diff --git a/CHANGELOG.md b/CHANGELOG.md
index 48052f6773..87d7e050ae 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -116,6 +116,7 @@ for their contributions to this release!
 
 **Bug Fixes:**
 - PIC:
+    - Fix missing euler number in ADK formula #4696
     - Fix incorrect assignment of Jz in 2d EmZ implementation #3892
     - Fix getExternalCellsTotal() to properly account for guard cells #4030
     - Fix incident field math around corners #4102
diff --git a/docs/source/models/field_ionization.rst b/docs/source/models/field_ionization.rst
index ac52a93eb5..9fb9e211ed 100644
--- a/docs/source/models/field_ionization.rst
+++ b/docs/source/models/field_ionization.rst
@@ -127,6 +127,7 @@ Leaving out the pre-factor distinguishes ``ADKCircPol`` from ``ADKLinPol``.
     .. attention::
 
         Be aware that :math:`Z` denotes the **residual ion charge** and not the proton number of the nucleus!
+        Be aware that :math:`e` in :math:`D` denotes Euler's number, not the elementary charge
 
 In the following comparison one can see the ``ADKLinPol`` ionization rates for the transition from Carbon II to III (meaning 1+ to 2+).
 For a reference the rates for Hydrogen as well as the barrier suppression field strengths :math:`F_\mathrm{BSI}` have been plotted.
diff --git a/include/picongpu/particles/ionization/byField/ADK/AlgorithmADK.hpp b/include/picongpu/particles/ionization/byField/ADK/AlgorithmADK.hpp
index 55a07008f7..e2355ab440 100644
--- a/include/picongpu/particles/ionization/byField/ADK/AlgorithmADK.hpp
+++ b/include/picongpu/particles/ionization/byField/ADK/AlgorithmADK.hpp
@@ -1,4 +1,4 @@
-/* Copyright 2015-2023 Marco Garten, Jakob Trojok
+/* Copyright 2015-2023 Marco Garten, Jakob Trojok, Brian Marre
  *
  * This file is part of PIConGPU.
  *
@@ -93,7 +93,8 @@ namespace picongpu
                         /* effective principal quantum number (unitless) */
                         float_X const nEff = effectiveCharge / math::sqrt(float_X(2.0) * iEnergy);
                         /* nameless variable for convenience dFromADK*/
-                        float_X const dBase = float_X(4.0) * util::cube(effectiveCharge) / (eInAU * util::quad(nEff));
+                        float_X const dBase = float_X(4.0) * math::exp(1._X) * util::cube(effectiveCharge)
+                            / (eInAU * util::quad(nEff));
                         float_X const dFromADK = math::pow(dBase, nEff);
 
                         /* ionization rate (for CIRCULAR polarization)*/
diff --git a/lib/python/picongpu/extra/utils/field_ionization.py b/lib/python/picongpu/extra/utils/field_ionization.py
index 3c71fbf618..1abba9fb34 100755
--- a/lib/python/picongpu/extra/utils/field_ionization.py
+++ b/lib/python/picongpu/extra/utils/field_ionization.py
@@ -2,7 +2,7 @@
 
 This file is part of the PIConGPU.
 Copyright 2019-2023 PIConGPU contributors
-Authors: Marco Garten
+Authors: Marco Garten, Brian Marre
 License: GPLv3+
 """
 
@@ -93,7 +93,7 @@ def ADKRate(self,
                 )
 
         nEff = np.float64(self.n_eff(Z, E_Ip))
-        D = ((4. * Z**3.) / (F * nEff**4.))**nEff
+        D = ((4. * np.exp(1.) * Z**3.) / (F * nEff**4.))**nEff
 
         rate = (F * D**2.) / (8. * np.pi * Z) \
             * np.exp(-(2. * Z**3.) / (3. * nEff**3. * F))