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Rework the answer to account for clarifications in the question
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Joel Harmon
Joel Harmon
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To answer the first part of the question, letOption 1 is correct.

Let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis.

For the second part, I have two points. First, I would agree you've found a mathematical contradiction if you assume the maximum length is along the axis. In that caseAnd indeed, the cone defines an isosceles triangle where the height equals the length of the base. In such a case,next sentence describes the two equal sides wouldwidth of course need to be longer than the triangle's height. This necessitates the cone endingat any given point in a flat plane, rather than being a surfaceterms of revolutionits length. This contradicts the presumption that the height/axis measurementThe only previous direction specified is the longest, and makes my response to the first section somewhat nonsensical. As you point out, it would be more consistent from this view to measure the sides asdirection you're aiming the maximumcone.

On the other handWhichever way you go, the purpose here is to decide whether or not a given target is inside the cone. You may not beIf you are using the optional grid rules from DMG 250. If not, then DMG 249 advises

go with your gut.

If you are, then all of your math is rounded to the nearest square. In this caseany of your options, I'd definitely advocate ending the cone inmargin of error is about half a planesquare for the 30' template. The main reasonCoincidentally, the margin of error for DM judgement is because it's quick an easyalso about a half square.

If you're still having trouble deciding, then my suggestion would be to docut out (or draw in a CAD program) the actual candidate arcs and thus keepsoverlay them to see how different they actually are. I think you'll find the game flowingdifference is minimal.

You may also be using some kind of exact placement system, ala WarhammerFinally, where you physically measure the distance between piecesremember that turnabout is fair play. InIf you do let that caseBurning Hands 30' cone stretch out to 33.5' at the edges, then the DMG offers no advice and I'd simply ask your DM to make a callred dragon's fire breath will as well.

Side note: if you were to use option 2, the width at any given point along that length would still depend on that point's distance from the origin. This would result in a slightly fatter cone than approach 1.

To answer the first part of the question, let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis.

For the second part, I have two points. First, I would agree you've found a mathematical contradiction if you assume the maximum length is along the axis. In that case, the cone defines an isosceles triangle where the height equals the length of the base. In such a case, the two equal sides would of course need to be longer than the triangle's height. This necessitates the cone ending in a flat plane, rather than being a surface of revolution. This contradicts the presumption that the height/axis measurement is the longest, and makes my response to the first section somewhat nonsensical. As you point out, it would be more consistent from this view to measure the sides as the maximum.

On the other hand, the purpose here is to decide whether or not a given target is inside the cone. You may not be using the optional grid rules from DMG 250. If not, then DMG 249 advises

go with your gut.

If you are, then all of your math is rounded to the nearest square. In this case, I'd definitely advocate ending the cone in a plane. The main reason is because it's quick an easy to do and thus keeps the game flowing.

You may also be using some kind of exact placement system, ala Warhammer, where you physically measure the distance between pieces. In that case, the DMG offers no advice and I'd simply ask your DM to make a call.

Option 1 is correct.

Let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis. And indeed, the next sentence describes the width of the cone at any given point in terms of its length. The only previous direction specified is the direction you're aiming the cone.

Whichever way you go, the purpose here is to decide whether or not a given target is inside the cone. If you are using the optional grid rules from DMG 250, then all of your math is rounded to the nearest square. In any of your options, the margin of error is about half a square for the 30' template. Coincidentally, the margin of error for DM judgement is also about a half square.

If you're still having trouble deciding, then my suggestion would be to cut out (or draw in a CAD program) the actual candidate arcs and overlay them to see how different they actually are. I think you'll find the difference is minimal.

Finally, remember that turnabout is fair play. If you do let that Burning Hands 30' cone stretch out to 33.5' at the edges, then the red dragon's fire breath will as well.

Side note: if you were to use option 2, the width at any given point along that length would still depend on that point's distance from the origin. This would result in a slightly fatter cone than approach 1.

deleted 2 characters in body
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Joel Harmon
Joel Harmon
  • 16.1k
  • 3
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To answer the first part of the question, let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis.

