Storage Converter

Binary vs decimal: the 1000 vs 1024 problem

There are two systems for counting digital storage, and they differ by exactly one number: whether a kilobyte is 1,000 bytes or 1,024 bytes.

The decimal system uses powers of 1,000, matching the metric prefixes everyone already knows. A kilobyte is 1,000 bytes, a megabyte is 1,000,000, a gigabyte is 1,000,000,000. Drive manufacturers, network engineers and standards bodies like NIST and the IEC all use this system.

The binary system uses powers of 1,024, because computers work in base 2 and 1,024 is 2 to the tenth power. Here a kibibyte is 1,024 bytes, a mebibyte is 1,048,576, and a gibibyte is 1,073,741,824. Windows, and many older programs, use these values but still label them KB, MB and GB.

Both are correct. The trouble is that they are frequently mixed. That single difference of 2.4% per step compounds: by the time you reach gigabytes it is 7.4%, and at terabytes it is 10%. The calculator above shows both systems for every value, so you always see what a manufacturer means and what your computer will say. Everything runs in your browser, nothing you type is uploaded or stored.

Why a 1 TB drive shows up as 931 GB

This is the most common storage question there is, and the answer is pure arithmetic.

• A drive sold as 1 TB holds 1,000,000,000,000 bytes, because the maker uses decimal gigabytes of 1,000,000,000 bytes each.
• Windows divides by 1,024 three times, not 1,000 three times. So it computes 1,000,000,000,000 ÷ 1,073,741,824 = 931.3.
• It labels that 931 GB, even though those units are gibibytes.

Nothing is missing. The drive has every byte it was sold with; the operating system is just reporting the same bytes in bigger units. The gap grows with the drive: a 500 GB drive shows 465 GB (a 35 GB difference), and a 4 TB drive shows about 3.64 TB (a 360 GB difference).

The NIST reference on binary prefixes lays out the official definitions, and the International Electrotechnical Commission introduced the KiB, MiB and GiB names in 1998 to stop exactly this confusion. In practice, the industry never switched over, so you will keep seeing both.

Worked example: converting 2 TB

Take a '2 TB' external drive and see what happens at each step.

• Bytes: 2 × 1,000,000,000,000 = 2,000,000,000,000
• Decimal: that is 2,000 GB, exactly as advertised
• Binary: 2,000,000,000,000 ÷ 1,073,741,824 = 1,862.6 GiB, or 1.82 TiB

So Windows reports a '2 TB' drive as about 1.81 TB, and a tool using binary units would call it 1.82 TiB. Both describe the same physical disk.

Now run it the other way. You have a folder of video that is 500 GB decimal and want to know how much room it takes on a 1 TB drive. 500,000,000,000 bytes is 465.7 GiB, so it fills just under half the drive. Feed your own numbers into the calculator above and it shows every unit from bytes to petabytes at once, in both systems, so you never have to guess which one a screen is using.

Storage units at a glance

This table is the whole conversion in one place. The decimal column is what drive makers and network engineers use; the binary column is what most operating systems report.

Watch the difference column: it grows by about 2.5 percentage points at every step. That is why the confusion is invisible at kilobyte scale but glaring at terabyte scale. For the official definitions and how they relate to the metric system, see the National Institute of Standards and Technology.

Bits, bytes and what your internet speed means

There is one more conversion that trips people up constantly, and it has nothing to do with 1000 versus 1024. It is bits versus bytes.

A bit is a single 1 or 0. A byte is eight bits. Network speeds are quoted in bits per second, while file sizes are quoted in bytes. That factor of eight is why a '100 Mbps' connection does not download 100 megabytes a second.

• 100 Mbps = 100,000,000 bits per second = 12.5 MB per second
• 1 Gbps = 1,000,000,000 bits per second = 125 MB per second
• A 1 GB file on a 100 Mbps line takes about 80 seconds

A useful rule of thumb for planning: multiply the file size in megabytes by 8 to get megabits, then divide by your speed. A 4 GB movie is 32,000 megabits, so on a 100 Mbps line it takes about 320 seconds, or a little over five minutes, before overhead.

So when your ISP advertises 300 Mbps and a download crawls, check whether the number you are comparing is in bits or bytes. Divide bits by 8 to get bytes. The calculator above includes bits as an input and an output, so you can convert between the two directly and stop guessing why the speed never matches the promise.

Which system should you use?

There is no single right answer, only the right system for the context.

• Use decimal (1000) when you are buying storage, comparing drive specs, talking about network throughput, or quoting a standard. This is what manufacturers and standards bodies mean.
• Use binary (1024) when you are reading what Windows reports, sizing a partition, or checking whether a file will fit on a disk as the operating system sees it.
• When in doubt, convert both. That is what this tool is for. If a number looks 7% smaller than expected at gigabyte scale, or 10% at terabyte scale, you have almost certainly crossed between the two systems.

Cloud storage and phone plans muddy this further, because they usually quote decimal units while the device reports binary ones. A 128 GB phone holds 128,000,000,000 bytes, which shows up as about 119 GiB of usable space before the operating system takes its own share, so you see closer to 110 GB free out of the box.

One practical tip: when you compare two drives, compare the byte count, not the label. A '1 TB' drive and a '931 GiB' drive are the same disk. The IEC's prefix standards exist so that a careful writer can say exactly which one they mean, and now you can read both without being fooled.