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Is a normal-sized rug (i.e. Medium or Small) with the Animate Objects spell cast on it able to carry a person and fly?

  1. If so, how many people can it carry?

  2. Can a bigger rug carry more people?

  3. Can a flying animated object even carry people?

In other words: can I turn any rug into a flying carpet using the Animate Objects spell?

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Yes, it can

First of all, a carpet that is animated by animate objects can, in fact, fly:

Its speed is 30 feet, if the objects lack legs or other appendages it can use for locomotion, it instead has a flying speed of 30 feet and can hover.

A carpet has no appendages to use for locomotion, so it gets a flying speed of 30 feet.

Next, how much it can carry and still fly; this depends on its Strength.

Carrying Capacity. Your carrying capacity is your Strength score multiplied by 15. This is the weight (in pounds) that you can carry, which is high enough that most characters don't usually have to worry about it.

This is then further changed by their size category.

So what strength does your animated carpet have? Well, it depends on how big it is, as determined by your DM:

Tiny - HP: 20, AC: 18, Attack: +8 to hit, 1d4 + 4 damage, Str: 4, Dex: 18 Carries 30 lbs.

Small - HP: 25, AC: 16, Attack: +6 to hit, 1d8 + 2 damage, Str: 6, Dex: 14 Carries 90 lbs.

Medium - HP: 40, AC: 13, Attack: +5 to hit, 2d6 + 1 damage, Str: 10, Dex: 12 Carries 150 lbs.

Large - HP: 50, AC: 10, Attack: +6 to hit, 2d10 + 2 damage, Str: 14, Dex: 10 Carries 420 lbs.

Huge - HP: 80, AC: 10, Attack: +8 to hit, 2d12 + 4 damage, Str: 18, Dex: 6 Carries 960 lbs.

A suitably large animated carpet should be able to carry roughly one, maybe two, people and their equipment, if they're not particularly heavy and don't carry a lot of gear.

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    \$\begingroup\$ Thanks for the answer! This is exactly what I was looking for. \$\endgroup\$ – Woolly Wyvern Jul 25 '19 at 7:15
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    \$\begingroup\$ As additional information, I believe the "hover" portion of its speed limits it to moving over a surface, rather than flying through the sky. \$\endgroup\$ – Michael Richardson Jul 25 '19 at 15:47
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    \$\begingroup\$ @MichaelRichardson Hover is an additional feature of flying which means that in addition to flying, it can also remain aloft and stationary. The monster manual mentions this on page 8 under Fly, and it is also mentioned in the Player's Guide on page 191 under flying movement where it basically says that a creature with hover does not fall when it is knocked prone or has its speed reduced to 0 as other flying creatures would. While not a creature, these are the only places that hover is explained, and so it is safe to assume that the rules also cover objects that can hover. \$\endgroup\$ – cpcodes Jul 25 '19 at 16:54
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    \$\begingroup\$ @MichaelRichardson No it doesn't. The hover tag refers to the proclivity for it to remain aloft if knocked prone or if its speed is reduced to 0. Most fliers fall if those conditions are met, whereas a creature with hover is not. \$\endgroup\$ – David Coffron Jul 25 '19 at 16:55
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    \$\begingroup\$ @DavidCoffron Yeah, that was my bad - I was looking at the actual Carpet of Flying magic item for comparison, which has similar verbiage ("You can ... make it hover and fly") and started down that path a little towards the end without a proper transition. \$\endgroup\$ – cpcodes Jul 25 '19 at 17:07

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