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Units Conversion Toolbox

version 1.5 (106 KB) by

This toolbox attaches units to Matlab variables and enables unit conversion.

17 Ratings



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Editor's Note: This file was selected as MATLAB Central Pick of the Week

Have you ever needed to convert horse power to watts but can't remember the conversion factor? How many inches light travels in a microsecond? This toolbox is designed to make getting these answers much easier.

The "unit" statement attaches units to a variable. For example,
>> x=unit(2,'yards')
x =
     1.8288 m

returns the answer in International (SI) units. If you would rather have you answer in feet it can be converted to feet by

>> convert(x,'feet')
ans =
     6 feet

Variables created by the "unit" statement can operated on by these operators:

      Unary plus, Unary minus, +,-,*,.*,/,\,./,.\,^,.^,',.'
      and sqrt

Variables are also supported by triginometric,hyperbolic, and exponential functions and can be compared by

       ==, ~=, >, <, >=, and <=

Special plotting routines are available for plotting variables with units. These are:

      plot, semilogx, semilogy, and loglog

The toolbox appears in the html help screens and has "GettingStarted', "User Guide", and function help screens.

Just down load the tool box to the directory of you choice and set the Matlab path to include this directory. To verify operation, type

>> unit('yards')
ans =
     0.9144 m

If you get this result, you are all set!

Comments and Ratings (28)

Karan Gill

Units are now in MATLAB if you have Symbolic Math Toolbox. Try:

>> u = symunit;
>> x = 2*u.meter
x =

>> x = rewrite(x,u.ft)
x =

>> double(separateUnits(x))
ans =

See the tutorial:

Israel Vieira

Dear John,

There seems to be a issue with temperature conversion and operations, for example:
Trial>> c15 = unit(15, 'degC')
c15 =
     288.15 K
Trial>> c20 = unit(20, 'degC')
c20 =
     293.15 K
Trial>> dt = c20-c15
dt =
     5 K
Trial>> convert(dt, 'degC')
ans =
     -268.15 degC

I can see anyway to get the °C back.



My patchfile for the error when using units which have a non integer exponent

Index: unit.m
--- unit.m (revision 210)
+++ unit.m (working copy)
@@ -2023,21 +2023,18 @@
                    digstr=[digstr s(p+1)];
                    end %if
- % If we at least two characters the end and the next two
- % characters are digits, add them to the digit string and
- % advance the position pointer by two characters
- if p+2<=L && all(isstrprop(s(p+1:p+2),'digit'))
- digstr=[digstr s(p+1:p+2)];
- p=p+2;
- % If we are at least one character from the end and the
- % next character is a digit, add the character to the digit
- % string and advance the position pointer
- elseif p<L && isstrprop(s(p+1),'digit')
- digstr=[digstr s(p+1)];
- p=p+1;
- else
- error('Exponent in units string is not a proper number!')
- end %if
+% +++++++++++++++++++++ MOD BY FVA STARTS HERE +++++++++++++++++++++++++++++++
+ % Deterermine the length of the digstr
+ p_end = p;
+ while (p_end+1) <= L && (isstrprop(s(p_end+1),'digit') || s(p_end+1) == '.' )
+ p_end = p_end + 1;
+ end
+ digstr = s(p+1:p_end);
+ p = p_end;
+% +++++++++++++++++++++ MOD BY FVA STOPS HERE +++++++++++++++++++++++++++++++
                    % Convert the digit string to a number and multiply it by
                    % the increment in case the previous operator was a "/".
                    % Then set the increment back to zero

Dear John

There seems to be an issue with units which have non integer exponents.

Say I need the unit m/sqrt(Hz) (I actually want V/sqrt(Hz), but m/sqrt(Hz) makes my discussion easier ;-) )

>> unit('m')
ans =
     1 m

>> unit('Hz')
ans =
     1 1/s

(I modified the Hz unit btw, see comment below)

>> sqrt(unit('Hz'))
ans =
     1 1/s^0.5

All seems ok till this point, but:
>> unit('m')/sqrt(unit('Hz'))
ans =
     1 m

After some debugging it seems that the issue is in the simplifyFund routine which is called by the mrdivide routine. The simplifyFund looses the 0.5 exponent on s

Another example:

>> sqrt(unit('m'))^2
ans =

Is it possible to have a look at this?


Best regards

Seems to work well so far, except that I had to manually add psi, which is a pretty common unit.

Very clean, useful, and expandable implementation.
Small issue with:
unit('Hz') = 6.28319 1/s
it should be unit('Hz') = 1 1/s

convConstant.m needs to be updated to:

case {'hertz','Hz'} % frequency in hertz y=units2convFac(unit('1/second'));

I would be much more useful if we could have the option to store a value in any unit instead of stacking with primitive units.
For example, instead of:

unit(1,'ft') = 0.3048 m

it would be better if the result was not automatically converted, like:

unit(1,'ft') = 1 ft

Anyway, your structure is very good. Congratulations!


Erich (view profile)


Hz is converted to rad/s, because 'Hz' is the same as 'cycle/s' and a cycle is 2π radians. Since radians are unitless, the unit displays as '1/s'.

>> unit(2,'Hz')
ans =
     12.5664 1/s
>> 2*2*pi
ans =
>> unit(2,'rad/s')
ans =
     2 1/s
>> unit(2,'cycle/s')
ans =
     12.5664 1/s

Looks like an error?

