Data Size Converter

Last verified: July 2026

Convert digital information storage capacities between Decimal (base-10 KB, MB, GB, TB) and Binary (base-2 KiB, MiB, GiB, TiB) systems.

Min: 0 TBMax: 10 TB
Real-World Data Milestones
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Operating System vs. Manufacturer Capacity Difference

Your storage drive is advertised as 1 TB (Decimal: 1012 bytes), but standard OS filesystems like Windows will report it as only 0.91 TiB (Binary: 240 bytes). This represents an apparent loss of about 9.1% of usable space due to unit definitions.

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Did you know? Did you know? Decimal prefixes (KB, MB, GB) are defined by the SI standard as powers of 10 (1000). Hard drive manufacturers use this standard to calculate capacity! Did you know? Operating systems like Windows report storage in binary units but display them with decimal labels (e.g. showing "GB" when they actually mean "GiB"). This is why a 1 TB hard drive appears as only 931 GB in Windows!
Primary Conversion Result
Gibibytes931.322575
Equivalency Matrix
Bits
8,000,000,000,000
Bytes
1,000,000,000,000
Kilobytes
1,000,000,000
Megabytes
1,000,000
Gigabytes
1,000
Terabytes
1
Kibibytes
976,562,500
Mebibytes
953,674.3164
Gibibytes
931.3226
Tebibytes
0.9095
Logarithmic Size Magnitude
1 B1 KB1 MB1 GB1 TB
Byte Equivalent1,000,000,000,000 Bytes
How is this calculated? (View worked mathematical solution)

Data size conversions normalize inputs into bits first, and then divide by the target factor:

Step 1: Convert source value to base bits:

Bits = 1 TB Γ— 8,000,000,000,000 = 8,000,000,000,000 b

Step 2: Convert base bits to target units:

Target (Gibibytes): 8,000,000,000,000 b / 8,589,934,592 = 931.322575 GiB
Scientific & Hardware Standards Reference

Digital information is measured in two standard systems:

  • Metric (SI) Decimal: Uses base-10 powers. Defined by NIST and BIPM (e.g. 1 Megabyte = 1,000,000 Bytes).
  • IEC Binary: Uses base-2 powers. Standardized by the International Electrotechnical Commission in 1998 (e.g. 1 Mebibyte = 1,048,576 Bytes) to resolve naming conflicts.
  • OS Discrepancy: Windows uses binary values for calculations but labels them using metric abbreviations (KB, MB, GB, TB). macOS and Linux use true decimal values for storage representations.

About the Data Size Converter

The Data Size Converter is a precision measurement instrument designed for software engineers, systems architects, network administrators, and digital storage professionals to translate capacities across SI metric decimal units (Bytes, KB, MB, GB, TB) and IEC binary units (KiB, MiB, GiB, TiB). Because computer operating systems and hardware manufacturers utilize fundamentally different mathematical base numbering systems when accounting for data storage, precise conversion is essential for resolving capacity discrepancies between hard drive labels and operating system reports.

Mathematical Formula & Logic

Our conversion engine operates via exact bit normalization (`1 Byte = 8 bits`). When you input any value in a source unit, the calculation first multiplies by the exact bit conversion factor to establish an unrounded base quantity in bits. To calculate the capacity in any target unitβ€”whether decimal base-10 powers (`10^3, 10^6, 10^9`) or binary base-2 powers (`2^{10}, 2^{20}, 2^{30}`)β€”the base bit quantity is divided by the target unit's exact bit factor, preserving full floating-point precision without intermediate rounding errors. Exact Bit Normalization Engine: - 1 Byte (B) = 8 bits (b) - 1 Kilobyte (KB) = 1,000 Bytes = 8,000 bits - 1 Kibibyte (KiB) = 1,024 Bytes = 8,192 bits - 1 Megabyte (MB) = 1,000,000 Bytes = 8,000,000 bits - 1 Mebibyte (MiB) = 1,048,576 Bytes = 8,388,608 bits - 1 Gigabyte (GB) = 1,000,000,000 Bytes = 8,000,000,000 bits - 1 Gibibyte (GiB) = 1,073,741,824 Bytes = 8,589,934,592 bits - 1 Terabyte (TB) = 1,000,000,000,000 Bytes = 8,000,000,000,000 bits - 1 Tebibyte (TiB) = 1,099,511,627,776 Bytes = 8,796,093,022,208 bits

