Toolarithm

Unit Converter

Data Storage Converter

Exact units. Clear storage budgets.

Convert data storage

Bits, bytes and explicit prefixes.

Nonnegative decimal, scientific value, fraction or proper mixed number. Bit and byte labels have different meanings.

The primary answer and conversion table always describe logical data. Decimal and binary prefixes are explicit. Allocation and capacity are separately labeled comparisons; display rounding never changes exact ceilings or file-fit counts.

Optional capacity comparison
View results
Precision and report

Decimal/scientific entry allows twenty significant digits, up to eighty characters and written exponents from negative thirty through thirty. Fractions allow one hundred digits per component and two hundred forty characters per field. Unit factors and rational intermediate values remain exact. Significant figures control only the visible decimal view. Complete copy and CSV always retain all forty-three units.

Worked examples

Logical data in Gibibyte (GiB)

Dt≈0.931322574615 GiBD_t\approx0.931322574615\,\mathrm{GiB}

Logical data is converted without rounding it into whole bytes. Allocation and capacity are separate comparisons. Only decimal displays are rounded.

Data storage conversion record

Source logical total

Ds=1.00000000000 GBD_s=1.00000000000\,\mathrm{GB}

Logical bits

Dbit=8.00000000000×109 bitD_{\mathrm{bit}}=8.00000000000\times10^{9}\,\mathrm{bit}

Logical bytes

DB=1.00000000000×109 BD_{\mathrm B}=1.00000000000\times10^{9}\,\mathrm B

Source bits per unit

fs=8.00000000000×109f_s=8.00000000000\times10^{9}

Target bits per unit

ft=8.58993459200×109f_t=8.58993459200\times10^{9}

Source unit: Gigabyte (GB). Target unit: Gibibyte (GiB). Lowercase bit labels and uppercase byte symbols have different meanings. Decimal prefixes use powers of one thousand; binary prefixes use powers of one thousand twenty-four.

Logical data unit comparison

The visible scope is common; every displayed row describes the same logical total. Complete copying and CSV always retain all forty-three units, including both bit and byte prefixes through quetta and quebi.

Logical data in the selected unit scope
Unit and prefix familyLogical amount
Bit (bit)base8.00000000000×109 bit8.00000000000\times10^{9}\,\mathrm{bit}
Byte (B)base1.00000000000×109 B1.00000000000\times10^{9}\,\mathrm B
Kilobyte (kB)decimal1000000.00000 kB1000000.00000\,\mathrm{kB}
Megabyte (MB)decimal1000.00000000 MB1000.00000000\,\mathrm{MB}
Gigabyte (GB)decimal1.00000000000 GB1.00000000000\,\mathrm{GB}
Terabyte (TB)decimal0.00100000000000 TB0.00100000000000\,\mathrm{TB}
Petabyte (PB)decimal1.00000000000×10−6 PB1.00000000000\times10^{-6}\,\mathrm{PB}
Kibibyte (KiB)binary976562.500000 KiB976562.500000\,\mathrm{KiB}
Mebibyte (MiB)binary≈953.674316406 MiB\approx953.674316406\,\mathrm{MiB}
Gibibyte (GiB)binary≈0.931322574615 GiB\approx0.931322574615\,\mathrm{GiB}
Tebibyte (TiB)binary≈0.000909494701773 TiB\approx0.000909494701773\,\mathrm{TiB}
Pebibyte (PiB)binary≈8.88178419700×10−7 PiB\approx8.88178419700\times10^{-7}\,\mathrm{PiB}

Step-by-step data storage conversion

  1. 1. Normalize logical data to bits

    Decimal prefixes use powers of one thousand; binary prefixes use powers of one thousand twenty-four. A byte contains eight bits. Keep the exact factor before rounding.

    Dbit=xfs=8.00000000000×109 bitD_{\mathrm{bit}}=x f_s=8.00000000000\times10^{9}\,\mathrm{bit}

  2. 2. Divide by the destination bit factor

    The primary answer and every conversion row describe the same logical data amount. Fractional bit and byte quantities remain mathematical estimates; they are not silently rounded into stored files.

    Dt=Dbitft≈0.931322574615 GiBD_t=\frac{D_{\mathrm{bit}}}{f_t}\approx0.931322574615\,\mathrm{GiB}
What Can You Create?

Compare data units, logical file totals and explicit storage budgets

Translate bits and bytes precisely

Convert a stated data amount among base, decimal and binary choices. Every prefix has an explicit family and bit factor, so a megabit is not confused with a megabyte and a gigabyte is not silently relabeled as a gibibyte.

