TB to Gbit converter

What is a terabyte?

A terabyte (TB) is a unit of digital information storage in the International System of Units (SI), which uses base-10 notation. Specifically:
$1 \text{ TB} = 10^{12} \text{ bytes} = 1,000,000,000,000 \text{ bytes}$
In contrast, tebibytes (TiB) belong to the binary system (IEC standard), where:
$1 \text{ TiB} = 2^{40} \text{ bytes} = 1,099,511,627,776 \text{ bytes}$
This distinction matters because storage devices often use SI units (TB), while operating systems may report sizes in TiB, leading to discrepancies.

What is a gigabit?

A gigabit (Gbit) measures data transfer rates or bandwidth, using the SI system:
$1 \text{ Gbit} = 10^9 \text{ bits} = 1,000,000,000 \text{ bits}$
In the binary system, gibibit (Gibit) is used:
$1 \text{ Gibit} = 2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$
Note that 1 byte = 8 bits, so converting between bytes and bits requires multiplying or dividing by 8.

Formula: Conversions between TB, Gbit, TiB, and Gibit

SI system (decimal)

1. TB to Gbit:
   $\text{Gbit} = \text{TB} \times 8,000$
   Explanation: Since 1 TB = $10^{12}$ bytes and 1 byte = 8 bits,
   $1 \text{ TB} = 10^{12} \times 8 \text{ bits} = 8 \times 10^{12} \text{ bits} = 8,000 \text{ Gbit}$

2. Gbit to TB:
   $\text{TB} = \frac{\text{Gbit}}{8,000}$

Binary system (IEC)

1. TiB to Gibit:
   $\text{Gibit} = \text{TiB} \times 8,192$
   Explanation: Since 1 TiB = $2^{40}$ bytes and 1 byte = 8 bits,
   $1 \text{ TiB} = 2^{40} \times 8 \text{ bits} = 8,796,093,022,208 \text{ bits} = 8,192 \text{ Gibit}$

2. Gibit to TiB:
   $\text{TiB} = \frac{\text{Gibit}}{8,192}$

Examples of conversions

Example 1: Converting 5 TB to Gbit (SI)

Using the formula:
$\text{Gbit} = 5 \times 8,000 = 40,000 \text{ Gbit}$
Real-world context: A 5 TB hard drive contains 40,000 gigabits of data.

Example 2: Converting 2 TiB to Gibit (Binary)

Using the formula:
$\text{Gibit} = 2 \times 8,192 = 16,384 \text{ Gibit}$
Real-world context: A 2 TiB SSD equates to 16,384 gibibits.

Example 3: Cross-system conversion (TB to Gibit)

Convert 1 TB to Gibit:

1. Convert TB to bits:
   $1 \text{ TB} = 10^{12} \times 8 = 8 \times 10^{12} \text{ bits}$
2. Convert bits to Gibit:
   $\frac{8 \times 10^{12}}{2^{30}} = \frac{8,000,000,000,000}{1,073,741,824} \approx 7,450.58 \text{ Gibit}$

Historical context: The emergence of decimal and binary prefixes

• SI units (1960s): The International System of Units introduced prefixes like kilo-, mega-, and giga- to denote powers of 10.
• IEC Standard (1998): To resolve confusion in computing, the International Electrotechnical Commission defined binary prefixes (kibi-, mebi-, gibi-) for powers of 2.

Notes on common mistakes and best practices

1. Bits vs. Bytes: Always verify whether the unit refers to bits (b) or bytes (B). A 1 Gbit/s internet connection transfers 125 megabytes per second (MB/s), since $\frac{1 \text{ Gbit}}{8} = 125 \text{ MB}$.
2. Unit symbols: Use uppercase “B” for bytes (TB, GB) and lowercase “b” for bits (Gbit, Mbit).
3. Storage vs. Bandwidth: Storage devices (e.g., HDDs) use TB, while network speeds use Gbit.

Frequently Asked Questions

How to convert 3 TB to Gbit?

Multiply by 8,000:
$3 \times 8,000 = 24,000 \text{ Gbit}$

What is the difference between 1 TB and 1 TiB?

• 1 TB = 1,000,000,000,000 bytes (SI)
• 1 TiB = 1,099,511,627,776 bytes (IEC)
  The difference is approximately 9.95%.

Why do networking technologies use gigabits instead of gigabytes?

Network speeds measure data transfer per second in bits, a legacy from early telecommunications systems that prioritized binary signal states (0s and 1s).

Why do I get different results when converting TB to Gbit on different websites?

Some tools use SI units (1 TB = 8,000 Gbit), while others might erroneously use binary multipliers (1 TiB = 8,192 Gibit). Always check the unit definitions.

How to convert 4 TiB to Gbit?

1. Convert TiB to Gibit:
   $4 \times 8,192 = 32,768 \text{ Gibit}$
2. Convert Gibit to Gbit:
   $\frac{32,768 \times 2^{30}}{10^9} \approx 35,184 \text{ Gbit}$
   Note: Cross-system conversions are less common and may produce non-integer values.