The Mathematical Foundation
This page converts between Gibibytes (GiB) and Gigabytes (GB) using the exact binary-to-decimal factor prescribed by international standards. The conversion is deterministic and direction-dependent:
- GiB → GB: Multiply by 1.073741824 exactly.
- GB → GiB: Multiply by 0.931322574615 exactly.
These factors are not approximations. They arise from the two different definitions of “giga” and “gibi”:
- 1 Gigabyte (GB) = 10⁹ bytes = 1,000,000,000 bytes (SI decimal).
- 1 Gibibyte (GiB) = 2³⁰ bytes = 1,073,741,824 bytes (IEC binary).
The ratio 1,073,741,824 ÷ 1,000,000,000 = 1.073741824, and its reciprocal 1 ÷ 1.073741824 = 0.931322574615... (repeating decimal, cut at the 12th digit by convention). No rounding is applied at the factor level; the page uses these constants without truncation.
Zero converts to zero in either direction. A very large input (e.g., 1,000,000 GiB ≈ 1.0737 PB) is handled by the same multiplier; the tool does not overflow because it works with the constant factor directly. Negative values are not meaningful for digital storage and are not supported.
The tool converts only GiB and GB. It does not handle kilobytes, megabytes, terabytes, or any other unit. If you need MiB↔MB, TiB↔TB, or any other pair, you need a separate conversion.
Why the Numbers Are Different: Binary vs. Decimal Prefixes
The confusion between GiB and GB dates to the mid‑1990s when hard disk capacities began to exceed the megabyte range and the two conventions started diverging visibly. The International Electrotechnical Commission (IEC) adopted standard 60027‑2 in 1998, defining binary prefixes: kibi (Ki), mebi (Mi), gibi (Gi), tebi (Ti), and so on. These are powers of 1024. The International System of Units (SI) prefixes (kilo, mega, giga, tera) are powers of 1000. IEEE 1541‑2002 endorsed the same binary terminology.
The practical consequence: 1 GiB is always 1,073,741,824 bytes; 1 GB is 1,000,000,000 bytes. The difference is 73,741,824 bytes, or about 7.4% of the nominal decimal value. This gap grows with each higher prefix because the exponent increases. For example, 1 TiB ÷ 1 TB = 1.099511627776, a 9.95% discrepancy.
Despite the standard, many operating systems (Windows, macOS in earlier versions, Linux file utilities with -h flag) report capacities in GiB but label them “GB” for historical reasons. Windows, for instance, uses binary units for file sizes and drive capacities but shows “GB” on the disk. This is the source of the famous “missing capacity” complaint.
The Industry Conflict: Manufacturers vs. Operating Systems
Drive manufacturers advertise in decimal units because SI is the international legal standard for trade and because the decimal numbers are larger on paper. A “1 TB” hard drive is exactly 1,000,000,000,000 bytes. When an operating system divides that number by 1,073,741,824 (the GiB factor), the result is ≈ 931.322574615 GiB. The same mathematical operation is performed by this page when you convert GB→GiB.
The full walkthrough for the classic 1 TB drive:
- Drive capacity in bytes: 1,000,000,000,000 (1 × 10¹²).
- Divide by 1,073,741,824 (bytes per GiB): 1,000,000,000,000 ÷ 1,073,741,824 = 931.322574615...
- Rounded to the nearest integer as displayed by most OS: 931 GiB.
If you want to confirm the advertised decimal value from the OS display, multiply the 931 GiB back: 931 × 1,073,741,824 = 999,653,837,344 bytes, which is slightly under 1 TB because the OS truncated. The exact conversion is 931.322574615 GiB → 1,000,000,000,000 bytes.
The same conflict appears in solid-state drives (SSDs), USB flash drives, and memory cards. A “256 GB” SSD will show about 238 GiB in your operating system. This is not a defect; it is a unit mismatch.
Precision and Rounding
The tool performs the calculation using the exact factor and returns full numerical precision. The user may choose a display precision (number of decimal places) after conversion. The underlying result is not rounded unless the user explicitly asks for a rounded display.
When you should keep many decimals:
- Cloud billing that uses GB but instance documentation lists quotas in GiB. A 1.0 GiB difference at scale can mean a few cents every hour.
- Performance monitoring where IOPS or throughput limits are defined in binary-based block sizes (e.g., 256 KiB aligned to a 4 KiB block) but reported in decimal bytes.
- Scripted conversions where rounding errors accumulate across thousands of rows.
When rounding to two or three decimal places is acceptable:
- Checking whether a “500 GB” drive is actually ~465 GiB – the practical answer is “close enough” for consumer sanity.
