diff --git a/lib/type/unit/Unit.js b/lib/type/unit/Unit.js
index b6f4a41c1..7035c2fd8 100644
--- a/lib/type/unit/Unit.js
+++ b/lib/type/unit/Unit.js
@@ -370,11 +370,13 @@ function factory (type, config, load, typed, math) {
       }
 
       // Replace the unit into the auto unit system
-      var baseDim = res.unit.base.key;
-      UNIT_SYSTEMS.auto[baseDim] = {
-        unit: res.unit,
-        prefix: res.prefix
-      };
+      if(res.unit.base) {
+        var baseDim = res.unit.base.key;
+        UNIT_SYSTEMS.auto[baseDim] = {
+          unit: res.unit,
+          prefix: res.prefix
+        };
+      }
     }
     
     // Has the string been entirely consumed?
@@ -538,6 +540,17 @@ function factory (type, config, load, typed, math) {
    * @private
    */
   function _findUnit(str) {
+  
+    // First, match units names exactly. For example, a user could define 'mm' as 10^-4 m, which is silly, but then we would want 'mm' to match the user-defined unit.
+    if(UNITS.hasOwnProperty(str)) {
+      var unit = UNITS[str];
+      var prefix = unit.prefixes[''];
+      return {
+        unit: unit,
+        prefix: prefix
+      }
+    }
+
     for (var name in UNITS) {
       if (UNITS.hasOwnProperty(name)) {
         if (endsWith(str, name)) {
@@ -2863,6 +2876,78 @@ function factory (type, config, load, typed, math) {
     }
   }
 
+  /**
+   * Create a user-defined unit and register it with the Unit type.
+   * Example: 
+   *  createUnit('knot', '0.514444444 m/s')
+   *  createUnit('acre', new Unit(43560, 'ft^2'))
+   *
+   * @param {string} name      The name of the new unit. Must be unique. Example: 'knot'
+   * @param {string, Unit} definition      Definition of the unit in terms of existing units. For example, '0.514444444 m / s'.
+   * @param {Object} options   (optional) An object containing any of the following properties:
+   *     prefixes {string} "none", "short", "long", "binary_short", or "binary_long". The default is "none".
+   *     aliases {Array} Array of strings. Example: ['knots', 'kt', 'kts']
+   *     offset {Numeric} An offset to apply when converting from the unit. For example, the offset for celsius is 273.15 and the offset for farhenheit is 459.67. Default is 0.
+   *
+   * @return {Unit} 
+   */
+  Unit.createUnit = function(name, definition, options) {
+    
+    if(typeof(name) !== 'string') {
+      throw new TypeError("createUnit expects first parameter to be of type 'string'");
+    }
+   
+    // Check collisions with existing units
+    if(UNITS.hasOwnProperty(name)) {
+      throw new Error("Cannot create unit '" + name + "': a unit with that name already exists");
+    }
+
+    // TODO: Validate name for collisions with other built-in functions (like abs or cos, for example), and for acceptable variable names. For example, '42' is probably not a valid unit. Nor is '%', since it is also an operator.
+
+    var defUnit;
+    if(typeof(definition) === 'string') {
+      defUnit = Unit.parse(definition);
+    }
+    else if(definition && definition.type === 'Unit') {
+      defUnit = definition.clone();
+    }
+    else {
+      throw new TypeError("createUnit expects second parameter to be of type 'string' or 'Unit'");
+    }
+
+    var prefixes = PREFIXES.NONE;
+    var aliases = [];
+    var offset = 0;
+    if(options) {
+      if(options.prefixes) {
+        prefixes = PREFIXES[options.prefixes.toUpperCase()] || PREFIXES.NONE;
+      }
+      aliases = options.aliases || [];
+      offset = options.offset || 0;
+    }
+
+    var newUnit = {
+      name: name,
+      value: defUnit.value,
+      dimensions: JSON.parse(JSON.stringify(defUnit.dimensions)),
+      prefixes: prefixes,
+      offset: offset
+    }
+    
+    Unit.UNITS[name] = newUnit;
+
+    for (var i=0; i<aliases.length; i++) {
+      var name = aliases[i];
+      var alias = Object.create(newUnit);
+      alias.name = name;
+      Unit.UNITS[name] = alias;
+    }
+
+    return new Unit(null, name);
+  };
+
+
+
   Unit.PREFIXES = PREFIXES;
   Unit.BASE_UNITS = BASE_UNITS;
   Unit.UNITS = UNITS;
diff --git a/lib/type/unit/function/createUnit.js b/lib/type/unit/function/createUnit.js
new file mode 100644
index 000000000..f614eba18
--- /dev/null
+++ b/lib/type/unit/function/createUnit.js
@@ -0,0 +1,39 @@
+'use strict';
+
+var deepMap = require('../../../utils/collection/deepMap');
+
+function factory (type, config, load, typed) {
+  /**
+   * Create a user-defined unit and register it with the Unit type.
