SCSS unit conversion functions

unitconversion.scss

    // ========================================================== 
    // Unit Conversion
    // ========================================================== 
    // 
    // Functions:
    // ----------------------------------------------------------  
    // 
    //  NUMBER:
    //    
    //  isNaN($value)  - returns true or false if type-of($value)==number
    // 
    //  number($value) - returns a unitless number.
    // 
    //  int($value)    - returns a unitless integer. 
    // 
    //  uint($value)   - returns a unitless unsigned integer. 
    //
    // 
    //  UNITS: 
    // 
    //  px($value)     - converts a number or unit to px.
    //                     
    //  em($args...)   - converts a number or unit to em. 
    // 
    //                    To adjust for em compounds you can add
    //                    aditional arguments to calculate the 
    //                    visual em size. em(visual-size,....)
    //                               
    //                    Example:  em(2, 2em, 2em) => 0.5em
    //
    //  rem($value)    - converts a number or unit to rem. 
    // 
    //  pt($value)     - converts a number or unit to pt. 
    // 
    //  pc($value)     - converts a number or unit to pc. 
    // 
    //  in($value)     - converts a number or unit to in. 
    // 
    //  cm($value)     - converts a number or unit to cm. 
    //
    // 
    // PERCENTAGE:
    // 
    //  pct($value,$base:100)   - similar to precentage, but takes a base
    //                            value (100%) to be used for calculating 
    //                            the precent value returned
    //                            
    //                            Example:  pct(1,100)     => 1%   
    //                                      pct(1,1)       => 100%
    //                                      pct(50,250)    => 20%
    //                                      pct(10px,16px) => 62.5%
    //                                      pct(1em,16px)  => 100%
    //   
    // ANGLE:
    // 
    //  deg($value)     - converts a number or angle unit to deg.  
    // 
    //  grad($value)    - converts a number or angle unit to grad.
    //
    //  turn($value)    - converts a number or angle unit to turn.
    //
    //  rad($value)     - converts a number or angle unit to rad.  
    // 
    //
    // CONVERT:
    // 
    //  Allows conversion by based on unit parameter
    // 
    //  $unit:px !default;
    //  convert($unit,2em)  - converts 2ems to pixels.  
    //     
    // ========================================================== 
    // Unit Conversion Table
    // http://www.translatorscafe.com/cafe/units-converter/typography/
    //      1px = 0.0625pc;
    //      1px = 0.75pt;  
    //      1px = 0.010416667in;    
    //      1px = 0.264583333mm;
    //      1px = 0.026458333cm;
    //
    // Angles
    // http://www.w3.org/TR/css3-values/#angles
    //      Full circle = 360deg = 400grad =  1turn = 2πrad
    //      1deg =  1.111111111grad  (400/360)
    //      1deg =  0.002777778turn  (1/360)
    //      1deg =  0.017453293rad   (180/π) 
    // 
    // ==========================================================
    // Base font size in percent (http://pxtoem.com/)
    // - used when calculating em and rem
    $base-font-scale:100% !default;

    // Number 
    @function isNaN($val) { @return type-of($val)!=number; }
    @function number($val){ @return if(isNaN($val), null, if(unitless($val), $val, $val/($val*0+1))); }
    @function int($val){ 
        @if(isNaN($val)){ @return null; }
        $val:number($val); 
        @return if($val<0,ceil($val),floor($val)); 
    }
    @function uint($val){ @return if(isNaN($val), null, abs(int($val))); }   
    // Aliases  
    @function num($val){ @return number($val); }
    @function parseFloat($val) { @return number($val);} // Really a math thing
    @function parseInt($val) { @return int($val); }   // Really a math thing
    
    // Absolute lengths
    @function px($val){ @return unit-handler($val,0px); }
    @function pt($val){ @return unit-handler($val,0pt); }
    @function pc($val){ @return unit-handler($val,0pc); }
    @function in($val){ @return unit-handler($val,0in); }
    @function mm($val){ @return unit-handler($val,0mm); }
    @function cm($val){ @return unit-handler($val,0cm); }

    // Relative lengths using px as base
    @function rem($val) { @return 0rem + if(unitless($val), $val, number(px($val)) * 0.0625 * 100% / $base-font-scale); }
    @function em($args...){ 
        $val:nth($args,1);
        $em:0em  + if(unitless($val), $val, number(px($val)) * 0.0625 * 100% / $base-font-scale); 
        @for $i from 2 through length($args){ $em:$em / number(em(nth($args,$i))) }
        @return $em;
    }
    
    // Percent
    @function pct($val,$base:1){ @return if(isNaN($val), null, percentage(number(px($val))/number(px($base)))); }


    // Length unit handler
    @function unit-handler($val,$unit){
        @if($val==null or type-of($val)!=number){ @return null; }
        $u:unit($val);
        @if($u==rem or $u==em){ @return 0px + number($val) / 0.0625 * 100% / $base-font-scale }
        @return $unit + $val;
    }

    
    // Angle conversion using deg as base
    @function deg($val){
        @if(isNaN($val)){@return null;}
        $u:unit($val);
        $u:if($u==deg ,1,
           if($u==grad,1.111111111,
           if($u==turn,0.002777778, 
           if($u==rad, 0.017453293, 
           1))));
        @return number($val) / $u * 1deg;
    }
    @function grad($val){ @return if(isNaN($val),null,if(unitless($val),$val * 1grad,number(deg($val)) * 1.11111111grad)); } 
    @function turn($val){ @return if(isNaN($val),null,if(unitless($val),$val * 1turn,number(deg($val)) * 0.002777778turn)); } 
    @function rad($val) { @return if(isNaN($val),null,if(unitless($val),$val * 1rad ,number(deg($val)) * 0.017453293rad)); }
    
    // Convert using unit parameter
    @function convert($unit,$args...){
        @if($unit==number){ @return number($args...); }
        @if($unit==num) { @return num($args...); }
        @if($unit==int) { @return int($args...); }
        @if($unit==uint){ @return uint($args...);}
        @if($unit==px)  { @return px($args...);  }
        @if($unit==pt)  { @return pt($args...);  }
        @if($unit==pc)  { @return pc($args...);  }
        @if($unit==in)  { @return in($args...);  }
        @if($unit==mm)  { @return mm($args...);  }
        @if($unit==cm)  { @return cm($args...);  }
        @if($unit==em)  { @return em($args...);  }
        @if($unit==rem) { @return rem($args...); }
        @if($unit==pct) { @return pct($args...); }
        @if($unit==deg) { @return int($args...); }
        @if($unit==grad){ @return grad($args...);}
        @if($unit==turn){ @return turn($args...);}
        @if($unit==rad) { @return rad($args...); }
    }
    
    
    

Added

isNaN instead of null check
pct($value, $base:100) - base used as 100% to calculate the percentage eg. pct(50, 250) => 20%
$base-font-scale:100% !default - to allow other than 16px based em+rem values

$base-font-scale:62.5%;  // or pct(10px,16px); 
html {
    font-size:$base-font-scale;
}

body {
    font-size: 16px;        /* Fallback for IE8 */
    font-size: rem(16px);
    padding: 20px 10px;     /* Fallback for IE8 */
    padding: rem(20px) rem(10px);
}


// Output 
html { font-size: 62.5%; }
body { 
    font-size: 16px;        /* Fallback for IE8 */ 
    font-size: 1.6rem; 
    padding: 20px 10px;     /* Fallback for IE8 */ 
    padding: 2rem 1rem;  
}