diff --git a/docs/datatypes/units.md b/docs/datatypes/units.md
index c7cb11e90..c63de0a78 100644
--- a/docs/datatypes/units.md
+++ b/docs/datatypes/units.md
@@ -88,9 +88,8 @@ var incorrect = math.unit('8.314 m^3 Pa / mol K');          // Unit 8.314 (m^3 P
 
 ## Calculations
 
-Basic operations `add`, `subtract`, `multiply`, `divide`, and `pow` can be performed
-on units. Trigonometric functions like `sin` support units with an angle as
-argument.
+The operations that support units are `add`, `subtract`, `multiply`, `divide`, `pow`, `abs`, `sqrt`, `square`, `cube`, and `sign`.
+Trigonometric functions like `cos` are also supported when the argument is an angle.
 
 ```js
 var a = math.unit(45, 'cm');        // Unit 450 mm
@@ -119,6 +118,22 @@ var q = math.eval('1 C');                    // 1 C
 var F = math.multiply(q, math.cross(v, B));  // [0 N, 0 N, -1 N]
 ```
 
+All arithmetic operators act on the value of the unit as it is represented in SI units.
+This may lead to surprising behavior when working with temperature scales like `celsius` (or `degC`) and `fahrenheit` (or `degF`).
+In general you should avoid calculations using `celsius` and `fahrenheit`. Rather, use `kelvin` (or `K`) and `rankine` (or `R`) instead.
+This example highlights some problems when using `celsius` and `fahrenheit` in calculations:
+
+```js
+var T_14F = math.unit('14 degF');          // Unit 14 degF (263.15 K)
+var T_28F = math.multiply(T1, 2);          // Unit 487.67 degF (526.3 K), not 28 degF
+
+var Tnegative = math.unit(-13, 'degF');    // Unit -13 degF (248.15 K)
+var Tpositive = math.abs(T1);              // Unit -13 degF (248.15 K), not 13 degF
+
+var Trate1 = math.eval('5 (degC/hour)');   // Unit 5 degC/hour
+var Trate2 = math.eval('(5 degC)/hour');   // Unit 278.15 degC/hour
+```
+
 The expression parser supports units too. This is described in the section about
 units on the page [Syntax](../expressions/syntax.md#units).
 
diff --git a/examples/units.js b/examples/units.js
index 72ba7fa21..db19d5ca0 100644
--- a/examples/units.js
+++ b/examples/units.js
@@ -61,7 +61,7 @@ console.log();
 console.log('compute speed of fluid flowing out of hole in a container');
 var g = math.unit('9.81 m / s^2');
 var h = math.unit('1 m');
-var v = math.pow(math.multiply(2, math.multiply(g, h)), 0.5);
+var v = math.pow(math.multiply(2, math.multiply(g, h)), 0.5); // Can also use math.sqrt
 console.log('g = ' + format(g));
 console.log('h = ' + format(h));
 console.log('v = (2 g h) ^ 0.5 = ' + format(v)); // 4.429... m / s
diff --git a/lib/function/arithmetic/abs.js b/lib/function/arithmetic/abs.js
index 8a483cc0c..1f24749f1 100644
--- a/lib/function/arithmetic/abs.js
+++ b/lib/function/arithmetic/abs.js
@@ -22,9 +22,9 @@ function factory (type, config, load, typed) {
    *
    *    sign
    *
-   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix} x
+   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x
    *            A number or matrix for which to get the absolute value
-   * @return {number | BigNumber | Fraction | Complex | Array | Matrix}
+   * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}
    *            Absolute value of `x`
    */
   var abs = typed('abs', {
@@ -60,6 +60,14 @@ function factory (type, config, load, typed) {
     'Array | Matrix': function (x) {
       // deep map collection, skip zeros since abs(0) = 0
       return deepMap(x, abs, true);
+    },
+
+    'Unit': function(x) {
+      // This gives correct, but unexpected, results for units with an offset.
+      // For example, abs(-283.15 degC) = -263.15 degC !!!
+      var ret = x.clone();
+      ret.value = Math.abs(ret.value);
+      return ret;
     }
   });
 
diff --git a/lib/function/arithmetic/cube.js b/lib/function/arithmetic/cube.js
index 90f01a31e..0c638abdd 100644
--- a/lib/function/arithmetic/cube.js
+++ b/lib/function/arithmetic/cube.js
@@ -26,8 +26,8 @@ function factory (type, config, load, typed) {
    *
    *    multiply, square, pow
    *
-   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix} x  Number for which to calculate the cube
-   * @return {number | BigNumber | Fraction | Complex | Array | Matrix} Cube of x
+   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x  Number for which to calculate the cube
+   * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} Cube of x
    */
   var cube = typed('cube', {
     'number': function (x) {
@@ -49,6 +49,10 @@ function factory (type, config, load, typed) {
     'Array | Matrix': function (x) {
       // deep map collection, skip zeros since cube(0) = 0
       return deepMap(x, cube, true);
+    },
+
+    'Unit': function(x) {
+      return x.pow(3);
     }
   });
 
