Data Storage Converter
Convert bytes, kilobytes, megabytes and terabytes across both the decimal SI and binary IEC systems — and see exactly why a 1 TB drive reports as 931 GiB.
Data Storage Converter
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What this result does not account for
- Filesystem overhead, reserved blocks and slack space are not modelled — usable capacity is always slightly below raw.
- The JEDEC convention of KB meaning 1,024 is described but not offered as a unit, because it conflicts with SI.
- A byte is taken as eight bits; historical machines with other byte widths are out of scope.
- Compression, deduplication and thin provisioning change effective capacity in ways no unit conversion can capture.
In short: There are two systems and they diverge. Decimal SI: a kilobyte is 1,000 bytes. Binary IEC: a kibibyte is 1,024. The gap compounds — 2.4% at kilo, 4.8576% at mega, 7.374% at giga and 9.951% at tera. That is why a 1 TB drive shows as 931.32 GiB: the manufacturer counts in decimal, correctly, while Windows displays binary and labels it “GB”.
Formula
Each factor is the number of bytes in one of that unit. Decimal prefixes are powers of one thousand; binary prefixes are powers of 1,024. A byte is eight bits, so the bit row carries a factor of 0.125.
Worked Example
- Identify the source factor. One decimal terabyte is 1012 = 1,000,000,000,000 bytes.
- Convert to bytes. 1 × 1012 = one trillion bytes.
- Identify the target factor. One gibibyte is 230 = 1,073,741,824 bytes.
- Divide. 1012 ÷ 230 = 931.32257 GiB.
- Recognise the number. That is exactly the “missing space” on a new 1 TB drive.
Nobody is cheating you. A drive advertised as 1 TB really does contain a trillion bytes. Windows then divides by 230 rather than 109 and prints the result with the label GB, giving 931. The manufacturer used the SI prefix correctly; the operating system used a binary quantity with a decimal label. The IEC introduced kibi, mebi and gibi in 1998 precisely to end this, and the storage industry adopted them while consumer operating systems largely did not.
Strengths & Limits Of This Model
Where this engine is strong
- Carries both decimal and binary families as clearly labelled separate units.
- Reports the same quantity in both systems at once, so the gap is visible.
- States the percentage divergence at the prefix level actually in use.
- Explains which system each part of the industry follows and why.
Where it stops
- Cannot tell you which convention an arbitrary piece of software intends.
- Does not model filesystem or formatting overhead.
Practical Use Cases
Sizing storage and capacity planning
Provisioning against a quoted decimal capacity while monitoring reports binary usage guarantees a discrepancy of nearly ten per cent at terabyte scale. Converting explicitly avoids over-committing an array.
Understanding a new drive's reported capacity
The single most common consumer question about storage has one answer: decimal on the box, binary on the screen, and both are internally consistent.
Estimating transfer volumes
File sizes are bytes but link rates are bits — see the Bandwidth Converter, where that factor of eight is the whole story.
Memory versus disk arithmetic
RAM is genuinely binary because address lines come in powers of two, while disk capacity and network throughput are genuinely decimal. Using one convention for both is where spreadsheets go wrong.
Methodology & Editorial Standards
All conversions route through the byte. Decimal prefixes follow the SI definition as exact powers of one thousand; binary prefixes follow IEC 80000-13, standardised in 1998, as exact powers of 1,024. Both families are offered as separate, clearly labelled rows rather than being merged, because they are genuinely different units rather than roundings of one another. The engine reports the same quantity simultaneously in decimal and binary at an appropriate scale for each, and states the percentage gap at the prefix level actually in play: 2.4 per cent at kilo, 4.8576 at mega, 7.3742 at giga and 9.9512 at tera. A byte is taken as eight bits, which has been effectively universal since the 1960s although six, seven and nine-bit bytes existed earlier, which is why the term octet exists for the unambiguous case. The JEDEC convention of writing KB while meaning 1,024 is described but deliberately not offered as a selectable unit, since it conflicts directly with SI. All conversion factors are exact by definition under the International System of Units, or exact by international agreement where the unit is defined by treaty. Values are held at full IEEE-754 double precision internally and rounded only for display, so chained conversions do not accumulate drift.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Data Storage Converter — 10 Expert FAQs
10 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does my 1 TB hard drive show as 931 GB?
Because two different units are in play. The manufacturer sells you a trillion bytes, which is correctly one terabyte under the SI definition. Windows divides by 1,073,741,824 rather than a billion, producing 931.32, and then labels the result GB when it is really GiB. No space is missing and nobody is exaggerating — the box and the screen are using different units with confusingly similar names.
What is the difference between a megabyte and a mebibyte?
A megabyte is 1,000,000 bytes under the SI decimal convention. A mebibyte is 1,048,576 bytes, or 2²⁰, under the IEC binary convention. The mebibyte is about 4.8576 per cent larger. The IEC introduced the kibi, mebi and gibi prefixes in 1998 specifically so that the binary quantities could be named unambiguously.
Is a kilobyte 1,000 or 1,024 bytes?
Both answers are in active use, which is the problem. Strictly, a kilobyte is 1,000 bytes and a kibibyte is 1,024. Historically, computing used kilo to mean 1,024 because it was close to 1,000 and matched binary addressing. Storage and networking now use decimal; RAM and Windows file sizes still use binary. Context decides.
Why is RAM measured in binary but disks in decimal?
Because memory is genuinely binary: address lines come in powers of two, so a memory chip's capacity is inherently 2ⁿ bytes and a 4 GB module is really 4 GiB. Disk capacity has no such constraint — it is just a count of sectors — so manufacturers use ordinary decimal prefixes.
What is JEDEC and why does it matter?
JEDEC is the semiconductor standards body, and its memory standards define KB, MB and GB as binary powers of 1,024. That directly conflicts with SI, where those symbols mean powers of a thousand. Windows and RAM vendors follow JEDEC, macOS and drive makers follow SI, and the collision is the root of the whole confusion.
Is a byte always eight bits?
In practice yes, and universally so since the 1960s. Historically some machines used six, seven or nine-bit bytes, which is why the term octet exists to mean exactly eight bits without ambiguity. Networking standards still often say octet for that reason.
How much bigger is a tebibyte than a terabyte?
9.9512 per cent. A terabyte is 10¹² bytes; a tebibyte is 2⁴⁰, or 1,099,511,627,776 bytes. The gap grows with each prefix level because it compounds: 2.4 per cent at kilo, 4.8576 at mega, 7.3742 at giga and 9.9512 at tera.
Should I write KB or KiB?
Use KiB when you mean 1,024 bytes and want to be unambiguous, and kB when you mean 1,000. In technical documentation the IEC prefixes are worth the small awkwardness because they remove all doubt. In consumer-facing text most readers will only recognise KB and MB, so state the convention explicitly instead.
Does formatting a drive lose capacity?
A little, but far less than the decimal-to-binary gap. The filesystem reserves space for metadata, journals and allocation tables, typically well under one per cent of a modern drive. The overwhelming majority of apparently missing space is simply the unit difference.
What comes after a petabyte?
Exabyte, zettabyte and yottabyte in the decimal system, each a further factor of a thousand, with exbi, zebi and yobi as the binary counterparts. At the yotta level the decimal and binary versions differ by more than twenty per cent.