Estimate an equal-size file batch

Multiply a whole count by a logical size per file, then optionally compare independently rounded allocation blocks. Main results stay logical, while allocated total and slack are labeled separately so a block model is not mistaken for a unit conversion.

Compare a known capacity with headroom

Enter the capacity you want to budget and choose a reserved percentage. Inspect whether the selected requirement fits, its remaining budget or shortfall, and the exact whole model-file count that can fit when a positive per-file cost is available.

Data storage formulas and worked examples

Normalize to bits before changing units

Let xx be the source quantity, fsf_s its bits per source unit and ftf_t the destination bit factor. The intermediate logical data amount is Dbit=xfsD_{\mathrm{bit}}=x f_s, and the destination amount is Dt=Dbit/ftD_t=D_{\mathrm{bit}}/f_t. All factors are defined integers. Fractional quantities remain rational values through conversion, so there is no need to round a small bit estimate up to a whole byte unless a separate allocation model is deliberately selected.

Dt=xfsft,1 B=8 bitD_t=x\frac{f_s}{f_t},\qquad 1\,\mathrm B=8\,\mathrm{bit}

Example: the original gigabyte comparison

One decimal gigabyte contains 10910^9 bytes. One gibibyte contains 2302^{30} bytes. Their exact quotient gives the number of gibibytes in that same logical quantity. The decimal display is about 0.931322574615 GiB0.931322574615\,\mathrm{GiB}, while the complete ratio remains available. The smaller numerical result reflects the larger destination unit, not a loss of stored bits. Changing the display precision does not alter either unit factor or the exact quotient.

1 GB=109230 GiB≈0.931322574615 GiB1\,\mathrm{GB}=\frac{10^9}{2^{30}}\,\mathrm{GiB}\approx0.931322574615\,\mathrm{GiB}

Example: distinguish a bit prefix from a byte prefix

A decimal megabit contains 10610^6 bits, while a decimal megabyte contains eight times that quantity. Therefore 8 Mbit=1 MB8\,\mathrm{Mbit}=1\,\mathrm{MB}. A binary mebibyte instead contains 2202^{20} bytes. This page uses full bit labels and explicit uppercase byte symbols in its dropdowns and reports. The factors describe data amounts; a network rate additionally requires a duration unit and is not inferred from a bare storage number.

1 Mbit=106 bit,1 MB=8×106 bit,1 MiB=220 B1\,\mathrm{Mbit}=10^6\,\mathrm{bit},\quad 1\,\mathrm{MB}=8\times10^6\,\mathrm{bit},\quad 1\,\mathrm{MiB}=2^{20}\,\mathrm B

Example: logical batch size versus selected allocation

Suppose three files each have a logical size of 1000 B1000\,\mathrm B. Their logical total is 3000 B3000\,\mathrm B. Under a simple independent allocation model with 4096 B4096\,\mathrm B blocks, each file needs one complete block, so the allocated total is 12288 B12288\,\mathrm B and the slack is 9288 B9288\,\mathrm B. Rounding only the combined logical total would produce a different result and would not implement the selected per-file model. Empty model files consume zero data blocks here; real metadata costs need separate information.

Bb=(8 bitB)b,a=Bb⌈dBb⌉,A=Na,S=A−NdB_b=\left(\frac{8\,\mathrm{bit}}{\mathrm B}\right)b,\quad a=B_b\left\lceil\frac{d}{B_b}\right\rceil,\quad A=Na,\qquad S=A-Nd

Reserve headroom before deciding which files fit

The capacity comparison first converts the entered capacity to bits, then applies its selected reserved percentage. A batch using allocation is compared using allocated bits; otherwise the logical requirement is used. Remaining capacity and shortfall are both nonnegative fields, and only the relevant one is positive. A whole-file count is obtained by an exact floor when its per-file cost is positive. The converter never decides fit from a decimal display that merely looks equal to the capacity.

Cu=C(1−r100),Nfit=⌊Cua⌋(a>0)C_u=C\left(1-\frac{r}{100}\right),\qquad N_{\mathrm{fit}}=\left\lfloor\frac{C_u}{a}\right\rfloor\quad(a>0)
Why Users Love This Tool

Keep prefix conversion and storage modeling auditable

Explicit unit meanings

  • The original twelve unit identifiers remain supported alongside the expanded bit and byte catalog.
  • Decimal and binary powers are exact integers through quetta and quebi.
  • Fractional logical quantities remain intact; whole-file and allocation decisions use separate exact floors and ceilings.

