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Number to Scientific Prefix

version 3.2.0 (18.3 KB) by Stephen Cobeldick
Convert a numeric value to an metric prefixed string (SI/engineering). Bonus: binary prefixes!


Updated 25 Jun 2020

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The function NUM2SIP converts a numeric scalar into a string with a metric prefix (aka SI prefix, or engineering prefix). For example the value 1000 is converted to '1 k'.

After testing the metric-prefix submissions on MATLAB FEX (see Acknowledgements) and not finding a single one that converted all values correctly and that supported the correct SI spacing, I wrote my own functions. And then exhaustively tested them to confirm that they actually give the correct output.

These functions are particularly useful to help create publications following SI standards, or where control over significant digits and trailing zeros is required, or for including numeric values in figures.

This submission:
* Always includes the space character (required by the SI standard).
* Automatically selects the most suitable prefix.
* Rounds to the requested significant figures (default==5).
* Prefix may be selected as either the full name ('kilo') or the symbol ('k').
* Trailing decimal zeros of the coefficient may be included or removed.
* Rounds up to the next prefix when significant figures require, e.g. '1 M', not '1000 k'.
* Uses simple integer even if precision is less than three (no exponent).

### Bonus Functions ###

The function NUM2BIP converts from numeric to binary-prefixed string, for example the value 1024 is converted to '1 Ki'.

The function NUM2RKM converts from numeric to RKM code, for example the value 1200 is converted to '1k2'.

### Reverse Conversion ###

To convert from metric-prefixed string to numeric:


### Metric Prefix Examples ###

>> num2sip(10000) OR num2sip(1e4)
ans = '10 k'
>> num2sip(10000,4,true)
ans = '10 kilo'
>> num2sip(10000,4,false,true)
ans = '10.00 k'

>> num2sip(999,3)
ans = '999 '
>> num2sip(999,2)
ans = '1 k'

>> num2sip(0.5e6)
ans = '500 k'
>> num2sip(0.5e6,[],'M')
ans = '0.5 M'

>> ['Power: ',num2sip(200e6,[],true),'watt']
ans = 'Power: 200 megawatt'

>> sprintf('Clock frequency is %shertz.',num2sip(1234567890,3,true))
ans = 'Clock frequency is 1.23 gigahertz.'

>> num2sip(sip2num('9 T')) % 9 tera == 9e12 == 9*1000^4
ans = '9 T'

### Binary Prefix Examples ###

>> num2bip(10240) OR num2bip(1.024e4) OR num2bip(pow2(10,10)) OR num2bip(10*2^10)
ans = '10 Ki'
>> num2bip(10240,4,true)
ans = '10 kibi'
>> num2bip(10240,4,false,true)
ans = '10.00 Ki'

>> num2bip(1023,3)
ans = '1020 '
>> num2bip(1023,2)
ans = '1 Ki'

>> num2bip(pow2(19))
ans = '512 Ki'
>> num2bip(pow2(19),[],'Mi')
ans = '0.5 Mi'

>> ['Memory: ',num2bip(pow2(200,20),[],true),'byte']
ans = 'Memory: 200 mebibyte'

>> sprintf('Data saved in %sbytes.',num2bip(1234567890,3,true))
ans = 'Data saved in 1.15 gibibytes.'

>> num2bip(bip2num('9 Ti')) % 9 tebi == pow2(9,40) == 9*1024^4
ans = '9 Ti'

### Metric Prefixes ###

Magnitude | Symbol / Name
1000^-8 | y / yocto
1000^-7 | z / zepto
1000^-6 | a / atto
1000^-5 | f / femto
1000^-4 | p / pico
1000^-3 | n / nano
1000^-2 | µ / micro
1000^-1 | m / milli
1000^0 |
1000^1 | k / kilo
1000^2 | M / mega
1000^3 | G / giga
1000^4 | T / tera
1000^5 | P / peta
1000^6 | E / exa
1000^7 | Z / zetta
1000^8 | Y / yotta

### Binary Prefixes (IEC 60027-2 A.2 and ISO/IEC 80000-13:2008) ###

Magnitude | Symbol / Name
1024^0 |
1024^1 | Ki / kibi
1024^2 | Mi / mebi
1024^3 | Gi / gibi
1024^4 | Ti / tebi
1024^5 | Pi / pebi
1024^6 | Ei / exbi
1024^7 | Zi / zebi
1024^8 | Yi / yobi

### Notes ###

These functions have been extensively tested against many edge cases, with particular attention to ensuring the correct rounding for all choices of significant figures. Compared to similar submissions available on MATLAB File Exchange, these functions correctly:
* include the space character between the coefficient and the prefix, even if there is no prefix (try 1).
* round to the requested significant figures (try 0.999 or 999e3, with 1 or 2 significant figures).
* return a coefficient without a prefix for zero and values outside the prefix range (try 0, Inf, 1E30).
* return a coefficient without an exponent when the significant digits are less than three (try 1e5 to 1 sigfig).

Cite As

Stephen Cobeldick (2020). Number to Scientific Prefix (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (10)


@Collin Pecora: a little bit late, but I changed the default "micro" symbol to 'µ', i.e. char(181). The Mfile can be edited to use 'u' if required.


nevermind.... you already have the inverse functionality integrated in another function. ta


Hi Stephen, I'd love to see an option or another function where you do the exact inverse. --> 1ms --> 0.001s. Basically make a 'remove scientific prefix'


Hi @Stephen Cobeldick - I've been trying to get hold of you but I've not been able to find any contact info anywhere. I recently submitted my own num2eng function; if I'd found your num2sip before I'd pretty much finished my version I'm sure I wouldn't have bothered writing it! As it is though, I was already using my own function in a number of other projects so it made sense to stick with mine. Your submission did help me make some final improvements though. My email can be found in the comment box of my submitted file. Please drop me a line if you feel so inclined.

@Collin Pecora. Thank you for your feedback. The function returns 'u' because I wanted to stick to ASCII characters only, as different file formats and character encoding are not always compatible. You can easily edit the file or use |strrep| to get the result that you want.

Very helpfull.
Could chage micro 'u' to char(181) in your prefix cell array



* Add second output argument that indicates if a prefix is used or not.
* Add bonus function NUM2RKM.


* More test cases.
* More robust whitespace handling.


* Update documentation.
* Default non-breaking space.


* Improve documentation.


* Return micro character 'µ' (rather than 'u').


* Improve documentation.

* Add "fixed" prefix input option.
* Rewrite algorithm to use local functions.

* Add HTML documentation.
* Empty inputs use default values.

* Split subimssion into two: one for num->str, other for str->num.
* Rename all functions.

- Improve handling of trailing zeros.
- Improve input checking.

- Default is now lower-case E-notation.

- Add control over allowing trailing zeros in string.
- Convert all string coefficients into numeric (not just the first one).
- Return split string parts as a cell array.

- Edit the help section a little.

- Str->Num: space character between coefficient and prefix is optional.
- Str->Num: NaN and Inf may occur with prefixes.
- Help: Simplify prefix tables.

Upload all four functions for converting between numeric and string, for both SI and binary.

- Fix edge case (val=1).

- Allow positive/negative input value.
- Consistent handling of Inf/NaN values.

Provide useage examples.

Edit file description to be more accurate.

MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
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