Data Storage Converter: Binary (1024) and Decimal (1000) Units Explained
Your 1 TB drive shows 931 GB in Windows. Your RAM is sold in MiB but marketed as MB. Your internet is sold in Mbps but downloads in MB/s. The storage unit system has two incompatible conventions — decimal (SI) used by hardware vendors and decimal-measured networks, and binary (IEC) used by operating systems and memory — and they compound into significant confusion. This converter handles both, letting you convert between bits, bytes, KB/KiB, MB/MiB, GB/GiB, TB/TiB, and PB/PiB with full transparency.
Network speeds are in bits (lowercase b): 1 Mbps = 1,000,000 bits/second. File sizes are in bytes (uppercase B): 1 MB = 1,000,000 bytes. To convert Mbps to MB/s, divide by 8.
Why There Are Two Systems — Binary vs. Decimal
The confusion has a historical root. Computer memory (RAM, cache) is built from circuits organized in powers of 2 — 2¹⁰ = 1,024 became the convenient 'kilo' for memory. Hard drive manufacturers, seeking to advertise larger numbers, adopted the SI decimal prefix where 1 kilo = 1,000. Both groups used the same labels (KB, MB, GB) to mean different things. Hardware storage uses decimal (drives, SSDs, flash): a 1 TB drive has exactly 1,000,000,000,000 bytes. Operating systems traditionally used binary: Windows still reports storage in binary units but calls them GB/TB instead of GiB/TiB. The gap between decimal and binary grows with each step: 1 KB vs 1 KiB is 2.4% different; 1 TB vs 1 TiB is 9.95% different.
IEC Standard Prefixes Explained
To end the ambiguity, the International Electrotechnical Commission (IEC) introduced binary prefixes in 1998 (formalized in IEC 80000-13, 2008): kibibyte (KiB) = 1,024 bytes, mebibyte (MiB) = 1,048,576 bytes, gibibyte (GiB) = 1,073,741,824 bytes, tebibyte (TiB) = 1,099,511,627,776 bytes. The Linux kernel, GNU tools, and disk utilities like df and fdisk now use the correct IEC labels. Hard drive and SSD manufacturers use SI (decimal). Windows uses SI labels with binary values — the most user-confusing approach.
Real-World Examples of the Binary/Decimal Gap
The gap between advertised and reported capacity increases at scale. A 1 TB drive shows 931 GiB in Windows (because 10¹² bytes ÷ 2³⁰ bytes/GiB ≈ 931). A 512 GB SSD shows 476 GiB. A 16 GB USB drive (16 × 10⁹ bytes) shows about 14.9 GiB. This also affects RAM: a 16 GiB RAM kit (sold and measured in binary GiB since RAM is manufactured in binary capacities) may be advertised as '16 GB' — here the label is wrong but the value happens to be binary. Network speeds add another layer: a 1 Gbps connection (10⁹ bits/second, decimal) delivers about 119 MiB/second (binary), not 125 MB/second (decimal), not 1,000 MB/second.
Bits vs. Bytes — Network Speeds vs. File Sizes
The bit/byte split is the most common source of confusion about internet speeds. Network speeds are in bits: your ISP's '100 Mbps' plan moves 100,000,000 bits per second. File sizes are in bytes: a 100 MB file is 800,000,000 bits. Dividing: 800,000,000 bits ÷ 100,000,000 bits/s = 8 seconds to download, which matches the '100 Mbps ÷ 8 = 12.5 MB/s' rule of thumb. Protocol overhead (TCP headers, SSL encryption, routing) typically reduces real-world sustained speed to about 85–90% of the theoretical maximum, so a 100 Mbps plan realistically delivers about 10–11 MB/s of actual file data.
Binary vs. Decimal Conversion Table
- 1 KiB = 1,024 bytes | 1 KB (SI) = 1,000 bytes — 2.4% difference
- 1 MiB = 1,048,576 bytes | 1 MB (SI) = 1,000,000 bytes — 4.9% difference
- 1 GiB = 1,073,741,824 bytes | 1 GB (SI) = 1,000,000,000 bytes — 7.4% difference
- 1 TiB = 1,099,511,627,776 bytes | 1 TB (SI) = 1,000,000,000,000 bytes — 9.95% difference
- 1 PiB = 1,125,899,906,842,624 bytes | 1 PB (SI) = 10¹⁵ bytes — 12.6% difference
Network Speed to File Transfer Conversion Tips
- Mbps ÷ 8 = MB/s maximum theoretical transfer speed
- 100 Mbps plan → ~12.5 MB/s max, ~10–11 MB/s realistic
- 1 Gbps plan → ~125 MB/s max, ~100–115 MB/s realistic
- 25 Mbps → ~3.1 MB/s — enough for 4K streaming but slow for large downloads
- Network speeds are decimal Mbps; file progress bars show decimal MB/s
Frequently Asked Questions
Why does my 1 TB hard drive show less than 1 TB in Windows?
