone block, but it's radically different on a 10 foot diameter sphere, which is the largest object it can target (it can't target a 10x10x10 stone block). Here are the two dimensions:
Anything less than or equal to in volume a 5x5x5 block: a 17x17 square, consisting of:
Center grid space: this is where the target object is. If the target object does not fill the space, such as a standard copper coin, the space is filled with bright light.
Inner 9x9 square, minus the center (80 spaces): bright light.
17x17 square with the inner 9x9 missing (208 spaces): dim light.
A 10 foot diameter sphere: an 18x18 square, consisting of:
Center 4x4 square (16 spaces): this holds the sphere, which is surrounded by bright light.
Inner 10x10 square, minus the center (84 spaces): bright light.
18x18 square with the inner 10x10 missing (224 spaces): dim light.
So under ordinary circumstances, the bright light of the Light spell covers more grid spaces than a Fireball does, despite them having the same listed radius. Of course, you could use the Xanathar's template method on the Light spell if you wanted your AOEs to be more realistic (this will have bizarre effects if you don't also use a ruler to measure other distances, like movement and ranged attacks).
When an AOE like Light comes into play, distances are measured using the Chebyshev distance, like on a chess board. In your example, Light on a coin acts the same way as on a 5x5x5 stone block, but it's radically different on a 10 foot diameter sphere, which is the largest object it can target (it can't target a 10x10x10 stone block). Here are the two dimensions:
Anything less than or equal to in volume a 5x5x5 block: a 17x17 square, consisting of:
Center grid space: this is where the target object is. If the target object does not fill the space, such as a standard copper coin, the space is filled with bright light.
Inner 9x9 square, minus the center (80 spaces): bright light.
17x17 square with the inner 9x9 missing (208 spaces): dim light.
A 10 foot diameter sphere: an 18x18 square, consisting of:
Center 4x4 square (16 spaces): this holds the sphere, which is surrounded by bright light.
Inner 10x10 square, minus the center (84 spaces): bright light.
18x18 square with the inner 10x10 missing (224 spaces): dim light.
So under ordinary circumstances, the bright light of the Light spell covers more grid spaces than a Fireball does, despite them having the same listed radius. Of course, you could use the Xanathar's template method on the Light spell if you wanted your AOEs to be more realistic (this will have bizarre effects if you don't also use a ruler to measure other distances, like movement and ranged attacks).
Light is a spell, so it uses the same range rules as all other spells.
I don't think that the PHB even mentions the ChevyChase method of distance calculation!
Light is a spell, so it uses the same range rules as all other spells.
I don't think that the PHB even mentions the ChevyChase method of distance calculation!
You are correct that it is a spell and follows the same range rules as all other spells, but for all spells, the mechanics of targeting a creature or object differ from the mechanics of targeting a point in space.
You are also correct that the PHB does not mention the Chebyshev distance by name! However, it is still the mathematical term for measuring grid distances the way the "standard" away. 5E does not use Chebyshev if you don't use the grid rules or use the variant rule for measuring diagonals.
AoE question:
A) Cast Light on a coin. Your effective radius is 20'... or 3.5 squares to either side, because the 5' square the coin is in consumes '0.5 squares' of radius.
B) Cast Light on a 5'x5' block. Your effective radius is 22.5'... or 4 full squares to either side, because you fill the 5' square the block is in.
C) Cast Light on a 10'x10' block. Your effective radius is 25'... or 5 full squares to either side, because you fill two 5' squares across the center.
Right?
But, you cast Fireball on a point, and it explodes 20' in all directions. Do you cast it at an intersection then (never actually at a real target), and it goes 4 squares in all directions? Or at a square ("I fireball the ogre!"), and it goes 4squares in all directions FROM THAT SQUARE (effectively a 45' DIAMETER, not 40')?
Torches shed 20' of bright light. Torches don't occupy space, so they are a "point" in the center of a "square"... so only 3.5 squares to any direction?
Determining AOEs on a grid always starts in a corner. If the source is in a square, pick a corner of that square.
Light sources can kind of be allowed some extra and just count squares from the source (it is just light). As long as the DM is consistent.
Technically, a 10ft x10ft cube is ineligible, because the diagonal would be ~17ft long point to point.
However, yeah, a "grid" is an optional way of representing the world. If you use one, then using corners is the easiest option. However, even with a coin versus a 10ft sphere, radius still means radius. The outer surface of the object wouldn't extend the illumination factor. You could interpret this as larger objects being dimmer per square inch.
There are 3 distinct ways you can adjudicate AOEs on a grid, per Xanathar's. I'll go over all of them, and assume you're measuring diagonals the "stock" way, not the variant of 5-10-15-25.... Also, note that Light can't target a point in space, so none of the three ways apply to it - all three are for AOEs emanating from a point in space.
When an AOE like Light comes into play, distances are measured using the Chebyshev distance, like on a chess board. In your example, Light on a coin acts the same way as on a 5x5x5 stone block, but it's radically different on a 10 foot diameter sphere, which is the largest object it can target (it can't target a 10x10x10 stone block). Here are the two dimensions:
So under ordinary circumstances, the bright light of the Light spell covers more grid spaces than a Fireball does, despite them having the same listed radius. Of course, you could use the Xanathar's template method on the Light spell if you wanted your AOEs to be more realistic (this will have bizarre effects if you don't also use a ruler to measure other distances, like movement and ranged attacks).
Light is a spell, so it uses the same range rules as all other spells.
I don't think that the PHB even mentions the ChevyChase method of distance calculation!
You are correct that it is a spell and follows the same range rules as all other spells, but for all spells, the mechanics of targeting a creature or object differ from the mechanics of targeting a point in space.
You are also correct that the PHB does not mention the Chebyshev distance by name! However, it is still the mathematical term for measuring grid distances the way the "standard" away. 5E does not use Chebyshev if you don't use the grid rules or use the variant rule for measuring diagonals.