+   *
+   * Syntax:
+   *
+   * math.createUnit(string, unit : string, [object])
+   *
+   * Example: 
+   *
+   *  math.createUnit('knot', '0.514444444 m/s', {aliases: ['knots', 'kt', 'kts]})
+   *
+   * @param {string} name      The name of the new unit. Must be unique. Example: 'knot'
+   * @param {string, Unit} definition      Definition of the unit in terms of existing units. For example, '0.514444444 m / s'.
+   * @param {Object} options   (optional) An object containing any of the following properties:
+   *     prefixes {string} "none", "short", "long", "binary_short", or "binary_long". The default is "none".
+   *     aliases {Array} Array of strings. Example: ['knots', 'kt', 'kts']
+   *     offset {Numeric} An offset to apply when converting from the unit. For example, the offset for celsius is 273.15. Default is 0.
+   *
+   * @return {Unit} The new unit
+   */
+  var createUnit = typed('createUnit', {
+    'string, Unit | string': function (name, def) {
+      return type.Unit.createUnit(name, def);
+    },
+    'string, Unit | string, Object': function (name, def, options) {
+      return type.Unit.createUnit(name, def, options);
+    }
+  });
+
+  return createUnit;
+}
+
+exports.name = 'createUnit';
+exports.factory = factory;
diff --git a/lib/type/unit/index.js b/lib/type/unit/index.js
index a567149bf..320847e61 100644
--- a/lib/type/unit/index.js
+++ b/lib/type/unit/index.js
@@ -5,6 +5,9 @@ module.exports = [
   // construction function
   require('./function/unit'),
 
+  // create new units
+  require('./function/createUnit'),
+
   // physical constants
   require('./physicalConstants')
 ];
diff --git a/test/type/unit/Unit.test.js b/test/type/unit/Unit.test.js
index 675c81ee3..1f083a37e 100644
--- a/test/type/unit/Unit.test.js
+++ b/test/type/unit/Unit.test.js
@@ -1040,4 +1040,60 @@ describe('Unit', function() {
       assert.equal(new Unit(1, 'eV')    .equals(new Unit(1.602176565e-19, 'J')), true);
     });
   });
+
+  describe('createUnit', function() {
+    it('should create a custom unit from a string definition', function() {
+      Unit.createUnit('widget', '5 kg bytes');
+      assert.equal(new Unit(1, 'widget').equals(new Unit(5, 'kg bytes')), true);
+      Unit.createUnit('woggle', '4 widget^2');
+      assert.equal(new Unit(1, 'woggle').equals(new Unit(4, 'widget^2')), true);
+      assert.equal(new Unit(2, 'woggle').equals(new Unit(200, 'kg^2 bytes^2')), true);
+    });
+
+    it('should create a custom unit from a Unit definition', function() {
+      var Unit1 = new Unit(5, 'N/woggle');
+      Unit.createUnit('gadget', Unit1);
+      assert.equal(new Unit(1, 'gadget').equals(new Unit(5, 'N/woggle')), true);
+    });
+
+    it('should return the new (value-less) unit', function() {
+      var Unit2 = new Unit(1000, 'N h kg^-2 bytes^-2');
+      var newUnit = Unit.createUnit('whimsy', '8 gadget hours');
+      assert.equal(Unit2.to(newUnit).toString(), '2500 whimsy');
+    });
+
+    it('should not override an existing unit', function() {
+      assert.throws(function () { Unit.createUnit('m', '1 kg'); }, /Cannot create unit .*: a unit with that name already exists/);