diff --git a/lib/function/arithmetic/sign.js b/lib/function/arithmetic/sign.js
index d1b2b7bfc..2fd7f700d 100644
--- a/lib/function/arithmetic/sign.js
+++ b/lib/function/arithmetic/sign.js
@@ -29,9 +29,9 @@ function factory (type, config, load, typed) {
    *
    *    abs
    *
-   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix} x
+   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x
    *            The number for which to determine the sign
-   * @return {number | BigNumber | Fraction | Complex | Array | Matrix}e
+   * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}e
    *            The sign of `x`
    */
   var sign = typed('sign', {
@@ -53,6 +53,10 @@ function factory (type, config, load, typed) {
     'Array | Matrix': function (x) {
       // deep map collection, skip zeros since sign(0) = 0
       return deepMap(x, sign, true);
+    },
+
+    'Unit': function(x) {
+      return number.sign(x.value);
     }
   });
 
diff --git a/lib/function/arithmetic/sqrt.js b/lib/function/arithmetic/sqrt.js
index 5105701de..a86e5a0f1 100644
--- a/lib/function/arithmetic/sqrt.js
+++ b/lib/function/arithmetic/sqrt.js
@@ -22,9 +22,9 @@ function factory (type, config, load, typed) {
    *
    *    square, multiply
    *
-   * @param {number | BigNumber | Complex | Array | Matrix} x
+   * @param {number | BigNumber | Complex | Array | Matrix | Unit} x
    *            Value for which to calculate the square root.
-   * @return {number | BigNumber | Complex | Array | Matrix}
+   * @return {number | BigNumber | Complex | Array | Matrix | Unit}
    *            Returns the square root of `x`
    */
   var sqrt = typed('sqrt', {
@@ -45,7 +45,13 @@ function factory (type, config, load, typed) {
     'Array | Matrix': function (x) {
       // deep map collection, skip zeros since sqrt(0) = 0
       return deepMap(x, sqrt, true);
+    },
+
+    'Unit': function (x) {
+      // Someday will work for complex units when they are implemented
+      return x.pow(0.5);
     }
+
   });
 
   /**
diff --git a/lib/function/arithmetic/square.js b/lib/function/arithmetic/square.js
index c6b868df5..dafaf1a5f 100644
--- a/lib/function/arithmetic/square.js
+++ b/lib/function/arithmetic/square.js
@@ -24,9 +24,9 @@ function factory (type, config, load, typed) {
    *
    *    multiply, cube, sqrt, pow
    *
-   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix} x
+   * @param  {number | BigNumber | Fraction | Complex | Array | Matrix | Unit} x
    *            Number for which to calculate the square
-   * @return {number | BigNumber | Fraction | Complex | Array | Matrix}
+   * @return {number | BigNumber | Fraction | Complex | Array | Matrix | Unit}
    *            Squared value
    */
   var square = typed('square', {
@@ -52,6 +52,10 @@ function factory (type, config, load, typed) {
     'Array | Matrix': function (x) {
       // deep map collection, skip zeros since square(0) = 0
       return deepMap(x, square, true);
+    },
+
+    'Unit': function(x) {
+      return x.pow(2);
     }
   });
 
diff --git a/test/function/arithmetic/abs.test.js b/test/function/arithmetic/abs.test.js
index 67c698013..d4bfb279f 100644
--- a/test/function/arithmetic/abs.test.js
+++ b/test/function/arithmetic/abs.test.js
@@ -69,10 +69,13 @@ describe('abs', function () {
     assert.deepEqual(a1.valueOf(), [2,1,0,1,2])
   });
 
-  it('should throw an error with a measurment unit', function () {
-    assert.throws(function () {
-      math.abs(math.unit(5, 'km'));
-    });
+  it('should return the absolute value of a unit', function () {
+    var u = math.abs(math.unit('5 m'));
+    assert.equal(u.toString(), '5 m');
+    u = math.abs(math.unit('-5 m'));
+    assert.equal(u.toString(), '5 m');
+    u = math.abs(math.unit('-283.15 degC'));
+    assert.equal(u.toString(), '-263.15 degC');
   });
 
   it('should throw an error in case of invalid number of arguments', function() {
@@ -86,8 +89,8 @@ describe('abs', function () {
   });
 
   it('should LaTeX abs', function () {
-	  var expression = math.parse('abs(-1)');
-	  assert.equal(expression.toTex(),'\\left|-1\\right|');
+    var expression = math.parse('abs(-1)');
+    assert.equal(expression.toTex(),'\\left|-1\\right|');
   });
 