Complete records beyond the visible table

  • Common, decimal, binary and all-unit table scopes affect visibility only.
  • Copy and CSV retain all forty-three rows, active context, exact certificates and generated working.
  • Share links preserve validated inputs, and exact swap loads the logical result without reapplying comparisons.
Perfect For

Useful for data comparisons, file estimates and capacity planning

Students and teachers

Explain the eight-bit byte, powers of one thousand and powers of one thousand twenty-four. Compare the same data amount in different prefix systems and show why a changed numerical representation does not mean that bits vanished.

People estimating a file collection

Use a whole count and a stated average or common logical file size. Compare a manually selected block model when per-file allocation matters, while retaining the distinction between the estimated logical total and assumed allocated requirement.

People comparing a known storage budget

Use the capacity you actually want to budget, choose headroom deliberately and inspect exact fit decisions. Unit conversion and this simple block model do not inspect a filesystem or predict all of its physical overheads.

How It Works

How it works in three quick steps.

1

Enter one quantity or an equal-size file batch

Choose a single nonnegative storage quantity, or enter a whole file count and the logical size per file. Select the unit explicitly; bit and byte choices are separate, and decimal versus binary prefixes are named. Decimals, scientific notation, fractions and proper mixed numbers are supported for quantities. File count must be a whole number, while zero-size files are allowed as a numerical model.

2

Choose destination units and optional storage comparisons

Select the destination unit for the logical total. In batch mode, optionally compare a positive whole-byte allocation block applied independently to each file. Optionally enter a known available capacity and a reserved percentage for headroom. The capacity comparison uses allocated data when allocation is selected for a batch, otherwise logical data. These comparisons never replace the main logical unit conversion.

3

Review exact factors, capacity decisions and the saved record

Choose significant figures, visible unit-table scope, exact target ratio and calculation steps. The common scope retains the original twelve choices; other scopes expose the full decimal and binary catalog. Review whole-file fit, remaining capacity and shortfall when enabled. Copy the complete record or LaTeX, download CSV, share validated active settings or print the chosen report. Exact swapping loads the logical result as a single value and switches comparisons off.

Download & Print

Save exact quantities with their prefix and model choices

Copy the complete record or LaTeX

Plain text retains source units, prefix meanings, active file and capacity inputs, exact certificates and every unit row. Mathematical copying supplies the generated LaTeX steps. Clipboard unavailability is announced with a CSV fallback.

Download all unit and planning results

The rectangular UTF-8 CSV includes hidden rows, integer block counts, exact whole-file fit, logical and allocated quantities and capacity decisions. Import very large integers and fraction certificates as text if a spreadsheet would otherwise round them.

Print a focused report

Choose the visible unit scope, exact ratio and working before printing or saving PDF. Editing controls and the supporting article are excluded. Long ratios receive a compact-print notice; complete coefficients remain available in copied text and CSV.

