The James Webb Space Telescope: From Wikipedia: “The telescope was originally estimated to cost $1.6 billion, but the cost estimate grew throughout the early development and had reached about $5 billion by the time the mission was formally confirmed for construction start in 2008. By October 2019, the estimated cost of the project had reached $10 billion for launch in 2021.”
Face mask sanitizers that will allow them to be used twenty times:
"…at $60 million for 60 machines on April 3, the price was right.
But over just a few days, the potential cost to taxpayers exploded to $413 million, according to notes of a coronavirus task force meeting obtained by NBC News. By May 1, the Pentagon pegged the ceiling at $600 million in a justification for awarding the deal without an open bidding process or an actual contract. "
“Even worse, scientists and nurses say the recycled masks treated by these machines begin to degrade after two or three treatments, not 20, and the company says its own recent field testing has only confirmed the integrity of the masks for four cycles of use and decontamination.”
According to Wikipedia: “On September 15, 1929, the Board of Transportation of the City of New York (BOT) tentatively approved the expansion, which included a Second Avenue Line with a projected construction cost of $98.9 million.”
The beginning of that article says that when the project is finally complete, some time perhaps ten years from now, it will have “cost more than $17 billion.” - almost 172 times the original estimate.
Shell (Oil Company) built the Pearl GTL (converting natural gas to oil) in Qatar. From an initial cost estimate of $5Billion , it went up to about $25 Billion.
“ In 2003, the project cost was estimated to be US$5 billion. However, after facing huge cost escalation, it was reported to be $18 billion in 2007,[1] and, according to Qatar Petroleum sources, final project cost is expected to reach as high as $24 billion.[9] Because Shell’s contract provided them with the input gas for free, the project was calculated to be viable once the price of oil exceeded $40 per barrel.”
$98.9M is $1.4B in 2020 dollars. That cost overrun calculation is more complicated given the extreme time. Also, has the scope changed? Not quite the same if the project doubles in size vs you get the original scope for twice the price.
Not as high in percentage terms as some of the others here, but in terms of sheer dollars the California high speed rail link between Los Angeles and San Francisco is a contender.
Projected costs under the original estimate in 2008 were $33.6 billion, and when voters approved the plan later that year it was at $40 billion. The plan in 2016 estimated costs at $64 billion, and that’s now up over $80 billion, with the opening of the full line pushed back to 2033. Some estimates now suggest that, if it’s ever actually finished, it will cost close to $100 billion.
Project Apollo initial cost projections were $7-12 billion for the whole shebang; it ended up costing over $25 billion (and still worth every penny, dammit!): Apollo program - Wikipedia
Costs for the B-2 Spirit bomber program rose so dramatically that each plane ended up costing over $1 billion. You could literally have made each plane out of solid gold and it would still have been cheaper (although, of course, not quite as flightworthy): Northrop Grumman B-2 Spirit - Wikipedia
The Superconducting Super Collider was cancelled after about $2 billion had already been spent but when cost projections rose from $4 billion to over $12 billion. It would surely have cost a good bit more had it actually been completed: Superconducting Super Collider - Wikipedia
Space Shuttle costs ended up being much higher than initially projected: “When all design and maintenance costs are taken into account, the final cost of the Space Shuttle program, averaged over all missions and adjusted for inflation, was estimated to come out to $1.5 billion per launch, or $60,000/kg (approximately $27,000 per pound) to LEO. This should be contrasted with the originally envisioned costs of $118 per pound of payload in 1972 dollars (approximately $635 per pound adjusting for inflation to 2011).” From here: Criticism of the Space Shuttle program - Wikipedia
The NYS Capitol Buiding took over 30 years to complete and a final cost of $25 million in 1899 ($768 million today). I can’t see the original cost, but on a percentage basis, it has to be up there. There were three architects and two different architectural styles, and people would run for governor promising to finish it. The “million dollar staircase” is so named because it supposedly cost a million dollars, which was real money at the time.
I don’t have the figures handy, but Bangkok’s Skytrain (aboveground rapid transit) and later its subway both were decried for cost overruns. As has Honolulu’s aboveground mass-transit project, yet to be finished. I guess this is common in projects like these.
Some of the grand Gothic projects of the medieval period might have really stretched their original budget. York Minster Cathedral
Construction began in 1220 and ended in 1472, 252 years to complete
The cornerstone for Cologne Cathedral was laid in 1248, and construction pace progressively slowed until 1473 when it stopped into the 1840s and finished in 1880 — 632 years.