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Lady Romana is quoted as saying a TARDIS weights 5x10^6 kilograms, but I've also read that she was mistaken in this or that she was referring to the inside.

The Doctor's TARDIS has been moved a number of times and has landed on soft ground and not sunk in at all. This indicates the full weight of the interior is not felt from the exterior. But in The Parting of the Ways, Rose, Jackie, and Mickey use a large truck with chains to free up part of the interior of the TARDIS, and when they pull with the truck, the TARDIS doesn't just get pulled along on the ground, so, at least when the door is open, there's some connection between the weight inside and the outside shell.

I've searched for this and Romana's answer is the only one I find, but if that were true and it weight that much on the outside, people could not pick it up and move it.

How much does the Doctor's TARDIS weight from the outside?

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Worth pointing out that the chain was attached inside the TARDIS, so the vehicle(s) would have been pulling against the internal weight. – Jeff Dec 18 '11 at 17:36

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I've never seen a in-universe explanation (Possibly because that's something they have avoided defining, lest it cause complications later), but observing it's behavior, I'd guess the following:

The external shell has a weight consistent with what the chameleon circuit has modeled it upon. For example, the Doctor's Tardis is set up as a police box, and, being made primarily of wood, isn't that heavy. Other disguised Tardis examples, however, weren't so light -- The Master's Tardis, disguised as the Melkur, should have weighed about the same as a stone statue of it's size. That being said, I've never seen anything to really confirm this, it's just supposition.

As to when Mickey, Rose and Jackie were pulling on the console, the cable they connected was crossing the threshold into the main Tardis; they were pulling against the actual full weight of the Tardis, not just it's exterior shell. (Goes back to the whole Dimensionally transcendental thing; just as the exterior shape doesn't pass back physical requirements to the interior shape, so does force exerted on the inside not translate to force on the outside) Had they simply hooked the cable around the Tardis, it most likely would have moved quite easily. One way to think of it is that the door of the Tardis is an opening to a Pocket Universe; it doesn't CONTAIN it, so much as provide a portal to it.

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Also remember that it can be moved without too much difficulty. It seems like a forklift is all that it takes to move it, and it occasionally seen being transported on the back of a truck. – erdiede Dec 18 '11 at 17:17
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Yep; and either in the Tom Baker or Peter Davidson era, I seem to remember a group people picking it up and carrying it. – KHW Dec 18 '11 at 17:18
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Although the exterior does in some way contain it, as seen when the Titanic crashed into it. The bow of the Titanic protuded into the interior of the TARDIS without passing through the door. – Xantec Dec 18 '11 at 19:12
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Yeah; that kind of bothered me, since it's not consistent with the rest of the series.. As I recall, he did mention forgetting to turn on the Force Field; it's possible (and perhaps logical) that the control rooms occupy a space at the perimeter of the interior structure -- if so, it may be 'mapped' to the outside of the Tardis to allow for other exits / ports. (Like the Melkur's eyes in Master's Tardis.') If so, you could break into any part of the exterior and enter the control room, with the force field off. – KHW Dec 18 '11 at 19:31
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@KeithHWeston: I can remember two instances, both in the Davidson era: Black Orchid, where the police of 1925 cart the Tardis off; and Frontios, where the Tractators drag it underground (that might not count though, as they have power over gravity so might have been able to move it no matter how much it weighed). – Daniel Roseman Dec 19 '11 at 9:30
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up vote 5 down vote

In the Hartnell era a group of egyptian slaves are easily able to drag the TARDIS into a tomb.

And then again in the Troughton era during the serial The Faceless Ones the airport security are able to load the TARDIS onto the back of a truck and carry it off. I like the explanation that the exterior weighs as much as the object the chameleon circuit has chosen to replicate.

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