FAQ

Frequently Asked Questions

What is the difference between a bit and a byte?
This converter uses the modern eight-bit byte: 1 B=8 bit1\,\mathrm B=8\,\mathrm{bit}. A bit quantity and a byte quantity with the same numerical value therefore describe different amounts of data. Select the complete labeled unit rather than relying on an ambiguous letter. For example, 8 Mbit=1 MB8\,\mathrm{Mbit}=1\,\mathrm{MB} with decimal prefixes. The tool also includes a nibble, explicitly defined here as four bits. It converts data amounts rather than interpreting binary digit strings or measuring a transfer rate.
Why are gigabytes and gibibytes different?
Decimal prefixes use powers of one thousand, while binary prefixes use powers of one thousand twenty-four. Thus 1 GB=109 B1\,\mathrm{GB}=10^9\,\mathrm B and 1 GiB=230 B1\,\mathrm{GiB}=2^{30}\,\mathrm B. They are distinct units, not two names for an identical capacity. The original example converts one decimal gigabyte into a smaller numerical gibibyte value. The actual number of bits does not change when its unit changes, and the converter never silently interprets a decimal label as binary.
Which prefix range and large-unit conventions are supported?
The catalog includes decimal bit and byte prefixes from kilo through quetta, and binary bit and byte prefixes from kibi through quebi. The largest decimal factor is 103010^{30} and the largest binary factor is 21002^{100} before the byte-to-bit factor is applied. Robi and quebi are included with the current binary-prefix definitions. Every unit displays its family and explicit symbol. These large choices use integer factors rather than native floating-point approximations, preserving exact conversions beyond ordinary integer precision.
Does converting a drive label explain all missing free space?
No. A decimal-to-binary conversion explains a change in the numerical unit representation, such as 1 TB≈931.323 GiB1\,\mathrm{TB}\approx931.323\,\mathrm{GiB}. It does not by itself calculate partitions, filesystem metadata, recovery data, snapshots or reserved device space. Enter a known capacity when making a budget and select a headroom percentage deliberately. The reserve is a model input rather than an automatically measured overhead. A byte quantity remains the same quantity even when a display uses a different prefix label.
How is a file batch converted, including fractional file sizes?
For an equal-size batch, the logical total is D=NdD=N d, where NN is a nonnegative whole file count and dd is the selected size per file. Quantities can use fractions, so an estimated average file size need not be forced into whole bytes. The converter preserves that mathematical estimate before display rounding. If the files actually have different sizes, use a known total directly or an appropriate average; the tool does not inspect files or infer their individual sizes.
Why is allocation rounded per file instead of rounding the total once?
The optional allocation model assumes each file independently occupies whole blocks. With a block of bb bytes and logical file size dd bits, write the block as BbB_b bits. Allocated bits per file are a=Bb⌈d/Bb⌉a=B_b\lceil d/B_b\rceil. Three files of 1000 B1000\,\mathrm B with 4096 B4096\,\mathrm B blocks therefore occupy 12288 B12288\,\mathrm B in this model, rather than one block for the combined logical total. The logical conversion remains separate. Compression, sparse files, metadata and shared blocks require additional information that this simple model does not infer.
How are usable capacity and the number of files that fit calculated?
For an entered capacity CC and reserved percentage rr, usable capacity is Cu=C(1−r/100)C_u=C(1-r/100). The comparison uses the batch’s allocated requirement when allocation is enabled, otherwise its logical requirement. Whole-file fit is ⌊Cu/a⌋\lfloor C_u/a\rfloor for a positive selected per-file cost aa. The floor is evaluated exactly before display rounding. A fully reserved capacity has zero usable space. A zero-size model has no finite count bound; actual filesystem file-count and metadata limits are separate information.
Do exact ratios, table filters and downloads change the calculation?
No. Significant figures and table filters control presentation. Rational intermediate values, allocation ceilings and file-fit floors remain independent of rounded displays. Complete text and CSV retain every one of the forty-three unit rows, exact numerators and denominators, active input context and generated steps, including hidden sections. The printed report follows the visible choices. Exact ratios preserve the entered numerical model and defined factors; they do not improve an estimated file size or measure a device’s real usable capacity.
About This Tool

About this Data Storage Converter

The Toolarithm Data Storage Converter gives a stated amount of data a clear representation without silently changing the meaning of its prefix. It preserves the original decimal gigabyte to gibibyte example and all twelve original identifiers. The expanded catalog includes bits, bytes, a defined four-bit nibble, decimal prefixes through quetta and binary prefixes through quebi for both bits and bytes. Names, symbols and prefix families are explicit throughout the unit controls and conversion table. The visible common scope provides a manageable starting point, while complete exports retain every defined unit.

The calculation engine normalizes quantities through exact bit factors and retains reduced rational intermediate values. Display precision is separate from arithmetic, so very large integer amounts do not lose their defining digits merely because a native floating-point number would round them. A mathematical fractional bit or byte estimate remains fractional. When a file model is useful, a whole file count multiplies the selected logical size per file. Optional allocation applies a ceiling independently to each file using the entered whole-byte block size, and labels allocated total and slack separately from the logical conversion.

A separate capacity comparison accepts a known capacity and a manually selected reserved percentage. It compares the appropriate logical or allocated requirement against the resulting usable budget and reports remaining capacity or shortfall. A positive per-file cost supports an exact integer file-fit floor. Zero-size model files do not receive an invented finite file-count limit. These are transparent numerical assumptions rather than a scan of a drive or a prediction of every filesystem behavior. Compression, sparse allocation, metadata, shared blocks and device reservations require additional information.

Complete copying and CSV preserve active input context, exact certificates, all unit rows and hidden working. Share links carry validated active settings, and exact swapping loads the logical result as a single source while switching comparisons off. The printed report follows visible preferences and keeps long certificates available in the complete export. Defined conversion factors do not create additional measurement precision in an estimated file size or establish the real usable capacity of a device.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Conversion factors are normalized to canonical units and checked in both directions. Exact definitions and offset formulas are preferred over rounded lookup values.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

Keep building

Explore more unit converters

Converters