How do you calculate the storage capacity of magnetic tape?

Magnetic tape was first developed in Germany in 1928 for audio recording, based on earlier magnetic wire recording technology (https://en.wikipedia.org/wiki/Magnetic_tape). It works by magnetizing iron oxide particles on the tape in patterns that represent data. As the tape passes by a read/write head, the changing magnetic fields induce currents that are decoded into data.

Tape offers important benefits as a storage medium including low cost per GB stored, high data density, longevity with a shelf life of 30+ years, portability so data can be physically transported, and energy efficiency requiring zero power when not being actively read or written to (https://tnmuseum.org/Stories/posts/beverley-gooch-and-the-evolution-of-magnetic-tape). These factors have kept tape storage relevant even with the rise of hard drives and cloud storage.

Measuring Tape Length

The length of magnetic tape is measured in feet or meters. Standard tape lengths range from 300 feet (91.4 meters) to 2,400 feet (732 meters) for enterprise tape drives and 50 to 260 meters for midrange and entry-level drives (1).

Longer tape lengths allow more storage capacity. For example, the Oracle StorageTek T10000D drive supports tapes up to 820 meters long and can store up to 8.5 TB per cartridge (2). Larger backup formats like LTO Ultrium can use over 6,000 feet of tape to reach capacities of 30 TB compressed (3).

So in summary, standard magnetic tape lengths range from 50 meters to over 1,800 meters depending on the tape format. And longer tape lengths directly correlate with increased storage capacity per cartridge.

Measuring Tape Width

The width of magnetic tape helps determine the overall storage capacity. Wider tapes allow more data to be stored across the width of the tape. Over time, tape widths have increased to pack more data onto each tape cartridge.

Early magnetic tapes used in data storage had widths of 1/2 inch (12.7mm). By 1956, IBM had developed tape that was 1 inch (25.4mm) wide, doubling the prior width. In the mid-1980’s, 4mm, 8mm, and 16mm widths emerged for various formats such as VHS, Video8, and Digital8. In more modern times, common tape widths used in data storage include 6.35mm (1/4 inch), 12.65mm (1/2 inch), and 15mm in formats like SLR, IBM 3592, Oracle T10000, etc. Wider tape allows more tracks to be recorded in parallel, which increases overall data capacity per tape.

So in summary, magnetic tape widths have steadily increased over decades of evolution to pack more data onto tapes. And wider tape strongly correlates with increased storage capacity per tape. Early IBM tapes stored 5-10MB per reel, while modern data cartridges with larger widths now store 10’s of TB per cartridge.

Source: https://en.wikipedia.org/wiki/Magnetic_tape

Measuring Bit Density

Bit density refers to how closely bits are packed together on the magnetic tape. There are two bit density measurements:

  • Linear bit density – measures the number of bits per inch along a single track on the tape
  • Track density – measures the number of tracks per inch across the tape width

Higher bit densities allows a tape cartridge to have higher storage capacity. As technology improves, manufacturers are able to increase bit densities.

Modern magnetic tape now uses barium-ferrite magnetic particles which allows manufacturers to achieve higher linear bit densities. The particle size and uniformity as well as improved tape transport systems allow a single track on the tape to store more bits per inch without errors (https://spectrum.ieee.org/why-the-future-of-data-storage-is-still-magnetic-tape).

Current LTO magnetic tape drives have linear bit densities up to 2 million bits per inch. Enterprise 3592 tape drives offer up to 16,384 tracks across the 1/2 inch tape width for a track density of over 32,000 tracks per inch (https://en.wikipedia.org/wiki/Magnetic-tape_data_storage). These ultra high bit and track densities are what gives modern tape cartridges tape storage capacities in the tens of terabytes.

Measuring Tracks

Magnetic tapes store data in tracks that run the length of the tape. A track is a longitudinal section of the tape that data can be written to and read from. Tapes have multiple parallel tracks going across the width of the tape to maximize capacity.

The number of tracks varies by tape format and generation:

  • LTO-9 tapes have 32 tracks.
  • LTO-8 tapes have 32 tracks.
  • LTO-7 tapes have 32 tracks.
  • Older LTO tape formats have between 8 to 32 tracks.

So for example, an LTO-9 tape drive using a brand new LTO-9 tape can simultaneously read or write to 32 parallel tracks as the tape advances.

