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What is a terabyte (TB) and petabyte (PB)?

A terabyte (TB) and petabyte (PB) are units of digital information storage. They belong to two distinct measurement systems:

  1. SI (International System of Units): Uses base-10 prefixes, where each unit is a multiple of 1000.
    • 1 TB (terabyte) = 101210^{12} bytes = 1,000,000,000,000 bytes.
    • 1 PB (petabyte) = 101510^{15} bytes = 1,000,000,000,000,000 bytes.
  2. Binary (IEC Standard): Uses base-2 prefixes, where each unit is a multiple of 1024.
    • 1 TiB (tebibyte) = 2402^{40} bytes = 1,099,511,627,776 bytes.
    • 1 PiB (pebibyte) = 2502^{50} bytes = 1,125,899,906,842,624 bytes.

The key difference lies in the systems they represent. SI units (TB, PB) are commonly used by storage manufacturers, while binary units (TiB, PiB) are used in software and operating systems to reflect the true binary nature of computing.

Understanding the conversion formulas

SI system (TB to PB)

To convert terabytes (TB) to petabytes (PB) in the SI system:

PB=TB1000\text{PB} = \frac{\text{TB}}{1000}

Example:
To convert 5,000 TB to PB:

PB=5,0001,000=5 PB\text{PB} = \frac{5{,}000}{1{,}000} = 5 \ \text{PB}

Binary system (TiB to PiB)

To convert tebibytes (TiB) to pebibytes (PiB) in the IEC standard:

PiB=TiB1024\text{PiB} = \frac{\text{TiB}}{1024}

Example:
To convert 2,048 TiB to PiB:

PiB=2,0481,024=2 PiB\text{PiB} = \frac{2{,}048}{1{,}024} = 2 \ \text{PiB}

Practical examples

Example 1: Data center storage

A data center reports 7,500 TB of storage. To express this in petabytes (SI):

PB=7,5001,000=7.5 PB\text{PB} = \frac{7{,}500}{1{,}000} = 7.5 \ \text{PB}

Example 2: Software reporting

An operating system shows 3,000 TiB of disk space. Converting to pebibytes (IEC):

PiB=3,0001,024≈2.9297 PiB\text{PiB} = \frac{3{,}000}{1{,}024} \approx 2.9297 \ \text{PiB}

Example 3: Cloud storage pricing

A cloud provider charges $0.03 per GB/month. For 1 PB (SI) of storage, the monthly cost is:

1 PB=1,000 TB=1,000,000 GB Cost=1,000,000×$0.03=$30,000/month1 \ \text{PB} = 1{,}000 \ \text{TB} = 1{,}000{,}000 \ \text{GB} \ \text{Cost} = 1{,}000{,}000 \times \$0.03 = \$30{,}000/\text{month}

Historical context

The binary system (IEC) was formalized in 1998 to resolve confusion caused by using SI prefixes (e.g., “giga” for both 10910^9 and 2302^{30}). Before this, terms like “megabyte” ambiguously referred to either system, leading to discrepancies in reported storage capacities.

Notes on accuracy

  1. Manufacturers vs. Operating Systems: A 1 TB hard drive (SI) will display as ~931 GiB (binary) in an OS, causing perceived “loss” of storage.
  2. Unit Symbols: Always use uppercase “B” for bytes (e.g., TB, PB) to avoid confusion with bits (e.g., Tb, Pb).
  3. Precision: For critical applications like scientific data, use binary units (TiB, PiB) to ensure exactness.

Frequently Asked Questions

How do I convert 2.5 PB to TB?

Using the SI formula:

TB=PB×1000=2.5×1000=2,500 TB\text{TB} = \text{PB} \times 1000 = 2.5 \times 1000 = 2{,}500 \ \text{TB}

What is the difference between TB and TiB?

  • TB (SI): 1 TB = 101210^{12} bytes.
  • TiB (IEC): 1 TiB = 2402^{40} bytes ≈ 1.0995 TB.
    The difference grows exponentially with larger units (e.g., 1 PiB ≈ 1.1259 PB).

How many PiB are in 4,096 TiB?

Using the binary formula:

PiB=4,0961,024=4 PiB\text{PiB} = \frac{4{,}096}{1{,}024} = 4 \ \text{PiB}

Why does my operating system show less storage than advertised?

Storage devices use SI units (e.g., 1 TB = 1,000 GB), but operating systems use IEC units (1 TiB = 1,024 GiB). For example:

1 TB (SI)=1,000,000,000,0001,099,511,627,776≈0.9095 TiB1 \ \text{TB (SI)} = \frac{1{,}000{,}000{,}000{,}000}{1{,}099{,}511{,}627{,}776} \approx 0.9095 \ \text{TiB}

How many 4K movies can fit in 1 PB?

Assuming a 4K movie averages 100 GB:

1 PB=1,000,000 GB Number of movies=1,000,000100=10,000 movies1 \ \text{PB} = 1{,}000{,}000 \ \text{GB} \ \text{Number of movies} = \frac{1{,}000{,}000}{100} = 10{,}000 \ \text{movies}

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