Digital Storage Converter

The digital storage converter translates file and drive sizes between bytes, kilobytes, megabytes, gigabytes, terabytes, and petabytes, in both the decimal system and the binary system. You enter a number, choose its unit, and read the equivalent value in every other unit at the same time. The tool exists because digital storage has two competing numbering conventions, and almost every confusion about "missing" disk space, overstated drive capacity, or mismatched file sizes traces back to the gap between them.

Storage sizes appear everywhere: file managers, camera specs, cloud plans, hard drive boxes, and memory card listings. A photo is measured in megabytes, a phone's storage in gigabytes, a hard drive in terabytes, and a data centre in petabytes. The numbers are only comparable when the units mean the same thing, which is exactly where the decimal-versus-binary distinction bites.

The two standards: decimal and binary

The decimal system, called SI after the International System of Units, treats every prefix as a power of 1000:

• 1 kilobyte (kB) = 1,000 bytes
• 1 megabyte (MB) = 1,000,000 bytes
• 1 gigabyte (GB) = 1,000,000,000 bytes
• 1 terabyte (TB) = 1,000,000,000,000 bytes
• 1 petabyte (PB) = 1,000,000,000,000,000 bytes

The binary system, called IEC after the International Electrotechnical Commission, treats every prefix as a power of 1024, because computers count in powers of two:

• 1 kibibyte (KiB) = 1,024 bytes
• 1 mebibyte (MiB) = 1,048,576 bytes
• 1 gibibyte (GiB) = 1,073,741,824 bytes
• 1 tebibyte (TiB) = 1,099,511,627,776 bytes
• 1 pebibyte (PiB) = 1,125,899,906,842,624 bytes

The difference grows with each step. One kilobyte and one kibibyte differ by 2.4%. One megabyte and one mebibyte differ by 4.9%. One gigabyte and one gibibyte differ by 7.4%. One terabyte and one tebibyte differ by 10%. The gap compounds because each prefix multiplies the previous gap.

The naming matters. "GB" is the decimal gigabyte of one billion bytes. "GiB" is the binary gibibyte of 1,073,741,824 bytes. A drive labelled 1 TB holds 1,000,000,000,000 bytes, which is 0.9095 TiB or 931.32 GiB. Both numbers describe the same physical drive; they just count in different bases.

Why hard drives "lose" space

The most common storage question is why a new drive shows less capacity than the box says. A drive advertised as 1 TB shows about 931 GB in Windows. The drive is not defective and nothing was stolen; the explanation is the unit mismatch.

Drive manufacturers market in decimal units because SI prefixes are the standard for physical quantities, and a 1 TB label is technically accurate: the drive really does hold one trillion bytes. Operating systems such as Windows display storage in binary units while printing the "GB" abbreviation, so the same 1,000,000,000,000-byte drive is reported as 1,000,000,000,000 ÷ 1,073,741,824 = 931.32 GiB, shown to the user as "931 GB". The hardware and the software are both correct; they are using different definitions of the same prefix.

The apparent loss is 7.37% of the nominal capacity for a gigabyte-scale conversion, and slightly more for larger drives because the gap compounds. A 2 TB drive shows 1.81 TB, and a 4 TB drive shows 3.63 TB. The same effect applies to memory cards, SSDs, and USB sticks, which is why a "32 GB" card formats to about 29.8 GB and a "64 GB" card to about 59.6 GB.

macOS behaves differently: it has displayed capacities in decimal since macOS 10.6, so a 1 TB drive shows as 1 TB. The same physical drive reports different numbers on Windows and macOS for no hardware reason at all.

Where each convention is used

The decimal system is standard for storage marketing, network speeds, and cloud billing. A 100 Mbps internet connection moves 100 megabits, or 12.5 megabytes, per second in decimal terms. Cloud providers bill bandwidth in gigabytes of 1,000,000,000 bytes. Drive and card manufacturers label products in decimal units.