 });
diff --git a/test/function/arithmetic/cube.test.js b/test/function/arithmetic/cube.test.js
index fd520af56..f471e2ecc 100644
--- a/test/function/arithmetic/cube.test.js
+++ b/test/function/arithmetic/cube.test.js
@@ -43,12 +43,14 @@ describe('cube', function() {
     assert.deepEqual(cube(math.complex('2')), math.complex('8'));
   });
 
-  it('should throw an error with strings', function() {
-    assert.throws(function () {cube('text')});
+  it('should return the cube of a unit', function() {
+    assert.equal(cube(math.unit('4 cm')).toString(), '64 cm^3');
+    assert.equal(cube(math.unit('-2 cm')).toString(), '-8 cm^3');
+    assert.equal(cube(math.unit('0 cm')).toString(), '0 cm^3');
   });
 
-  it('should throw an error with units', function() {
-    assert.throws(function () {cube(unit('5cm'))});
+  it('should throw an error with strings', function() {
+    assert.throws(function () {cube('text')});
   });
 
   it('should throw an error if there\'s wrong number of args', function() {
diff --git a/test/function/arithmetic/sign.test.js b/test/function/arithmetic/sign.test.js
index 61d4ceaa3..c244202d3 100644
--- a/test/function/arithmetic/sign.test.js
+++ b/test/function/arithmetic/sign.test.js
@@ -39,8 +39,13 @@ describe('sign', function() {
     approx.deepEqual(math.sign(math.complex(2,-3)), math.complex(0.554700196225229, -0.832050294337844));
   });
 
-  it('should throw an error when used with a unit', function() {
-    assert.throws(function () { math.sign(math.unit('5cm')); });
+  it('should calculate the sign of a unit', function() {
+    assert.equal(math.sign(math.unit('5 cm')), 1);
+    assert.equal(math.sign(math.unit('-5 kg')), -1);
+    assert.equal(math.sign(math.unit('0 mol/s')), 0);
+    assert.equal(math.sign(math.unit('-283.15 degC')), -1);
+    assert.equal(math.sign(math.unit('-273.15 degC')), 0);
+    assert.equal(math.sign(math.unit('-263.15 degC')), 1);
   });
 
   it('should throw an error when used with a string', function() {
diff --git a/test/function/arithmetic/sqrt.test.js b/test/function/arithmetic/sqrt.test.js
index 2bb69f55e..e37ebdae4 100644
--- a/test/function/arithmetic/sqrt.test.js
+++ b/test/function/arithmetic/sqrt.test.js
@@ -64,10 +64,14 @@ describe('sqrt', function() {
     assert.deepEqual(sqrt(math.complex(1e10, 1e-10)), math.complex(1e5, 5e-16));
   });
 
-  it('should throw an error when used with a unit', function() {
-    assert.throws(function () {
-      sqrt(math.unit(5, 'km'));
-    });
+  it('should return the square root of a unit', function() {
+    assert.equal(sqrt(math.unit('25 m^2/s^2')).toString(), '5 m / s');
+    assert.equal(sqrt(math.unit('4 kg')).toString(), '2 kg^0.5');
+  });
+
+  it('should return NaN when computing the square root of a negative unit', function() {
+    // Update this when support for complex units is added
+    assert.equal(sqrt(math.unit('-25 m^2/s^2')).toString(), 'NaN m / s');
   });
 
   it('should throw an error when used with a string', function() {
diff --git a/test/function/arithmetic/square.test.js b/test/function/arithmetic/square.test.js
index ce77e62c6..52b2fe488 100644
--- a/test/function/arithmetic/square.test.js
+++ b/test/function/arithmetic/square.test.js
@@ -48,8 +48,10 @@ describe('square', function() {
     assert.deepEqual(square(math.complex('2')), math.complex('4'));
   });
 
-  it('should throw an error when used with a unit', function() {
-    assert.throws(function () {square(unit('5cm'))});
+  it('should return the square of a unit', function() {
+    assert.equal(square(math.unit('4 cm')).toString(), '16 cm^2');
+    assert.equal(square(math.unit('-2 cm')).toString(), '4 cm^2');
+    assert.equal(square(math.unit('0 cm')).toString(), '0 cm^2');
   });
 
   it('should throw an error when used with a string', function() {