Binary and Decimal Storage Converter
Explain the “missing” storage on new drives by converting advertised decimal capacity (TB) to binary units (TiB) and back.
Your inputs
Results
Shown by a binary-reporting OS (TiB)
0.909495 TiB
- Exact bytes
- 1,000,000,000,000
- Difference between the two figures
- 9.051%
- In GiB
- 931.323
✓Exact calculation — rounded only for display
Notes for this result
- Windows labels binary units as “GB”/“TB”; macOS (since 10.6) and most drive makers use decimal units. Neither is “missing” space.
What this calculator does
Manufacturers use decimal prefixes (1 TB = 10¹² bytes) while some operating systems report binary units (1 TiB = 2⁴⁰ bytes), often labelled “TB”. The bytes are the same.
Formula and method
Worked example
Calculated by this tool with its default inputs:
Inputs
- Capacity: 1
- Unit: Decimal (as advertised: TB = 10¹² bytes)
- Scale: Tera / Tebi
Results
- Shown by a binary-reporting OS (TiB): 0.909495 TiB
- Exact bytes: 1,000,000,000,000
- Difference between the two figures: 9.051%
- In GiB: 931.323
How to read the results
A 1 TB drive shows about 931 GiB — 9 % smaller-looking, with no missing bytes.
Assumptions and limitations
- IEC 80000-13 defines the binary prefixes KiB, MiB, GiB, TiB.
Questions
Which systems use binary units?
Windows reports binary sizes but labels them GB/TB; macOS has used decimal units since 10.6.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
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