Step-by-Step Example

Example 1: Why does a 1 TB external hard drive show as only 931 GB on Windows? Step 1: Convert the manufacturer's 1 Terabyte capacity to base bits using the metric SI definition (`1 TB = 10^{12} Bytes Γ— 8 = 8,000,000,000,000 bits`). Step 2: Microsoft Windows calculates drive capacities using binary IEC Tebibytes (`1 TiB = 2^{40} Bytes Γ— 8 = 8,796,093,022,208 bits`) but displays the label as 'TB' or 'GB'. Step 3: Divide base bits by the binary Tebibyte factor (`8,000,000,000,000 / 8,796,093,022,208 = 0.93132257... TiB`), which equals exactly 931.32 GiB (displayed as 931 GB in Windows). Example 2: Converting 5 Gigabytes (GB) to Mebibytes (MiB). Step 1: Convert 5 GB to base bits (`5 Γ— 8,000,000,000 = 40,000,000,000 bits`, or `5,000,000,000 Bytes`). Step 2: Divide base bits by the exact Mebibyte bit factor (`8,388,608 bits per MiB`): `40,000,000,000 / 8,388,608 = exactly 4,768.37158203125 MiB`.

Reference Data & Values

rule nameformulaapplicability
Bit (b)1 bit = 0 or 1 binary choiceThe most fundamental unit of digital data in computing and communications, representing a single logical state.
Byte (B)1 Byte = exactly 8 bitsA contiguous sequence of 8 bits, established as the standard unit for encoding a single alphanumeric character in computer memory.
SI Decimal Prefixes (KB, MB, GB, TB)Powers of 10 (10³, 10⁢, 10⁹, 10¹² Bytes)Standardized metric prefixes universally used by storage device manufacturers (hard drives, SSDs, USB drives) and network communications.
IEC Binary Prefixes (KiB, MiB, GiB, TiB)Powers of 2 (2¹⁰, 2²⁰, 2³⁰, 2⁴⁰ Bytes)Standardized prefixes published by the International Electrotechnical Commission in 1998, specifically designed for computer RAM and operating system file accounting.

Frequently Asked Questions

Hard drive manufacturers define 1 Terabyte using the metric decimal standard (`10^{12} = 1,000,000,000,000` Bytes). Microsoft Windows calculates disk capacities using binary IEC powers (`2^{40} = 1,099,511,627,776` Bytes per Tebibyte) but labels the display as 'TB' or 'GB'. Dividing 1,000,000,000,000 Bytes by `2^{30}` yields exactly 931.32 GiB.
A Megabyte (MB) is an SI decimal unit equal to exactly `10^6` (`1,000,000`) Bytes. A Mebibyte (MiB) is an IEC binary unit equal to exactly `2^{20}` (`1,048,576`) Bytes. Consequently, 1 MiB is approximately 4.86% larger than 1 MB.
A bit (abbreviated with a lowercase 'b') is the smallest unit of digital information, representing a single binary value of 0 or 1. A Byte (abbreviated with an uppercase 'B') is a sequence of 8 bits. Network transfer speeds are typically advertised in bits per second (e.g., 100 Mbps), whereas file sizes and disk capacities are measured in Bytes (e.g., 500 MB).
In the standard metric SI system, 1 Gigabyte (GB) equals exactly 1,000,000 Kilobytes (KB), because `10^9 / 10^3 = 10^6`. In the binary IEC system, 1 Gibibyte (GiB) equals exactly 1,048,576 Kibibytes (KiB), because `2^{30} / 2^{10} = 2^{20}`.
Since macOS 10.6 (Snow Leopard), Apple has strictly adopted the SI decimal standard for all file system displays. On macOS, 1 KB equals 1,000 Bytes, 1 MB equals 1,000,000 Bytes, and a 1 TB external hard drive will display exactly as 1 TB of available capacity.
Because there are exactly 8 bits in every Byte, you divide the speed in Megabits per second by 8 to get Megabytes per second. For example, a 100 Mbps fiber internet connection transfers data at a maximum theoretical rate of 12.5 MB/s (`100 / 8 = 12.5`).
In the SI decimal system, the hierarchy progresses from Terabyte (TB, `10^{12}`) to Petabyte (PB, `10^{15}`), Exabyte (EB, `10^{18}`), Zettabyte (ZB, `10^{21}`), and Yottabyte (YB, `10^{24}`). In the IEC binary system, Tebibyte (TiB, `2^{40}`) is followed by Pebibyte (PiB, `2^{50}`), Exbibyte (EiB, `2^{60}`), Zebibyte (ZiB, `2^{70}`), and Yobibyte (YiB, `2^{80}`).
During the early decades of computing before IEC standards were published in 1998, programmers appropriated the prefix 'kilo-' to mean 1,024 because `2^{10} = 1,024` is remarkably close to 1,000. Many legacy applications and operating systems maintain this historical practice for backward compatibility, despite formal international standards designating 1,024 Bytes strictly as a Kibibyte (KiB).