Distinguish bytes, bits and prefixes first
Start with the complete symbol rather than the number. Here B denotes byte and bit denotes bit. A byte contains eight bits under the definition used here. KiB and Kibit share a binary prefix but have different underlying units. By contrast, kB and KiB already differ in their prefix factors. Retain the unit in every intermediate line.[3]
The byte is the data-quantity unit used in this article; Ki multiplies it by exactly 1024.
Capitalization matters: k is kilo, M is mega and Ki is kibi. An informal “KB” label does not reliably establish whether 1000 or 1024 bytes are intended without an additional convention. Do not carry that ambiguity into a calculation: find the display definition or explicitly document both interpretations.
Read the table and know its current scope
The factors are powers of two. Between consecutive rows, the exponent increases by ten and the factor by 1024. The current list runs from Ki at 210 to Qi at 2100. Robi (Ri, 290) and quebi (Qi, 2100) were added in IEC 80000-13:2025 and are included in the current SI Brochure. Older lists with six or eight entries remain correct for the factors they list, but are incomplete.[1][2]
Binary prefixes are not SI prefixes. Decimal SI prefixes multiply by powers of ten. Choose a factor from the actual unit label, not merely from whether the subject is RAM, a drive or a file. A quantity in GiB can be converted into GB without changing the amount of data.[3]
Derive the conversion factor
Let D be the data quantity in bytes. If a binary unit contains 2n bytes, its numerical value is D/2n. Between two binary units, the conversion can be expressed as a difference of exponents. Conversion to a decimal unit instead leaves a quotient of a power of two and a power of ten.
Division subtracts exponents; one step corresponds to a factor of 1024.
The quotient is exact. A GiB is larger than a GB, so conversion from GiB to GB increases the numerical value.
A magnitude check is useful: moving to a smaller binary unit must increase the number by 1024. Converting GB to GiB must make the number slightly smaller. An opposite result usually means the quotient was inverted. Round only after the final conversion.
A further short storage check shows the direct path from the table: 4 GiB = 4 × 230 B = 4,294,967,296 B. Dividing by 109 gives exactly 4.294967296 GB, approximately 4.295 GB when rounded. Dividing 100 Mbit/s by eight gives an ideal 12.5 MB/s; the decimal prefix factor M remains unchanged.
Example: compare a capacity in GB and GiB
Express 512 GB in GiB
- Given
- An example capacity is exactly 512 GB, meaning 512 × 109 bytes. Formatting and reserved space are initially excluded.
- Find
- What is the numerical value in GiB?
First express the decimal quantity entirely in bytes.
Divide by the number of bytes in one GiB; the byte units cancel.
Round to two decimal places for display.
Result: 512 GB is approximately 476.84 GiB. The amount of data is unchanged.
Check: The number decreases because a GiB contains more bytes. Multiplying the unrounded GiB value by 230 recovers exactly 512 × 109 bytes.
A smaller number on a display therefore does not by itself establish a loss of storage. Actual deductions for filesystem metadata, reserved areas or existing files are separate. First check the unit, then compare usable byte quantities under the same conditions.
Example: connect data quantity and transfer rate
Transfer 750 MiB at 120 Mbit/s
- Given
- A file contains 750 MiB. For an ideal calculation, the constant available payload rate is 120 Mbit/s.
- Find
- How long does the transfer take in this model?
Convert the file size to bytes using the binary factor.
Since the rate is in bits per second, express the quantity in bits as well.
Insert the decimal rate and divide quantity by rate.
Result: The ideal transfer time is 52.4288 s, or approximately 52.43 s for display.
Check: 120 Mbit/s equals 15 MB/s. The file contains 786.432 MB; 786.432/15 again gives 52.4288 s. This independent calculation checks both the factor of eight and the prefix conversion.
