diff --git a/Framework/PythonInterface/plugins/functions/ChudleyElliot.py b/Framework/PythonInterface/plugins/functions/ChudleyElliot.py
index 792f7f4c16a979dc006fb91ff3bc08b756ddbf13..4a72abd2e7399d0c209d664b7ecdca896e288b45 100644
--- a/Framework/PythonInterface/plugins/functions/ChudleyElliot.py
+++ b/Framework/PythonInterface/plugins/functions/ChudleyElliot.py
@@ -24,13 +24,16 @@ File change history is stored at: <https://github.com/mantidproject/mantid>
 Code Documentation is available at: <http://doxygen.mantidproject.org>
 '''
 from __future__ import (absolute_import, division, print_function)
-import math
 import numpy as np
 from mantid.api import IFunction1D, FunctionFactory
+from scipy import constants
 
 
 class ChudleyElliot(IFunction1D):
 
+    planck_constant = constants.Planck / constants.e * 1E15  # meV*psec
+    hbar = planck_constant / (2 * np.pi)  # meV * ps  = ueV * ns
+
     def category(self):
         return "QuasiElastic"
 
@@ -42,23 +45,13 @@ class ChudleyElliot(IFunction1D):
     def function1D(self, xvals):
         tau = self.getParameterValue("Tau")
         length = self.getParameterValue("L")
-
         xvals = np.array(xvals)
-        hwhm = (1.0 - np.sin(xvals * length) / (xvals * length)) / tau
+        with np.errstate(divide='ignore'):
+            hwhm = self.hbar*(1.0 - np.sin(xvals * length)
+                              / (xvals * length))/tau
 
         return hwhm
 
-    def functionDeriv1D(self, xvals, jacobian):
-        tau = self.getParameterValue("Tau")
-        length = self.getParameterValue("L")
-        i = 0
-        for x in xvals:
-            s = math.sin(x*length)/(x*length)
-            h = (1.0-s)/tau
-            jacobian.set(i,0,-h/tau)
-            jacobian.set(i,1,(math.cos(x*length)-s)/(length*tau))
-            i += 1
-
 
 # Required to have Mantid recognise the new function
 FunctionFactory.subscribe(ChudleyElliot)
diff --git a/Framework/PythonInterface/test/python/plugins/functions/ChudleyElliotTest.py b/Framework/PythonInterface/test/python/plugins/functions/ChudleyElliotTest.py
new file mode 100644
index 0000000000000000000000000000000000000000..1e858ccf23d60acc9796254835da5c3449bd50e8
--- /dev/null
+++ b/Framework/PythonInterface/test/python/plugins/functions/ChudleyElliotTest.py
@@ -0,0 +1,35 @@
+from __future__ import (absolute_import, division, print_function)
+
+import unittest
+import numpy as np
+
+from MsdTestHelper import (is_registered, check_output, do_a_fit)
+
+
+class ChudleyElliotTest(unittest.TestCase):
+
+    def test_function_has_been_registered(self):
+        status, msg = is_registered("ChudleyElliot")
+        if not status:
+            self.fail(msg)
+
+    def test_function_output(self):
+        input = [0.01, 0.1, 1.0, 10.0]
+        expected = [4.52422472e-05, 4.51112743e-03,
+                    3.37001059e-01, 4.78915177e-01]
+        tolerance = 1.0e-04
+        status, output = check_output("ChudleyElliot", input, expected,
+                                      tolerance, Tau=1.42, L=2.42)
+        if not status:
+            msg = 'Computed output {} from input {} unequal to expected: {}'
+            self.fail(msg.format(*[str(a) for a in (output, input, expected)]))
+
+    @staticmethod
+    def test_do_fit():
+        do_a_fit(np.asarray([0.01, 0.1, 1.0, 10.0]), 'ChudleyElliot',
+                 guess=dict(Tau=1.0, L=1.0),
+                 target=dict(Tau=1.42, L=2.42), atol=0.01)
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/Testing/SystemTests/tests/analysis/ISISIndirectBayesTest.py b/Testing/SystemTests/tests/analysis/ISISIndirectBayesTest.py
index 687464ba1d4cad0a7ddeaba17d8b34e899d66ad0..4295810502f47b3a3192806be049530b3fb85afb 100644
--- a/Testing/SystemTests/tests/analysis/ISISIndirectBayesTest.py
+++ b/Testing/SystemTests/tests/analysis/ISISIndirectBayesTest.py
@@ -369,7 +369,7 @@ class JumpCETest(JumpFitFunctionTestBase):
     def __init__(self):
         JumpFitFunctionTestBase.__init__(self)
 
-        self._function = 'name=ChudleyElliot,Tau=3.31,L=1.42'
+        self._function = 'name=ChudleyElliot,Tau=1.42,L=2.42'
         self.tolerance = 5e-3
 
     def get_reference_files(self):
diff --git a/Testing/SystemTests/tests/analysis/reference/ISISIndirectBayes_JumpCETest.nxs.md5 b/Testing/SystemTests/tests/analysis/reference/ISISIndirectBayes_JumpCETest.nxs.md5
index 4b36586a486a363b41d76818d1604300fb34e648..d4c89bf40a19e1c9d961d7df1a3b11a674a3d5b9 100644
--- a/Testing/SystemTests/tests/analysis/reference/ISISIndirectBayes_JumpCETest.nxs.md5
+++ b/Testing/SystemTests/tests/analysis/reference/ISISIndirectBayes_JumpCETest.nxs.md5
@@ -1 +1 @@
-98fbf74ea7914ee4bce2a6e032d823f5
\ No newline at end of file
+150dd41d09950d0fd0073cae136ce6cf
diff --git a/docs/source/fitting/fitfunctions/ChudleyElliot.rst b/docs/source/fitting/fitfunctions/ChudleyElliot.rst
index 228945d1e1ae2560ccc37a424a9c2617794f663d..b865f3547509169501e2716777e5b8ace3a51df8 100644
--- a/docs/source/fitting/fitfunctions/ChudleyElliot.rst
+++ b/docs/source/fitting/fitfunctions/ChudleyElliot.rst
@@ -15,7 +15,13 @@ associated long range diffusive motions of molecules.
 
 The Chudley-Elliot Jump diffusion model [1]_ has the form:
 
-.. math:: Gamma(Q) = (1 - sin(Ql)/Ql)/tau
+.. math:: HWHM(Q) = \frac{\hbar}{\tau} \cdot \frac{1 - sin(Ql)}{Ql}
+
+Units of :math:`l` are inverse units of :math:`Q`.
+
+Units of :math:`HWHM` are :math:`meV` if units of :math:`\tau` are *ps*.
+Alternatively, units of :math:`HWHM` are :math:`\mu eV` if units of
+:math:`\tau` are *ns*.
 
 .. attributes::
 
diff --git a/docs/source/release/v3.14.0/framework.rst b/docs/source/release/v3.14.0/framework.rst
index 4c29021bfc9c8c4f50ec2810217a59275331ac2f..8c56a7797cc0f8ac5e88dc9626ba659b94269e31 100644
--- a/docs/source/release/v3.14.0/framework.rst
+++ b/docs/source/release/v3.14.0/framework.rst
@@ -36,7 +36,7 @@ Algorithms
 
 
 New Algorithms
-**************
+##############
 
 
 
@@ -59,10 +59,12 @@ New
 Improvements
 ############
 
-
+- :ref:`ChudleyElliot <func-ChudleyElliot>` includes hbar in the definition
 
 Bugfixes
 ########
 
 
 :ref:`Release 3.14.0 <v3.14.0>`
+
+