More tracks equals higher overall capacity since more data is written at the same physical area of tape.

Tape Capacity Formula

The tape capacity formula helps calculate the total storage capacity of a magnetic tape. Here is the formula:

Storage capacity (bytes) = Length (inches) x Width (inches) x Tracks x Bit density (bits/inch)1

Let’s walk through an example calculation:

Suppose we have a magnetic tape with the following specs:

  • Length: 2400 feet = 28,800 inches (1 foot = 12 inches)
  • Width: 0.5 inches
  • Tracks: 8
  • Bit density: 160,000 bits/inch

Plugging this into the formula:

Storage capacity = 28,800 in x 0.5 in x 8 tracks x 160,000 bits/in
= 3.66 terabytes

So the total storage capacity of this tape is 3.66 terabytes. As we can see, the tape’s length, width, number of tracks, and bit density all factor into the total capacity. Engineers work to improve each of these parameters to increase tape capacities.

Current Maximum Capacities

The current highest capacity linear tape formats are LTO-9 and LTO-10, though LTO-10 is still in development.

LTO-9 drives launched in late 2020 and provide a native capacity of 18 TB per cartridge, with 2.5:1 compression that enables capacities up to 45 TB (https://www.lto.org/lto-9/). The maximum compressed LTO-9 capacity is over 20x higher than the first LTO generation.

The next generation, LTO-10, is expected to provide at least 36 TB native capacity and 90 TB compressed capacity per cartridge once drives launch (potentially 2023). This doubling of capacity from one generation to the next continues the long-running LTO format’s trajectory (https://www.ibm.com/docs/en/ts4500-tape-library?topic=cartridges-capacity-supported-lto-tape).

Industry analysts project that LTO roadmaps and technology improvements will enable capacities ranging from 120-160 TB per cartridge in LTO-12, which could launch around 2030 (https://en.wikipedia.org/wiki/Linear_Tape-Open).

Increasing Tape Capacity

There are two main methods for improving the storage capacity of magnetic tapes:

  • Increasing the bit density – This refers to packing more bits of data per square inch on the tape. Higher bit densities allow more data to be stored on the same tape length. However, there are challenges with increasing density too far, as it requires more precise writing and reading of data.
  • Increasing the tape length – Lengthening the tape directly increases the total area to store data. But longer tapes can cause issues like increased likelihood of breakage and more strain on tape transport mechanisms.

Recent advances have pushed capacities up considerably. For example, the Particle Tape Consortium demonstrated a breakthrough of 201 Gb per square inch, indicating there is still room for growth using higher densities.

However, there are physical limitations that provide engineering challenges. As bit density increases, the precision needed also scales up dramatically. The tape mechanism parts like read/write heads and servos must operate with nanometer tolerances.

Tape Capacity vs. Hard Drives

Compared to modern hard disk drives (HDDs), magnetic tape has both advantages and disadvantages when it comes to storage capacity:

Advantages of Tape:

  • Tape has a lower cost per terabyte stored. Especially with the larger tape cartridges like LTO-8, the per-terabyte storage cost is significantly lower for tape (source).
  • Tape cartridges can hold very large capacities, with LTO-8 holding up to 12TB per cartridge. Some specialized formats can store even more data (source).
  • Tape is more robust for long-term archiving since tape is stored offline and at ambient temperatures.

Disadvantages of Tape:

  • Access speeds are much slower than hard disk drives, especially for random access.
  • Tape suffers from higher read/write error rates compared to hard drives.
  • The tape drive mechanism is more complex and prone to mechanical failures.

For large sequential data sets that need infrequent access, tape remains the most cost-effective backup storage medium. But for online storage that requires quick and reliable random access, hard disk drives are superior.

Conclusion

Magnetic tape continues to have an important role in data storage and backup due to its low cost and high data capacity. We covered the key factors that determine tape capacity: tape length, width, bit density, and number of tracks. Using the formula of capacity = length x width x bit density x tracks, modern tape cartridges can store up to 360 TB of compressed data.

While hard drives have higher capacities for single units, tape offers a more cost-effective solution for long-term archiving of large datasets. Tape technology continues to advance with increases in bit density through techniques like barium ferrite magnetic particles. So we can expect cartridge capacities to continue improving. Tape remains a crucial piece of IT infrastructure, often used for daily backups and long-term archives.