- Reporting file sizes in an email or user interface where 1.07 GB (for 1 GiB) is more readable than 1.073741824 GB.
The tool does not automatically round unless the user selects a precision. This ensures that someone pulling numbers for a billing audit gets the full decimal string.
Who Needs This Conversion
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A consumer who just bought a 1 TB external drive and sees “931 GiB” in Windows. This page confirms the math is correct and explains why the numbers differ.
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A cloud engineer comparing storage tiers listed in GiB (e.g., AWS EBS volumes) with billing that uses GB. AWS provisions in GiB but bills for GB? Actually AWS bills in GB‑months for EBS, but the volume size you specify is in GiB. The difference can be budget‑critical.
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A sysadmin provisioning virtual disks where the hypervisor uses binary units but the OS reports in decimal. VMware’s vSphere, for example, uses GiB for virtual disk size; Windows guest sees bytes and may display “GB” but actually uses GiB internally. A 100 GiB VMDK will appear as 107.374 GB in decimal notation.
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A student learning computer architecture who needs to understand the difference between powers of two and powers of ten. The distinction between GiB and GB is the canonical example.
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Anyone converting file sizes in a script or spreadsheet that needs the precise factor. For example, a Bash script that sums up disk usage from
du(binary) and compares it with cloud storage API responses (decimal) must multiply by 0.931322574615 or divide by 1.073741824. -
A consumer shopping for memory cards, SSDs, or USB drives who wants to calculate the real usable capacity before buying. If a 512 GB SSD is sold, expect 512 ÷ 1.073741824 ≈ 476.8 GiB of capacity in the OS.
Common Pitfalls and How to Avoid Them
1. Assuming GiB and GB are interchangeable. They are not. A 10% error accumulates when you treat them the same, especially at petabyte scale. Always check which unit the source uses.
2. Using the wrong direction. Converting GB→GiB when you intended GiB→GB swaps the factor. If you multiply by 1.073741824 when you should have divided, your result will be 15% off (because 1.073741824² ≈ 1.1529). Always verify: “am I going from the number shown on the box (decimal) to what the OS shows (binary)?” Then use GB→GiB.
3. Using a rounded factor in code. Many online calculators or spreadsheet formulas use 1.024 for GiB↔GB, which is a rough approximation (error ~0.001%). For a single conversion it’s harmless; for 10,000 files the error becomes 10 GB. Use the exact 7‑digit (or 12‑digit) constant.
4. Confusing GiB with GB in cloud console settings. Some cloud providers let you provision storage in GiB but list quotas in GB. When you set a 500 GiB volume, the quota may deduct 536.87 GB from your limit. Always check the unit label in the dropdown.
5. Network throughput confusion. Bandwidth is typically measured in bits per second (decimal Gbps), but file sizes are in bytes (binary GiB). The conversion from 1 Gbps to actual transfer speed involves both the bit/byte factor (8) and the GiB/GB factor (1.073741824). The page does not handle bits or time, but users often mix units incorrectly.
FAQ
Q: Why does my 1 TB hard drive show only 931 GiB in Windows?
A: The manufacturer sells the drive as 1,000,000,000,000 bytes (1 decimal TB). Windows divides that number by 1,073,741,824 (bytes per GiB) and gets 931.32 GiB, which it then labels “GB” in the UI. The drive is not defective; the units differ.
Q: What is the exact formula to convert GiB to GB?
A: Multiply the number of GiB by 1.073741824. For example, 100 GiB × 1.073741824 = 107.3741824 GB.
Q: What is the exact formula to convert GB to GiB?
A: Multiply the number of GB by 0.931322574615. For example, 100 GB × 0.931322574615 = 93.1322574615 GiB.
Q: Can I use these same numbers for terabytes (TB and TiB)?
A: No. The conversion factors are different because the exponent changes. For TiB↔TB, the factor is 1.099511627776 (TiB→TB) and 0.909494701772 (TB→TiB). This page only handles GiB and GB.
Q: Is it always true that 1 GiB = 1.073741824 GB?
A: Yes, by definition. The IEC and IEEE standards fix the binary and decimal multipliers. There is no rounding in the factor itself. The number 1.073741824 is exact.
Q: Why do some programs show “GB” when they actually mean GiB?
A: Most operating systems and many file managers still use the binary calculation (powers of 1024) but display “GB” because the term “gigabyte” was historically used before the binary prefix standard existed. macOS and Linux (with ls -lh) now show “GiB” correctly in modern versions; check your settings.