Hard drive manufacturers define 1 TB as 1,000,000,000,000 bytes (10¹², decimal). Windows reads storage using the binary system, where 1 TB = 1,099,511,627,776 bytes (2⁴⁰). Dividing the drive's actual byte count by the binary 1 TB gives approximately 0.909 TiB, which Windows displays as ~931 GB (Windows uses the label 'GB' but actually calculates GiB). The drive has not lost any capacity — it is just being reported in different units. macOS switched to using decimal (SI) units in macOS 10.6, so the same drive shows as the advertised 1 TB on a Mac.
What is the difference between MB and MiB?
Formally, MB (megabyte) = 1,000,000 bytes (decimal, SI prefix). MiB (mebibyte) = 1,048,576 bytes (binary, IEC prefix). In practice, the industry used 'MB' to mean 1,048,576 bytes for decades before the IEC formalized the binary prefixes in 1998. Today, storage hardware and network speeds use decimal MB; operating system memory reporting and RAM specs typically use binary MiB (often still labeled MB). The difference is about 4.9% — small for a single unit, but it compounds across conversions.
What does the IEC standard say about storage units?
The IEC 80000-13 standard (2008) introduced unambiguous binary prefixes: kibi (Ki, 2¹⁰), mebi (Mi, 2²⁰), gibi (Gi, 2³⁰), tebi (Ti, 2⁴⁰), pebi (Pi, 2⁵⁰). These map directly to the binary powers that computer hardware uses. The SI prefixes (kilo, mega, giga) are formally decimal. The standard resolved the longstanding ambiguity of 'kilobyte = 1000 or 1024?' by assigning each meaning its own unambiguous name. Adoption has been partial: Linux kernel, hard drive specs, and network equipment use SI/decimal; Windows, Java, and older software still use binary but with SI labels.
What is the difference between bits and bytes?
A bit is the smallest unit of digital information — a single binary value, 0 or 1. A byte is 8 bits. Most file sizes are measured in bytes (or kilobytes, megabytes, etc.). Network speeds are measured in bits per second (bps, Kbps, Mbps, Gbps) — a holdover from serial communication where data was transmitted one bit at a time. This distinction matters: a 100 Mbps network connection can transfer approximately 12.5 MB per second (100 ÷ 8), not 100 MB per second.
Why are internet speeds measured in bits and file sizes in bytes?
The convention predates the modern internet. Early telecommunications measured transmission rate in bits per second because data was sent serially, bit by bit, over phone lines. File sizes were always measured in bytes because computers store and process data in byte-aligned chunks (characters, instructions, pixels are all multiples of 8 bits). The convention stuck: ISPs advertise speeds in Mbps, while download managers show progress in MB/s. To convert: divide Mbps by 8 to get MB/s. A 1 Gbps fiber connection delivers about 125 MB/s to your download manager.
How do I convert Mbps to MB/s?
Divide by 8 (since 1 byte = 8 bits): MB/s = Mbps ÷ 8. Examples: 100 Mbps = 12.5 MB/s. 1 Gbps = 125 MB/s. 25 Mbps = 3.125 MB/s. In practice, real-world download speeds are 10–20% lower than the advertised connection speed due to protocol overhead, TCP/IP headers, and network contention. A 100 Mbps connection typically sustains about 10–11 MB/s in realistic download conditions.
What is a petabyte?
A petabyte (PB) is 1,000 terabytes in decimal (10¹⁵ bytes) or 1,024 tebibytes in binary. To put it in perspective: 1 PB of text could hold approximately 500 billion pages of plain text. Major cloud providers and data centers operate at petabyte and exabyte scale. Facebook reported storing over 100 petabytes of photos and videos in 2012; current estimates for the world's total stored data are in the zettabyte (1,000 exabytes = 1,000,000 petabytes) range. The unit above petabyte is exabyte (EB), then zettabyte (ZB), then yottabyte (YB).