The binary system is standard for memory, file systems, and most operating system displays. RAM sizes are binary: an 8 GB stick is really 8 GiB. File sizes reported by Windows, Linux, and Android file managers are usually binary values printed with SI abbreviations. This split is why a file that "weighs" 1.5 GB on your screen does not match the 1.5 GB decimal figure a hosting dashboard reports for the same transfer.

Worked examples

Example 1: a 500 GB drive in GiB.

500,000,000,000 bytes ÷ 1,073,741,824 = 465.66 GiB. Windows reports this as 465 GB. The user sees 35 GB "missing", which is 7% of the label, exactly as the unit difference predicts.

Example 2: a 1 TB drive in TiB.

1,000,000,000,000 ÷ 1,099,511,627,776 = 0.9095 TiB. Displayed as "0.91 TB" in a binary-reporting system. The same drive shows 1.0 TB on a decimal-reporting system.

Example 3: a 4 GB video file, converted to decimal gigabytes.

4 GiB = 4 × 1,073,741,824 = 4,294,967,296 bytes. In decimal terms that is 4.295 GB. If a transfer quota counts decimal GB, the file consumes 4.295 GB of the quota, not 4 GB, a difference that matters for people near their cap.

Example 4: a 2 TB drive with 500 GB used.

In decimal bytes, 2 TB = 2,000,000,000,000 and 500 GB = 500,000,000,000, leaving 1,500,000,000,000 bytes, or 1.5 TB. In binary display terms, 2 TB = 1.819 TiB and 500 GB = 465.66 GiB, leaving 1.353 TiB, shown as "1.35 TB". Two systems, two "free space" numbers for the same drive.

Example 5: converting 1 PB to decimal and binary.

1 PB = 1,000,000,000,000,000 bytes. In binary terms that is 1,000,000,000,000,000 ÷ 1,125,899,906,842,624 = 0.888 PiB. A petabyte-scale array advertised as 1 PB delivers about 0.89 PiB to a binary-reporting file system.

Practical rules for everyday use

• For buying storage: the decimal figure on the box is what the drive holds in raw bytes. Expect the formatted capacity to be about 93% of the label (931 GB for a 1 TB drive, 1.81 TB for 2 TB) when the OS reports in binary.
• For file transfers: confirm whether the quota, plan, or meter counts decimal or binary units. Most web and cloud quotas are decimal; most local file managers are binary.
• For RAM and swap: always binary. An 8 GB stick is 8 GiB, and memory tools that report decimal GB are showing the same module with a different ruler.
• For archives and backups: decide on one unit and stick to it across the whole project. Mixing decimal and binary figures in a backup plan produces capacity estimates that are wrong by up to 10%.

Common mistakes to avoid

• Subtracting decimal and binary numbers. Comparing a decimal drive capacity with a binary "used" figure and calling the difference a fault is the classic "missing space" error. Convert both to the same base first.
• Assuming every "GB" is the same. The same abbreviation is printed for one billion bytes in some places and 1,073,741,824 bytes in others. Look at the context: drive labels are decimal, OS displays are usually binary.
• Treating drive formatting overhead as the whole story. A small amount of capacity goes to the file system and partition tables, but on modern drives that is a fraction of a percent. The visible 7% shortfall is the decimal-binary conversion, not overhead.
• Multiplying the gap incorrectly. The conversion factor is not a flat percentage; it compounds per step. kB to KiB is 1.024, MB to MiB is 1.024 squared, GB to GiB is 1.024 cubed, and TB to TiB is 1.024 to the fourth power.
• Assuming all cloud providers bill the same way. Read the plan documentation. Some bill in GiB and some in GB, and on large transfers the difference is material.

Limitations and assumptions

The converter uses the exact SI powers of 1000 and the exact IEC powers of 1024, with no rounding in the underlying arithmetic. Results are rounded for display only. The tool converts units; it does not predict the formatted capacity of a specific drive, which also depends on the file system, partition layout, and reserved blocks. Those overheads vary by manufacturer and OS and are not part of a unit conversion.