An advertised link rate is not automatically the file payload rate. Protocol overhead, packet loss, latency and endpoint behavior affect achieved throughput. The example time applies to the explicitly assumed constant payload rate; it is not a promise for a real download. With a variable rate, transferred quantities must be accumulated over time.[4]
Common errors and limits of the calculation
- Do not apply 1024 to every data label: 1 MB = 106 B, whereas 1 MiB = 220 B.
- Do not confuse bits and bytes: a rate of 80 Mbit/s equals 10 MB/s, not 80 MB/s.
- Compare a result together with its unit. “476.84 is less than 512” is insufficient when the numbers use GiB and GB.
- An exact unit definition does not make a measurement or rounded product specification exact. Extra decimal places do not add measurement accuracy.
- Capacity describes a quantity of stored bytes. Whether a file fits depends on its actual encoding and the usable storage.
Three exercises with calculations
1. Convert 3.5 GiB into MiB and bytes.
Show hint
Gi and Mi are separated by exactly one binary prefix step.
Show solution and calculation
3.5 × 1024 = 3584 MiB.
In bytes this is 3.5 × 230 = 3,758,096,384 B.
Check: 3584 × 220 gives the same byte quantity.
2. Which is larger: 900 MB or 900 MiB? Find the difference in bytes.
Show hint
First convert both quantities into the same unit.
Show solution and calculation
900 MB is 900,000,000 B. 900 MiB is 943,718,400 B, larger by 43,718,400 B.
Relative to 900 MB, the difference is 4.8576%.
The comparison uses the same byte unit rather than merely comparing the two numbers 900.
3. What ideal time does a 2 GiB file require at a constant payload rate of 80 Mbit/s?
Show hint
Convert to bits; M here means 106.
Show solution and calculation
The file contains 2 × 230 × 8 = 17,179,869,184 bits.
Dividing by 80,000,000 bit/s gives 214.7483648 s, approximately 3 min 34.75 s.
Check in bytes: 80 Mbit/s is 10,000,000 B/s; dividing 2,147,483,648 B by this rate gives the same time.
Common questions about choosing a unit
Why does a drive appear smaller in GiB? A GiB contains more bytes than a GB, so the same quantity has a smaller numerical value. The example 512 GB → approximately 476.84 GiB describes only that unit conversion. Claims about usable or occupied storage additionally require checking the filesystem and its display.
Must RAM always be stated in GiB? An unambiguous calculation depends on the actual definition. When a specification uses powers of two, GiB expresses that clearly. A general rule of “RAM binary, drives decimal” cannot replace checking the unit; applications, specifications and displays may use different conventions.
Can binary prefixes precede bit? Yes: 1 Kibit is 1024 bit. Conversion to bytes is a separate, independent step. Thus 1 Kibit = 128 B and 1 KiB = 8192 bit. A data rate also requires a time unit, such as Kibit/s or Mbit/s.[3]
Sources for this explanation
Quanta · Updated October 1, 2026
- BIPM: SI Brochure, 9th edition, version 4.01, Section 3 (binary prefixes)
- IEC 80000-13:2025: Information science and technology; binary-prefix additions
- NIST: Binary prefixes and byte/bit conversion
- IETF RFC 6349: Framework for TCP Throughput Testing
Editorial responsibility: Quanta Study editorial team
Review scope
This explanation, 2 worked examples and 3 exercises are available in German and English. Structure, source references and mathematical notation undergo automated checks. Calculations, model assumptions and both language versions receive a separate AI review.
An internal human subject review is documented for an earlier release of this page. That confirmation does not apply automatically to the revised explanation and new exercises.
An independent, named human subject review has not yet been documented. Our exercise numbers are worked examples, rather than measurements published by the cited sources.
Editorial responsibility, sources and methodsCite this reference page
Quanta. Binary prefixes for data quantities. Updated October 1, 2026. https://quanta-study.de/en/formula-sheet/tables/binaerpraefixe
When citing a specific scientific statement, also cite the specialist source linked to that statement.