What are exabytes and exbibytes?
Exabytes (EB) and exbibytes (EiB) represent colossal units of digital information storage. An exabyte in the SI (International System of Units) decimal system equals 1,000,000,000,000,000,000 bytes ($10^{18}$ bytes). This measurement follows the standard metric prefixes where each step increases by a factor of 1,000. The term “exa” comes from the Greek “hex” meaning six, signifying it as the sixth power of 1000 (1000⁶ = 10¹⁸ bytes).
In contrast, exbibytes (EiB) belong to the binary system standardized by the International Electrotechnical Commission (IEC). One exbibyte equals 1,152,921,504,606,846,976 bytes ($2^{60}$ bytes). This system uses base-2 increments, where each step grows by a factor of 1,024 ($2^{10}$). The “bi” in exbibyte explicitly indicates binary measurement.
What are megabytes and mebibytes?
Megabytes (MB) and mebibytes (MiB) are smaller but more commonly encountered storage units. A megabyte in the SI system equals 1,000,000 bytes ($10^{6}$ bytes). This unit has been widely used since the early days of computing to measure file sizes, storage capacity, and memory.
The mebibyte (MiB) is its binary counterpart, representing 1,048,576 bytes ($2^{20}$ bytes). The IEC introduced the mebibyte in 1998 to eliminate confusion between decimal and binary interpretations that had persisted for decades in computing. While “megabyte” was historically used for both $10^{6}$ and $2^{20}$ bytes, modern technical contexts now distinguish between MB (decimal) and MiB (binary).
The two measurement systems: SI vs IEC
Digital storage employs two distinct measurement systems, leading to significant numerical differences:
SI (Decimal) System:
- Base-10 system (powers of 10)
- Standard prefixes: kilo, mega, giga, tera, peta, exa
- 1 EB = $10^{6}$ TB = $10^{9}$ GB = $10^{12}$ MB = $10^{15}$ kB = $10^{18}$ bytes
- Primarily used by storage manufacturers, telecommunications, and networking
IEC (Binary) System:
- Base-2 system (powers of 2)
- Binary prefixes: kibi, mebi, gibi, tebi, pebi, exbi
- 1 EiB = $2^{10}$ PiB = $2^{20}$ TiB = $2^{30}$ GiB = $2^{40}$ MiB = $2^{60}$ bytes
- Used by operating systems, software applications, and memory measurement
The discrepancy arises because computers naturally operate in binary, while the metric system is decimal-based. This difference becomes substantial at larger scales - a 1 EB hard drive contains 7.2% less raw capacity than a 1 EiB drive.
Conversion formulas
Accurate conversions require different formulas for each system:
SI (Decimal) System Conversions:
IEC (Binary) System Conversions:
Cross-system Conversions:
Step-by-step conversion examples
Example 1: Converting 2.5 EB to MB (SI System)
- Formula: MB = EB × $10^{12}$
- Calculation: $2.5 \times 1,000,000,000,000 = 2,500,000,000,000$ MB
- Result: 2.5 EB = 2.5 trillion MB
Example 2: Converting 0.8 EiB to MiB (IEC System)
- Formula: MiB = EiB × $2^{40}$
- $2^{40} = 1,099,511,627,776$
- Calculation: $0.8 \times 1,099,511,627,776 = 879,609,302,220.8$ MiB
- Result: 0.8 EiB ≈ 879.6 billion MiB
Example 3: Converting 5 EB to EiB
- Formula: EiB = EB × ($10^{18} ÷ 2^{60}$)
- $10^{18} = 1,000,000,000,000,000,000$
- $2^{60} = 1,152,921,504,606,846,976$
- Conversion factor: $1,000,000,000,000,000,000 ÷ 1,152,921,504,606,846,976 \approx 0.867361738$
- Calculation: $5 \times 0.867361738 \approx 4.3368$ EiB
- Result: 5 EB ≈ 4.337 EiB
Why two systems exist: A historical perspective
The dual-system approach emerged from historical necessity. Early computer scientists naturally used binary measurements since digital circuits operate in base-2. However, they adopted metric prefixes (kilo, mega) for simplicity, creating an implicit understanding that “kilobyte” meant 1,024 bytes rather than 1,000.
This ambiguity became problematic as storage capacities grew exponentially. By the 1990s, a 1 GB hard drive could be interpreted as either 1,000,000,000 bytes (manufacturer specification) or 1,073,741,824 bytes (operating system). This 7.37% difference meant consumers received less apparent storage than expected.
The IEC resolved this in 1998 by standardizing binary prefixes (kibi, mebi, gibi), creating clear distinction. Today, storage manufacturers typically use decimal units (EB, MB) while operating systems use binary units (EiB, MiB) for file management.
Real-world applications and significance
Understanding these conversions has practical implications across technology:
Data center management: When provisioning 100 EB of cloud storage (SI), administrators must calculate actual capacity as approximately 86.7 EiB (binary) for accurate resource allocation.
Media production: A 4K movie file averaging 100 GB equals 0.0000001 EB or approximately 95,367 MiB - crucial calculations for content distribution networks.
Global internet traffic: With annual global internet traffic exceeding 3,000 EB (Cisco, 2023), conversion to 2,602,085 EiB reveals the true scale of digital infrastructure.
Storage manufacturing: A 20 TB hard drive marketed in decimal units actually provides 18.19 TiB (binary) - explaining why available space appears less than advertised.
Frequently asked questions
How many MB in an EB?
In the SI decimal system, 1 exabyte (EB) equals exactly 1,000,000,000,000 megabytes (MB). This conversion uses the formula: MB = EB × $10^{12}$. For example:
- 1 EB = 1,000,000,000,000 MB
- 0.5 EB = 500,000,000,000 MB
- 2.3 EB = 2,300,000,000,000 MB
Why does my operating system show less space than advertised?
Storage manufacturers use SI decimal units (1 GB = 1,000,000,000 bytes), while operating systems use IEC binary units (1 GiB = 1,073,741,824 bytes). A 1 terabyte (TB) drive contains 1,000,000,000,000 bytes, which your OS displays as approximately 931 gibibytes (GiB). The “missing” space isn’t actually missing - it’s a different measurement system.
When should I use EB vs EiB?
Use exabytes (EB) when working with storage capacities in scientific, telecommunications, or manufacturing contexts where decimal units are standard. Use exbibytes (EiB) when measuring memory allocation, file systems, or any context where binary addressing is fundamental, such as operating systems or programming.
How much data is 1 exabyte in practical terms?
1 EB is an almost unimaginable amount of data:
- Equivalent to 250 million DVDs
- Approximately 5 million laptop hard drives (assuming 200 GB each)
- The entire printed collection of the US Library of Congress 20,000 times over
- About 200,000 years of continuous music playback
Can I convert directly between EB and MiB?
Yes, but it requires a two-step conversion since they belong to different measurement systems. First convert EB to bytes ($\times 10^{18}$), then convert bytes to MiB ($\div 1,048,576$). The combined formula is:
For example, $0.000000001$ EB (1 GB) equals approximately 953,674 MiB.