# Umrechner für Datenspeicher

> Rechnen Sie GB in MB, TB in GB und GiB in GB um, mit getrennten dezimalen (kB, MB, GB, TB) und binären (KiB, MiB, GiB, TiB) Präfixen sowie Bits und Bytes.

Interaktive Version: https://www.calcopenly.com/de/conversion/data-storage-converter
Thema: Einheitenumrechner

Data sizes use two sets of prefixes. The decimal ones follow the SI: 1 kB = 1,000 bytes, 1 MB = 10⁶ and 1 GB = 10⁹ bytes. The binary ones, approved by the IEC in December 1998 and now part of IEC 80000-13, step by 1,024: 1 KiB = 1,024 bytes, 1 MiB = 2²⁰ and 1 GiB = 2³⁰ bytes. A byte is 8 bits, and every conversion between these units is exact.

The default converts 1 GiB to 1,073.741824 MB. The same gap explains why a new drive looks smaller: a 1 TB drive holds 10¹² bytes, which software counting in binary units shows as 931.32 GiB, often labelled “931 GB”.

The gap grows with each prefix: 2.4% at kilo, 7.37% at giga, 9.95% at tera and 20.9% at yotta. Memory chips come in powers of two, so RAM sizes are binary even when written GB, while drive makers and network speeds use decimal prefixes.

## Eingaben

- **Wert**: Eine Zahl in der Ausgangseinheit oder mit eigener Einheitenangabe
- **Von** (Optionen: bit, nibble, byte (B), kilobyte (kB), megabyte (MB), gigabyte (GB), terabyte (TB), petabyte (PB), exabyte (EB), zettabyte (ZB), yottabyte (YB), kibibyte (KiB), mebibyte (MiB), gibibyte (GiB), tebibyte (TiB), pebibyte (PiB), exbibyte (EiB), zebibyte (ZiB), yobibyte (YiB), kilobit (kbit), megabit (Mbit), gigabit (Gbit), terabit (Tbit), kibibit (Kibit), mebibit (Mibit))
- **Nach** (Optionen: bit, nibble, byte (B), kilobyte (kB), megabyte (MB), gigabyte (GB), terabyte (TB), petabyte (PB), exabyte (EB), zettabyte (ZB), yottabyte (YB), kibibyte (KiB), mebibyte (MiB), gibibyte (GiB), tebibyte (TiB), pebibyte (PiB), exbibyte (EiB), zebibyte (ZiB), yobibyte (YiB), kilobit (kbit), megabit (Mbit), gigabit (Gbit), terabit (Tbit), kibibit (Kibit), mebibit (Mibit))

## Ergebnisse

- Umgerechneter Wert — Hauptergebnis
- Umrechnung
- Umrechnungsfaktor
- Genauigkeit

## Formel

$$
\begin{gathered} x_{\text{to}} = x_{\text{from}} \times \dfrac{f_{\text{from}}}{f_{\text{to}}} \\ f = \text{one unit expressed in } \text{bit} \end{gathered}
$$

## Durchgerechnete Beispiele

### 1 GiB in MB

- Wert: 1 GiB
- Von: gibibyte (GiB)
- Nach: megabyte (MB)
- **Umgerechneter Wert: 1,073.741824 MB**
- **Genauigkeit: Exakt**
- Prüfquelle: 2³⁰ bytes = 1,073,741,824 bytes (IEC 80000-13); ÷ 10⁶

### A 1 TB drive in GiB

- Wert: 1 TB
- Von: terabyte (TB)
- Nach: gibibyte (GiB)
- **Umgerechneter Wert: 931.322574615 GiB**
- Prüfquelle: 10¹² / 2³⁰ = 244140625/262144, a terminating decimal (Python fractions)

### 1 KiB in kB

- Wert: 1 KiB
- Von: kibibyte (KiB)
- Nach: kilobyte (kB)
- **Umgerechneter Wert: 1.024 kB**
- Prüfquelle: 1024 bytes / 1000 bytes

### Largest gap: 1 YiB in YB

- Wert: 1 YiB
- Von: yobibyte (YiB)
- Nach: yottabyte (YB)
- **Umgerechneter Wert: 1.20892581961 YB**
- Prüfquelle: 2⁸⁰ / 10²⁴ = 1.208925819614629174706176 exactly (Python fractions)

### 1 byte in bits

- Wert: 1 B
- Von: byte (B)
- Nach: bit
- **Umgerechneter Wert: 8 bit**
- Prüfquelle: 1 byte = 8 bits (IEC 80000-13)

## Fragen

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

Because the maker and the operating system count differently. The drive's 1 TB is 10¹² bytes; Windows divides by 2³⁰ and shows 931.32 while labelling it GB. Nothing is missing, since 10¹² ÷ 1,073,741,824 = 931.32; formatting and recovery partitions take a little more. macOS has counted in decimal since OS X 10.6 and shows the same drive as 1 TB.

### Is 1 GB 1,000 MB or 1,024 MB?

Under the SI and IEC 80000-13, 1 GB is exactly 1,000 MB (10⁹ bytes), and the binary unit is 1 GiB = 1,024 MiB (2³⁰ bytes). Drive makers and macOS use the decimal meaning; RAM and Windows use the binary one while writing GB. The “1.44 MB” floppy disk mixed the two: 1,440 × 1,024 bytes.

### How many bits are in a byte?

Eight. IEC 80000-13 defines the byte as 8 bits, also called an octet. File sizes are counted in bytes (B) and network speeds in bits per second (bit/s), so a 100 Mbit/s connection moves at most 12.5 MB per second; a capital B marks bytes.

### What is a GiB?

A gibibyte, 2³⁰ = 1,073,741,824 bytes. The IEC created the binary prefixes kibi, mebi, gibi and tebi so that kilo, mega and giga could keep their SI meanings of 10³, 10⁶ and 10⁹. Many Linux tools and technical specifications use GiB; Windows shows the same quantity labelled GB.

### How many GB are in 1 TB?

1,000 GB in decimal units, which is how drives are sold. In binary units 1 TiB is 1,024 GiB, and a decimal 1 TB is 931.32 GiB. The converter keeps TB, TiB, GB and GiB separate, so you can see that 1 TiB is 1,099.51 GB, about 10% more than 1 TB.

### Wie genau arbeitet „Umrechner für Datenspeicher“?

Die Genauigkeit hängt von Ihren Eingaben und den Annahmen der Methode ab. Die Dezimalrechnung nutzt 50 signifikante Stellen, doch Schätzungen, numerische Verfahren und Quelldaten können ungenauer sein. Die angezeigte Rundung beseitigt diese Grenzen nicht. Anhand unabhängiger Quellen geprüfte Rechenbeispiele: 5. Beispielsweise wird „1 GiB in MB“ anhand von 2³⁰ bytes = 1,073,741,824 bytes (IEC 80000-13); ÷ 10⁶ geprüft.

### Woher stammt die Methode?

NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors; NIST Handbook 44, Appendix C — General tables of units of measurement; NIST — Prefixes for binary multiples (IEC 80000-13).

## Quellen

- [NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors](https://www.nist.gov/pml/special-publication-811)
- [NIST Handbook 44, Appendix C — General tables of units of measurement](https://www.nist.gov/pml/owm/nist-handbook-44-current-edition)
- [NIST — Prefixes for binary multiples (IEC 80000-13)](https://physics.nist.gov/cuu/Units/binary.html)