+      assert.throws(function () { Unit.createUnit('gadget', '1 kg'); }, /Cannot create unit .*: a unit with that name already exists/);
+    });
+
+    it('should throw an error for invalid parameters', function() {
+      assert.throws(function() { Unit.createUnit(); }, /createUnit expects first parameter/);
+      assert.throws(function() { Unit.createUnit(42); }, /createUnit expects first parameter/);
+      assert.throws(function() { Unit.createUnit('42'); }, /createUnit expects second parameter/);
+      assert.throws(function() { Unit.createUnit('42', 3.14); }, /createUnit expects second parameter/);
+    });
+
+    it('should apply the correct prefixes', function() {
+      Unit.createUnit('millizilch', '1e-3 m', {prefixes: 'long'});
+      assert.equal(new Unit(1e-6, 'millizilch').toString(), '1 micromillizilch');
+    });
+
+    it('should override prefixed built-in units', function() {
+      Unit.createUnit('mm', '1e-4 m', {prefixes: 'short'});   // User is being silly
+      assert.equal(new Unit(1e-3, 'mm').toString(), '1 mmm'); // Use the user's new definition
+      assert.equal(new Unit(1e-3, 'mm').to('m').format(4), '1e-7 m'); // Use the user's new definition
+    });
+
+    it('should create aliases', function() {
+      Unit.createUnit('knot', '0.51444444 m/s', {aliases:['knots', 'kts', 'kt']});
+      assert.equal(new Unit(1, 'knot').equals(new Unit(1, 'kts')), true);
+      assert.equal(new Unit(1, 'kt').equals(new Unit(1, 'knots')), true);
+    });
+
+    it('should apply offset correctly', function() {
+      Unit.createUnit('whatsit', '3.14 kN', {offset:2});
+      assert.equal(new Unit(1, 'whatsit').to('kN').toString(), '9.42 kN');
+    });
+  });
 });
diff --git a/test/type/unit/function/createUnit.test.js b/test/type/unit/function/createUnit.test.js
new file mode 100644
index 000000000..8caceaace
--- /dev/null
+++ b/test/type/unit/function/createUnit.test.js
@@ -0,0 +1,33 @@
+var assert = require('assert');
+var math = require('../../../../index');
+var createUnit = math.createUnit;
+var Unit = math.type.Unit;
+
+describe('createUnit', function() {
+
+  it('should create a unit', function () {
+    var u = createUnit('flibbity', '4 hogshead');
+    assert.equal(math.eval('2 flibbity to hogshead').toString(), '8 hogshead');
+  });
+
+  it('should accept a unit as second parameter', function () {
+    assert.equal(math.eval('50 in^2 to createUnit("bingo", 25 in^2)').toString(), '2 bingo');
+  });
+
+  it('should accept a unit as second parameter', function () {
+    assert.equal(math.eval('50 in^2 to createUnit("zingo", "25 in^2")').toString(), '2 zingo');
+  });
+
+  it('should return the created unit', function() {
+    assert.equal(math.eval('createUnit("giblet", "6 flibbity")').toString(), 'giblet');
+    assert.equal(math.eval('120 hogshead to createUnit("fliblet", "0.25 giblet")').format(4), '20 fliblet');
+  });
+
+  it('should accept options', function() {
+    math.eval('createUnit("whosit", 3.14 kN, {prefixes:"long"})');
+    assert.equal(math.eval('1e-9 whosit').toString(), '1 nanowhosit');
+
+    math.eval('createUnit("wheresit", 3.14 kN, {offset:2})');
+    assert.equal(math.eval('1 wheresit to kN').toString(), '9.42 kN');
+  });
+});