units_example.m

This function contains the unit conversion factors for metric and Imperial units. It demonstrates these concepts:

• Functions
• Structures
• Switch/case statements
• Defensive programming
• Help strings

In your coursework, you will encounter physical constants defined in metric, while working on a problem with givens that are Imperial.

Don’t let units be a barrier.

Instead, convert all your inputs to the same unit system, calculate your answer, and choose which units to use for your output. Using this function in homework for other classes will help you avoid unit conversion mistakes!

function U = units(sys)
% UNITS  Unit conversion factors
%   U = units('metric') generates conversion factors to metric.
%   U = units('imperial') generates conversion factors to imperial.
%
%   To apply units to numbers, multiply its conversion factor.
%   To convert to a different unit, divide by the conversion factor.
%
%   Example usage:
%   U = units('metric');
%   dist = 10*U.FT
%
%   dist = 
%
%        3.048
%
%   dist/U.IN
%
%   ans =
%        120
%
%   Here, a distance is input in feet and saved in the dist variable
%   in meters. Calculatiions and formulas can be applied to this
%   variable. To output a variable in a specific unit, divide by
%   that unit.
%
%   Source: <a href="matlab:
%   web('https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9')">
%   NIST Guide to the SI, Appendix B.9</a>
%
%   Author: Kip Hart
%   Last Modified: 23 FEB 2025
%
%   See also UNITS_EXAMPLE
%

    %% Load base units
    switch lower(sys)
        case 'metric'
            U = base_metric();
        case 'imperial'
            U = base_imperial();
        otherwise
            error('Unexpected input: %s', sys)
    end

    %% Additional Units
    U.G0     = 9.80665*U.M/U.S^2;
    U.LBM    = U.SLUG/(U.G0/(U.FT/U.S^2));

    %% Angle
    U.RAD    = 1;
    U.DEG    = pi*U.RAD/180;

    U.ARCMIN = U.DEG/60;
    U.ARCSEC = U.ARCMIN/60;

    %% Area
    U.ACRE   = (60*U.FT) * (660*U.FT);
    U.HA     = (100*U.M)^2;

    %% Electricity and Magnetism
    U.AMPERE = 1;
    U.MA     = 1e-3*U.AMPERE;
    U.C      = U.AMPERE*U.S;
    
    U.V      = U.KG*U.M^2/(U.S^2*U.C);
    U.OHM    = U.V/U.AMPERE;
    U.H      = U.OHM*U.S;
    U.F      = U.C/U.V;

    U.WB     = U.V*U.S;
    U.T      = U.WB/U.M^2;

    %% Energy and Work
    U.J       = U.KG*U.M^2/U.S^2;
    U.KJ      = 1000*U.J;
    U.ERG     = 1e-7*U.J;
    
    U.CAL_IT  = 4.1868*U.J;
    U.CAL_TH  = 4.184*U.J;
    U.KCAL_IT = 1000*U.CAL_IT;
    U.KCAL_TH = 1000*U.CAL_TH;

    C_WATER_IT = U.CAL_IT/(U.KG*U.K);
    C_WATER_TH = U.CAL_TH/(U.KG*U.K);
    U.BTU_IT  = C_WATER_IT*U.LBM*U.R;
    U.BTU_TH  = C_WATER_TH*U.LBM*U.R;
    U.BFS     = U.BTU_IT/(U.FT^2*U.S);  % Heat Flux

    U.EV       = 1.602177e-19*U.J;
    U.TON_TNT  = 1e9*U.CAL_TH;

    %% Force
    U.N        = U.KG*U.M/U.S^2;
    U.LBF      = U.SLUG*U.FT/U.S^2;

    U.DYNE     = 1e-5*U.N;
    U.KIP      = 1e3*U.LBF;

    %% Frequency
    U.HZ       = 2*pi*U.RAD/U.S;

    %% Length
    U.ANGSTROM = 1e-10*U.M;
    U.NM       = 1e-9*U.M;
    U.UM       = 1e-6*U.M;
    U.MM       = 1e-3*U.M;
    U.CM       = 1e-2*U.M;
    U.KM       = 1e3*U.M;

    U.IN       = U.FT/12;
    U.MIL      = 1e-3*U.IN;
    U.YD       = 3*U.FT;
    U.KFT      = 1000*U.FT;
    U.MI       = 5280*U.FT;
    U.NMILE    = 6076.11549*U.FT;

    U.AU       = 149597870700*U.M;
    U.PARSEC   = U.AU/tan(U.ARCSEC/U.RAD);

    %% Mass
    U.GRAM   = 1e-3*U.KG;
    U.MG     = 1e-6*U.KG;

    U.OZ     = U.LBM/16;

    %% Power
    U.W      = U.J/U.S;
    U.HP     = 33000*U.FT*U.LBF/(60*U.S);

    %% Pressure or Stress
    U.PA     = U.N/U.M^2;
    U.MBAR   = 1e2*U.PA;
    U.KPA    = 1e3*U.PA;
    U.BAR    = 1e5*U.PA;
    U.MPA    = 1e6*U.PA;
    U.GPA    = 1e9*U.PA;

    U.PSI    = U.LBF/U.IN^2;
    U.PSF    = U.LBF/U.FT^2;
    U.KSI    = U.KIP/U.IN^2;

    U.ATM    = 101325*U.PA;
    U.TORR   = U.ATM/760;
    U.MMHG   = 133.322387415*U.PA;
    U.INHG   = U.MMHG*(U.IN/U.MM);
    U.CMH20  = 98.0665*U.PA;
    U.INH20  = U.CMH20*(U.IN/U.CM);

    %% Time
    U.MS     = 1e-3*U.S;
    U.MIN    = 60*U.S;
    U.HR     = 60*U.MIN;
    U.DAY    = 24*U.HR;
    U.YR     = 365*U.DAY;
    U.DAY_SIDEREAL = 86164.09*U.S;
    U.YR_SIDEREAL  = 3.155815e7*U.S;

    %% Velocity
    U.KMH    = U.KM/U.HR;
    
    U.FPS    = U.FT/U.S;
    U.MPH    = U.MI/U.HR;
    U.KNOT   = U.NMILE/U.HR;

    U.RPM    = U.HZ/60;

    %% Viscosity
    U.POISE  = 0.1*U.PA*U.S;
    U.CP     = U.POISE/100;

    U.ST     = 1e-4*U.M^2/U.S;
    U.CST    = U.ST/100;

    %% Volume
    U.CC     = (U.CM)^3;
    U.ML     = U.CC;
    U.L      = 1000*U.ML;

    U.GAL    = 231*U.IN^3;
    U.BBL    = 42*U.GAL;
    U.QT     = U.GAL/4;
    U.PT     = U.QT/2;
    U.CUP    = U.PT/2;

    U.FLOZ   = U.GAL/128;
    U.TBSP   = U.FLOZ/2;
    U.TSP    = U.FLOZ/6;

end

function U = base_metric()
    U.KG     = 1;
    U.M      = 1;
    U.S      = 1;
    U.K      = 1;
    U.MOL    = 1;

    U.SLUG   = 14.59390*U.KG;
    U.FT     = 0.3048006*U.M;
    U.R      = 1.8*U.K;
    U.LBMOL  = 453.59237*U.MOL;
end

function U = base_imperial()
    U.SLUG   = 1;
    U.FT     = 1;
    U.S      = 1;
    U.R      = 1;
    U.LBMOL  = 1;

    U.KG   = U.SLUG/14.59390;
    U.M    = U.FT/0.3048006;
    U.K    = U.R/1.8;
    U.MOL  = U.LBMOL/453.59237;
end