Frequently Asked Questions

Why does my 1 TB hard drive show only 931 GB?

The drive holds exactly 1,000,000,000,000 bytes, which is 1 TB in decimal units. Windows and many other systems display storage in binary units, where the same capacity is 931.32 GiB. The label and the display are both correct; they count in different bases. The 7% difference is the unit conversion, not a defect.

What is the difference between GB and GiB?

GB is a decimal unit equal to 1,000,000,000 bytes. GiB is a binary unit equal to 1,073,741,824 bytes. One GiB is about 7.4% larger than one GB. The abbreviation GB is commonly printed for both, which causes the confusion.

How many bytes are in a petabyte?

In decimal, 1 PB = 1,000,000,000,000,000 bytes. In binary, 1 PiB = 1,125,899,906,842,624 bytes. The decimal figure is used by storage vendors; the binary figure appears in binary-reporting systems.

Is my 32 GB memory card really 32 GB?

The card holds 32,000,000,000 bytes, which is 32 GB decimal. After formatting, most systems show about 29.8 GB because they display in binary units. The card is not undersized; the numbers just use different definitions.

Why does macOS show more free space than Windows on the same drive?

macOS reports storage in decimal units since version 10.6, so a 1 TB drive shows as 1 TB. Windows reports in binary units, showing the same drive as about 931 GB. The drive is identical; the operating systems count differently.

Should I buy storage based on GB or GiB?

Buy on the decimal capacity printed on the box, which is what the device actually holds in bytes. Then expect the operating system to report roughly 93% of that figure. For planning, work in the same unit your tools display, which is usually binary on local systems and decimal on cloud dashboards.

Do SSDs and HDDs differ in this respect?

No. Both are marketed in decimal units and both report less in binary-displaying systems. The 7% conversion gap applies identically. SSDs do reserve some cells for wear levelling and over-provisioning, which is a separate and smaller effect, usually not visible in the formatted capacity.

How do I convert GB to GiB?

Divide the decimal bytes by 1,073,741,824. For example, 1 GB = 1,000,000,000 ÷ 1,073,741,824 = 0.9313 GiB. Multiply by 1.0737 to go the other way: 1 GiB = 1.0737 GB.

References

• IEC 80000-13, Quantities and units: Part 13, Information science and technology, which defines the KiB, MiB, GiB, TiB, and PiB binary prefixes.
• NIST Special Publication 811, Guide for the Use of the International System of Units (SI), which documents both the SI prefixes and the IEC binary prefixes.
• BIPM, The International System of Units (SI Brochure), 9th edition, for the decimal prefix definitions.
• Microsoft documentation on Windows capacity display conventions, which explains the binary reporting of storage in Windows.

Q: Can the Digital Storage Converter: Bytes to PB be used for professional or commercial purposes? A: Yes, the Digital Storage Converter: Bytes to PB provides mathematically correct results that are suitable for professional, commercial, and educational use. For the Digital Storage Converter: Bytes to PB, For the Digital Storage Converter: Bytes to PB, For high-stakes applications (medical, legal, financial), verify results with a domain expert. For the Digital Storage Converter: Bytes to PB, the Digital Storage Converter: Bytes to PB formulas used are well-established and validated against reference standards.

Q: How often are the Digital Storage Converter: Bytes to PB formulas updated? A: the Digital Storage Converter: Bytes to PB formulas are based on established scientific, mathematical, or industry-standard references and rarely require updates. When standards change (e.g., new physical constants, revised tax brackets, updated standards), the Digital Storage Converter: Bytes to PB is updated to reflect the current authoritative source. For the Digital Storage Converter: Bytes to PB, For the Digital Storage Converter: Bytes to PB, Each calculator's references section lists the specific sources used.