Convert B to TB

A byte is eight bits, though that was not always fixed — early machines used six, seven or nine. The eight-bit byte won because it holds one character of text and divides neatly in half.

A terabyte is a trillion bytes. A drive sold as 1 TB is exactly that — the space that seems to go missing is a unit disagreement, not a defect.

Going from bytes to terabytes moves the decimal point 12 places to the left and changes nothing else. There is no factor to remember and no rounding to decide: the digits stay in the same order and only their position changes.

1,234 B is 1.234e-9 TB — same digits, moved along. That is worth knowing because it is the one kind of conversion you can check at a glance: if the digits of the answer are not the digits you started with, something other than the conversion has happened to them.

Nothing anybody stores as a single object reaches thirteen digits. A number in this range is the sum of something: every object in a bucket, every row in a table, a month of logs, a backup set, the drives in a rack added together by a script that reported the only unit it had. Knowing that changes what the conversion is for — it is not sizing a file, it is sizing a decision about capacity or cost.

It also changes how much the answer can be trusted. A single file has one exact length, but a total is assembled from thousands or millions of measurements taken at slightly different moments, usually with some category quietly left out. The terabyte figure is as good as the sum behind it, and the sum is almost always approximate before it is large.

The conversion is a decimal point moved twelve places to the left, which is easy to state and easy to get wrong by three. Group the digits in threes from the right and name the groups aloud — units, thousands, millions, billions, trillions — and the number of full groups tells you the unit. 3,847,201,553,920 has four groups after the leading digits, so it is 3.847 TB and not 384.7 GB.

The failure mode is specific and worth guarding against: a thirteen-digit count read as twelve produces an answer ten times too small, and it looks entirely reasonable, because a figure of 384 GB and a figure of 3.8 TB are both ordinary things to have. There is nothing inside the answer that reveals the mistake. Counting the groups deliberately, once, is cheaper than discovering it downstream.

Spreadsheets and language runtimes stop printing long integers in full and switch to a form like 3.8472e12. The exponent counts the places the decimal point has moved, and twelve places is exactly the distance between bytes and terabytes — so when a byte count appears with an exponent of 12, the mantissa is already the terabyte figure and no arithmetic is left to do. An exponent of 11 means hundreds of gigabytes; one of 13 means tens of terabytes.

The hazard of that display is not the notation but what it hides. A spreadsheet cell showing 3.85e12 has usually kept the exact integer and is only shortening the display, but a cell that was typed or pasted in that form has lost everything below the mantissa. If the byte count is going to be reconciled against a bill or a quota later, keep the integer somewhere it is stored as text or as a 64-bit value.

The gap between the decimal and binary conventions widens at every rung, and the terabyte is where it is widest: a tebibyte is 1,099,511,627,776 bytes, 10% above a terabyte. Converting 3,847,201,553,920 bytes gives 3.85 TB or 3.50 TiB, and those two numbers do not look like the same quantity at a glance. Every step of the ladder contributes 2.4% — 2.4% at kilo, 4.9% at mega, 7.4% at giga, 10% at tera.

Ten per cent of a terabyte is a hundred gigabytes, which is enough to be the whole difference between a total fitting somewhere and not fitting. When a capacity figure and a usage figure come from different tools, the first thing to check is not the arithmetic but whether one of them was counting in powers of two while calling itself TB.

Aggregate byte counts are usually logical sizes: what the data would be if written once, plainly, with nothing around it. What sits on disk is larger for several reasons at once. Every file is rounded up to a block boundary. Replication stores two or three copies. Snapshots and versioned objects keep blocks alive that no current file points at. Indexes, write-ahead logs and free-space overhead in a database are real bytes that a table-size query may not report.

Compression and deduplication push in the other direction, and can push hard: a backup set of similar machines may store a fraction of its logical total. The consequence is that the terabyte figure needs a label as well as a number. A total meant for a capacity decision and a total meant for a transfer estimate are different quantities, and converting the wrong one is a larger error than any rounding on this page.

Two decimal places on a terabyte total claims the number is good to ten gigabytes, which is a claim almost no aggregate can support. The measurement moved while it was being taken, some category was excluded, and the tool that produced it may itself have been rounding. One decimal is usually the most that is defensible, and a whole number with a hedge is often more honest than either.

The exception is a figure that will be checked against money or against a quota, where the exact integer is the thing being agreed and rounding is somebody else’s job. There, carry the byte count itself and convert only for display — the terabyte figure is a way of talking about the number, and the number is what the invoice or the limit is actually computed from.

Two rough anchors catch most order-of-magnitude slips. Everything a phone can hold is well under a terabyte; a terabyte is a thousand of the gigabytes that a video or a virtual machine image is measured in. If a conversion says a mailbox is 4 TB or that a video library is 0.004 TB, the byte count has almost certainly been read with one group of three digits too many or too few.

The second check runs the arithmetic backwards. Multiply the terabyte answer by a trillion and compare the leading digits against the original byte count — 3.85 TB gives 3,850,000,000,000, which should match the first three or four digits and the total length of the number you started with. Matching digits and a mismatched length is precisely the failure this catches.