For the second part, I have two points. First, I would agree you've found a mathematical contradiction if you assume the maximum length is along the originaxis. In that case, the cone defines an isosceles triangle where the height equals the length of the base. In such a case, the two equal sides would of course need to be longer than the triangle's height. This necessitates the cone ending in a flat plane, rather than being a surface of revolution. This contradicts the presumption that the height/axis measurement is the longest, and makes my response to the first section somewhat nonsensical. As you point out, it would be more consistent from this view to measure the sides as the maximum.

On the other hand, the purpose here is to decide whether or not a given target is inside the cone. You may not be using the optional grid rules from DMG 250. If not, then DMG 249 advises

go with your gut.

If you are, then all of your math is rounded to the nearest square. In this case, I'd definitely advocate ending the cone in a plane. The main reason is because it's quick an easy to do and thus keeps the game flowing.

You may also be using some kind of exact placement system, ala Warhammer, where you physically measure the distance between pieces. In that case, the DMG offers no advice and I'd simply ask your DM to make a call.

To answer the first part of the question, let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis.

For the second part, I have two points. First, I would agree you've found a mathematical contradiction if you assume the maximum length is along the origin. In that case, the cone defines an isosceles triangle where the height equals the length of the base. In such a case, the two equal sides would of course need to be longer than the triangle's height. This necessitates the cone ending in a flat plane, rather than being a surface of revolution. This contradicts the presumption that the height/axis measurement is the longest, and makes my response to the first section somewhat nonsensical. As you point out, it would be more consistent from this view to measure the sides as the maximum.

On the other hand, the purpose here is to decide whether or not a given target is inside the cone. You may not be using the optional grid rules from DMG 250. If not, then DMG 249 advises

go with your gut.

If you are, then all of your math is rounded to the nearest square. In this case, I'd definitely advocate ending the cone in a plane. The main reason is because it's quick an easy to do and thus keeps the game flowing.

You may also be using some kind of exact placement system, ala Warhammer, where you physically measure the distance between pieces. In that case, the DMG offers no advice and I'd simply ask your DM to make a call.

To answer the first part of the question, let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis.

For the second part, I have two points. First, I would agree you've found a mathematical contradiction if you assume the maximum length is along the axis. In that case, the cone defines an isosceles triangle where the height equals the length of the base. In such a case, the two equal sides would of course need to be longer than the triangle's height. This necessitates the cone ending in a flat plane, rather than being a surface of revolution. This contradicts the presumption that the height/axis measurement is the longest, and makes my response to the first section somewhat nonsensical. As you point out, it would be more consistent from this view to measure the sides as the maximum.

On the other hand, the purpose here is to decide whether or not a given target is inside the cone. You may not be using the optional grid rules from DMG 250. If not, then DMG 249 advises

go with your gut.

If you are, then all of your math is rounded to the nearest square. In this case, I'd definitely advocate ending the cone in a plane. The main reason is because it's quick an easy to do and thus keeps the game flowing.

You may also be using some kind of exact placement system, ala Warhammer, where you physically measure the distance between pieces. In that case, the DMG offers no advice and I'd simply ask your DM to make a call.

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Joel Harmon
Joel Harmon
  • 16.1k
  • 3
  • 60
  • 92

To answer the first part of the question, let me quote the first sentence of the Cone description:

A cone extends in a direction you choose from its point of origin.

That is, the cone is defined by the direction you shot it in, which is the axis of the cone. As such, it makes the most sense to refer to the other properties of the cone in terms of the axis.

For the second part, I have two points. First, I would agree you've found a mathematical contradiction if you assume the maximum length is along the origin. In that case, the cone defines an isosceles triangle where the height equals the length of the base. In such a case, the two equal sides would of course need to be longer than the triangle's height. This necessitates the cone ending in a flat plane, rather than being a surface of revolution. This contradicts the presumption that the height/axis measurement is the longest, and makes my response to the first section somewhat nonsensical. As you point out, it would be more consistent from this view to measure the sides as the maximum.

On the other hand, the purpose here is to decide whether or not a given target is inside the cone. You may not be using the optional grid rules from DMG 250. If not, then DMG 249 advises

go with your gut.

If you are, then all of your math is rounded to the nearest square. In this case, I'd definitely advocate ending the cone in a plane. The main reason is because it's quick an easy to do and thus keeps the game flowing.

You may also be using some kind of exact placement system, ala Warhammer, where you physically measure the distance between pieces. In that case, the DMG offers no advice and I'd simply ask your DM to make a call.