Decimal (SI) vs binary (IEC) units reference table
The table lists the exact byte value of each unit under the two standardized prefix systems. SI decimal prefixes are defined in the BIPM SI Brochure; binary prefixes are defined in IEC/ISO 80000-13.
| Unit | System | Exact bytes |
|---|---|---|
| 1 KB (kilobyte) | Decimal (SI) | 1,000 |
| 1 KiB (kibibyte) | Binary (IEC) | 1,024 |
| 1 MB (megabyte) | Decimal (SI) | 1,000,000 |
| 1 MiB (mebibyte) | Binary (IEC) | 1,048,576 |
| 1 GB (gigabyte) | Decimal (SI) | 1,000,000,000 |
| 1 GiB (gibibyte) | Binary (IEC) | 1,073,741,824 |
| 1 TB (terabyte) | Decimal (SI) | 1,000,000,000,000 |
| 1 TiB (tebibyte) | Binary (IEC) | 1,099,511,627,776 |
- Operating systems differ in how they report sizes: some use binary units (historically labeled with decimal symbols), others use true decimal units, so the same file can display different numbers on different systems.
- Storage devices are marketed in decimal units; RAM capacities are inherently binary (a '16 GB' memory module is actually 16 GiB).
- Formatted usable capacity is further reduced slightly by file-system structures, separate from the unit-convention difference.
What are decimal and binary file size units?
File sizes are counted in bytes, and larger sizes are expressed with prefixes. Two prefix systems coexist. The decimal system uses SI prefixes in powers of 1,000: 1 KB = 1,000 bytes, 1 MB = 10⁶ bytes, 1 GB = 10⁹ bytes, 1 TB = 10¹² bytes. The binary system uses IEC prefixes in powers of 1,024: 1 KiB = 1,024 bytes, 1 MiB = 1,048,576 bytes, 1 GiB = 1,073,741,824 bytes, 1 TiB = 1,099,511,627,776 bytes.
The binary prefixes kibi (Ki), mebi (Mi), gibi (Gi) and tebi (Ti) were standardized by the International Electrotechnical Commission (originally in IEC 60027-2, now carried in ISO/IEC 80000-13) precisely because the same word — for example 'gigabyte' — was being used for both 10⁹ and 2³⁰ bytes. Under the standards, GB always means 10⁹ bytes and GiB always means 2³⁰ bytes.
The practical consequence is the famous 'missing' drive space. Storage manufacturers label capacity in decimal units, so a 1 TB drive holds 10¹² bytes. An operating system that reports sizes in binary units divides that byte count by 1,024³ and displays about 931 GiB — historically often labeled 'GB', which makes the drive look smaller than advertised. No space is actually missing; the two numbers describe the same byte count in different units.
How to use this file size calculator
- Enter the size value you want to convert.
- Select its unit — decimal (KB, MB, GB, TB) or binary (KiB, MiB, GiB, TiB).
- Read the exact byte count, which is the unambiguous common denominator of both systems.
- Compare the decimal (MB/GB) and binary (MiB/GiB) equivalents to see how the same data is reported under each convention.
The formulas behind file size conversion
Every conversion goes through bytes. Multiply the entered value by its unit's byte factor to get bytes, then divide by the target unit's factor. Decimal units use factors of 1,000ⁿ and binary units use factors of 1,024ⁿ.
Worked example: 1 TB = 10¹² bytes. Divided by 1,024³ (= 1,073,741,824) this is 931.32 GiB, and divided by 1,024⁴ it is 0.9095 TiB. Conversely, 1 GiB = 1,073,741,824 bytes = 1.0737 GB. The gap between decimal and binary units grows with each prefix step: about 2.4% at kilo, 4.9% at mega, 7.4% at giga and 10.0% at tera.
Common mistakes
- Assuming a '1 TB' drive is faulty because the OS shows ~931 GB — the drive holds 10¹² bytes; the OS is reporting in binary GiB.
- Treating 1 GB as 1,024 MB — under the SI standard 1 GB = 1,000 MB; 1,024 MiB is 1 GiB.
- Mixing prefix systems mid-calculation (e.g. multiplying GB by 1,024 to get MB), which compounds a ~5–10% error.
- Confusing bytes (B) with bits (b): file sizes use bytes, network speeds use bits, and they differ by a factor of 8.
常见问题
Why does my 1 TB drive show only 931 GB?
The drive genuinely contains 1 TB = 10¹² bytes, as labeled under decimal SI units. Operating systems that report in binary units divide by 1,024³, giving 931.32 GiB — a number historically displayed with the label 'GB'. Both figures describe the same capacity; only the unit convention differs.
What is the difference between a GB and a GiB?
A gigabyte (GB) is 10⁹ = 1,000,000,000 bytes under the SI decimal convention. A gibibyte (GiB) is 2³⁰ = 1,073,741,824 bytes under the IEC binary convention. A GiB is about 7.4% larger than a GB. The binary prefixes (KiB, MiB, GiB, TiB) were standardized to end the ambiguity of using one word for two different sizes.
Is 1 MB 1,000 KB or 1,024 KB?
Under the SI standard, 1 MB = 1,000 KB = 1,000,000 bytes. The value 1,024 KiB corresponds to 1 MiB (mebibyte) = 1,048,576 bytes in the IEC binary system. Historically 'megabyte' was used loosely for both, which is exactly the ambiguity the binary prefixes were created to resolve.
How many bytes are in a terabyte?
One terabyte (TB) is 10¹² = 1,000,000,000,000 bytes under SI decimal prefixes. One tebibyte (TiB) is 2⁴⁰ = 1,099,511,627,776 bytes — about 10% more. Storage manufacturers use the decimal terabyte for drive capacities.
Why do RAM sizes use binary units?
Memory chips are addressed in powers of 2, so their capacities are naturally binary: a module marketed as 16 GB actually contains 16 GiB = 17,179,869,184 bytes. Storage drives, by contrast, are marketed in decimal units, which is one reason drive and RAM capacities appear to follow different rules.
参考文献
- ISO/IEC 80000-13:2008. Quantities and units — Part 13: Information science and technology (binary prefixes kibi, mebi, gibi, tebi).
- IEC 60027-2. Letter symbols to be used in electrical technology — Part 2: Telecommunications and electronics (original binary-prefix standard, 1998 amendment).
- Bureau International des Poids et Mesures (BIPM). The International System of Units (SI Brochure), 9th edition, 2019 — SI decimal prefixes.
- NIST. Prefixes for binary multiples. physics.nist.gov reference on IEC binary prefixes.