>> unit(2,'Hz')
ans =
     12.5664 1/s

To be precise, this test case fails:

classdef UnitConversionTests < matlab.unittest.TestCase
    methods (Test)
        function convertMustNotEditOriginal(self)
            feet = unit(3.3, 'ft');
            meter = feet.convert('m');
            feet2 = meter.convert('ft');
            self.verifyEqual(, 'ft');
            self.verifyEqual(, 'm');
            self.assertEqual(, 'ft');
            self.verifyEqual(feet2.value, feet.value);

While this does work, a central part is misleading with bad code style:

% this example is obvious, convert changes the object
feet = unit('ft');
convert(feet, 'm');

% in this case, the feet object must not change, however, both feet and meter are identical then
feet = unit('ft');
meter = convert(feet, 'm');

Kurt Feigl

GREAT JOB! I use this code every day (at work). However, I found out (the hard way) that the symbol "g" does not denote "gram".

Instead, it "g" is coded as the gravitational acceleration on Earth as
unit(1,'g') = 9.80665 m/s^2

To get units of mass, I use:
unit(1,'gram') = 0.001 kg
Error using unit/convert (line 315)
Incompatible conversion! Fundamental units of kg/m^3 vs. 1/m^2/s^2

This issue led to the error message below:

density = unit(1000,'kg/m^3')

Error using unit/convert (line 315)
Incompatible conversion! Fundamental units of kg/m^3 vs. 1/m^2/s^2

Nick Dutton


I noticed that the conversion from eV to Joules is incorrect.

Line 104 of convConstant.m should read:


Besides this one error, very nice utility!


Sinan (view profile)

There is an error using units with offset.

test = unit('C');
answer = 2*(test+test);

answer should give result of
1096.6 = 2*(274.15+274.15);

I implemented the following to avoid this error.

In classdef unit in function U=unit(varargin) ...
  switch nargin
    case 2
     %find this line

if isa(varargin{1},'double') && isa(varargin{2},'char')
if U.hasBeenConverted == false
  U.offset = 0;

I hope this does not interfer with other functionalities, but my verifications showed no strange behaviour anymore.

Many thanks for your tool!
Best regards

Matthew M.

I've been thinking about incorporating this for a while, hemming and hawing. Tried it today, finally, and I'm sold. Great job.

I wish there were a way to match the display to the Command Window format setting - I generally like to display more significant digits than short g allows. But it appears that there's no easy way to retrieve the current command window display format (I'll bet Yair Altman could figure one out, but I couldn't). I know you can use the .value method to display it in the desired format, but that's sort of inelegant.

The workaround for me was to edit unit\display directly, changing the sprintf format from %g to %0.12g (I chose 12 rather arbitrarily).



Marco (view profile)

I cannot use this toolbox to find roots of polynomial using the roots function when coefficientes are unit-class type. I first have to define a isfinite function in the unit class, but then I have problems with the transpose and ctranspose function I am unable to solve myself. Can someone help?


Marco (view profile)

can you add this function to the unit class? Some formulas has absolute value in them, and I need to preserve units.

function C=abs(A)
C=A; C.value=abs(A.value);

Perfect :)


Collin (view profile)


Collin (view profile)

Great toolbox.

Ran into a small problem with non-dimensional unit's plus and minus (unit class with .name = ''). I fixed the problem by replacing all the

  if ==


    if strcmpi(,

as ''=='' is an empty matrix


John (view profile)

Thanks Erich, that works perfectly


Erich (view profile)

>> a= unit([1 2],'m')

Michael Katz


John (view profile)

This is a great toolbox to have handy but it seems to have problems with vectors and arrays of objects. For example, (I am running MATLAB 2010b):

>> a = [unit(1,'m') unit(2,'m')]
a =
??? Error using ==> plus
Too many input arguments.

Error in ==> unit>unit.display at 1827
                s=sprintf(' %g %s',x.value+x.offset,;

But when I change it to

>> a = [unit(1,'m') unit(2,'m')];

there is not issue. It seems the call to sprintf is having trouble with multiple inputs.
Overall this printing issue is not what concerns me, it is when I try to perform an operation on this array when I really run into trouble:

>> a * unit(1,'m')
??? Comma separated list must have exactly one item.

Error in ==> unit>unit.unit at 163
                    if U.hasBeenConverted

Error in ==> unit>unit.mtimes at 387

I was hoping to get back a <1x2 unit> where both values are now in m^2. I run some highly vectorized code and it was be great if this issue could be resolved, overall great toolbox. Thanks


Erich (view profile)

Very easy to work with units using this toolbox. Author quickly updated the files when R2011b introduced an incompatibility.


Erich (view profile)

In MATLAB R2011b I get:

>> Units(3, 'ft')
Error using Units
Error: File: Units.m Line: 1 Column: 10
Naming a class 'Units' is not allowed, because it is already a built-in class.



This update corrects the addition and subtraction of dimensionless quantities (previously reported an error) and also corrects the definition of a weber.


I made an omission on the last submission and no file (or the old file) was attached. This is the correct file!


This update was submitted and approved but did not end up in Matlab Central. Instead, the old one was there.


This program has been updated to resolve a problem that appeared in R2011b.
R2011B used "Units" as a built in function in a toolbox and does not check to see if you have the toolbox before throwing an error. "Units" has been renamed to "unit".

MATLAB Release
MATLAB 7.11 (R2010b)

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