Feat[]
During the episode The Name of the Doctor, The TARDIS shuts off all systems except Anti-Gravity, meaning the TARDIS has literally no defences. The Doctor turns off the Anti-Gravity systems, and falls from orbit to Trenzalore's surface, with a mere crack in one window to show for it.
Trenzalore is a human colony planet, so it's comparable to Earth. The only difference is shorter days and longer nights. That picture to the right shows a heavily burned Trenzalore after a 900-year long war.
Calculation[]
Trenzalore is 928 pixels/1.2742e+7 meters
The panel height is 1083 pixels
2atan(tan(70/2)*(928/1083)) = 1.08082895 radians
Converting to degrees gets 61.92693721071 degrees
Using the Angular size calculator I get 1.0618e+7 meters
I found a source, an official one, that says it's significantly less than 1200 pounds, I'll use just 600 pounds, or 272.155 kg.
Using this formula (G*M*m)/r1 - (G*M*m)/r2
(6.674*(10^-11) * 5.972*10^24 * 272.155) / 6371000 = 17026081731 J
(6.674*(10^-11) * 5.972*10^24 * 272.155) / (6371000+1.0618e+7) = 6384905921.97 J
17026081731 - 6384905921.97 = 10641175809 J
Final Tally[]
The TARDIS' Unshielded Durability = 2.54330205761 Tons of TNT (Large Building level)
It's consistent with another feat from Journey to the Centre of the TARDIS; The TARDIS is completely deactivated by a Magno-Grab, yet it can still tank a laser saw able to slice through other vessels.