diff --git a/src/base/serialiser.h b/src/base/serialiser.h
index c1efe6ac1d..e77fca1082 100644
--- a/src/base/serialiser.h
+++ b/src/base/serialiser.h
@@ -54,6 +54,14 @@ class Serialisable
 
         return false;
     }
+    // Place the named value into the supplied object, but only if it exists
+    template <typename T, typename U> bool getIfPresent(const SerialisedValue &node, std::string name, U &destination)
+    {
+        if (!node.contains(name))
+            return false;
+        destination = toml::find<T>(node, name);
+        return true;
+    }
     // A helper function to add elements of a vector to a node under the named heading
     template <serialisablePointer T>
     static void fromVectorToTable(const std::vector<T> &vector, std::string name, SerialisedValue &node)
@@ -176,14 +184,14 @@ class Serialisable
         SerialisedValue result;
         for (auto &[key, value] : map)
             if constexpr (serialisablePointer<V>)
-                value->serialise(std::string(key), result);
+                value->serialise(std::format("{}", key), result);
             else if constexpr (std::is_base_of_v<Serialisable, V>)
-                value.serialise(key, result);
+                value.serialise(std::format("{}", key), result);
             else
                 // We use the direct value (with casting) instead of
                 // value.serialise() to handle the case where the value
                 // is a raw type (e.g. int)
-                result[std::string(key)] = value;
+                result[std::format("{}", key)] = value;
         if (!map.empty())
             node[name] = result;
     }
diff --git a/src/math/data3D.cpp b/src/math/data3D.cpp
index 4c3f84a376..0e54800132 100644
--- a/src/math/data3D.cpp
+++ b/src/math/data3D.cpp
@@ -440,3 +440,30 @@ bool Data3D::serialise(LineParser &parser) const
 
     return true;
 }
+
+// Express as a serialisable value
+void Data3D::serialise(std::string tag, SerialisedValue &target) const
+{
+    target[tag] = {{"tag", tag_}, {"x", x_}, {"y", y_}, {"z", z_}, {"values", values_.linearArray()}};
+    if (hasError_)
+        target[tag]["errors"] = errors_.linearArray();
+}
+
+// Read values from a serialisable value
+void Data3D::deserialise(const SerialisedValue &node)
+{
+    tag_ = toml::find<std::string>(node, "tag");
+    x_ = toml::find<std::vector<double>>(node, "x");
+    y_ = toml::find<std::vector<double>>(node, "y");
+    z_ = toml::find<std::vector<double>>(node, "z");
+    values_.initialise(x_.size(), y_.size(), z_.size());
+    values_.linearArray() = toml::find<std::vector<double>>(node, "values");
+
+    Serialisable::optionalOn(node, "errors",
+                             [this](const auto errors)
+                             {
+                                 hasError_ = true;
+                                 errors_.initialise(x_.size(), y_.size(), z_.size());
+                                 errors_.linearArray() = toml::get<std::vector<double>>(errors);
+                             });
+}
diff --git a/src/math/data3D.h b/src/math/data3D.h
index f9bb4c98b1..404ecb285a 100644
--- a/src/math/data3D.h
+++ b/src/math/data3D.h
@@ -11,7 +11,7 @@
 class Histogram3D;
 
 // One-Dimensional Data
-class Data3D : public Data3DBase
+class Data3D : public Data3DBase, public Serialisable
 {
     public:
     Data3D();
@@ -122,4 +122,8 @@ class Data3D : public Data3DBase
     bool deserialise(LineParser &parser);
     // Write data through specified LineParser
     bool serialise(LineParser &parser) const;
+    // Express as a serialisable value
+    void serialise(std::string tag, SerialisedValue &target) const override;
+    // Read values from a serialisable value
+    void deserialise(const SerialisedValue &node) override;
 };
diff --git a/src/math/histogram2D.cpp b/src/math/histogram2D.cpp
index b29f86ec6d..528ecabd23 100644
--- a/src/math/histogram2D.cpp
+++ b/src/math/histogram2D.cpp
@@ -43,6 +43,22 @@ void Histogram2D::clear()
  * Data
  */
 
+// Update accumulated data
+void Histogram2D::updateAccumulatedData()
+{
+    // Set up arrays
+    accumulatedData_.initialise(bins_.size(), true);
+
+    // Store bin centres and accumulated averages in the object
+    for (auto n = 0; n < bins_.size(); ++n)
+    {
+        accumulatedData_.xAxis(n) = xBinCentres_[n];
+        accumulatedData_.yAxis(n) = yBinCentres_[n];
+        accumulatedData_.values().linearArray()[n] = averages_[n];
+        accumulatedData_.errors().linearArray()[n] = averages_[n].stDev();
+    }
+}
+
 // Initialise with specified bin range
 void Histogram2D::initialise(double xMin, double xMax, double xBinWidth, double yMin, double yMax, double yBinWidth)
 {
@@ -244,3 +260,28 @@ bool Histogram2D::serialise(LineParser &parser) const
 
     return true;
 }
+
+// Express as a serialisable value
+void Histogram2D::serialise(std::string tag, SerialisedValue &target) const
+{
+    target[tag] = {{"xMinimum", xMinimum_}, {"xMaximum", xMaximum_}, {"xBinWidth", xBinWidth_},
+                   {"yMinimum", yMinimum_}, {"yMaximum", yMaximum_}, {"yBinWidth", yBinWidth_},
+                   {"nBinned", nBinned_},   {"nMissed", nMissed_},   {"averages", averages_.linearArray()}};
+}
+
+// Read values from a serialisable value
+void Histogram2D::deserialise(const SerialisedValue &node)
+{
+    clear();
+
+    initialise(toml::find<double>(node, "xMinimum"), toml::find<double>(node, "xMaximum"),
+               toml::find<double>(node, "yBinWidth"), toml::find<double>(node, "yMinimum"),
+               toml::find<double>(node, "yMaximum"), toml::find<double>(node, "yBinWidth"));
+
+    nBinned_ = toml::find<long>(node, "nBinned");
+    nMissed_ = toml::find<long>(node, "nMissed");
+
+    averages_.linearArray() = toml::find<std::vector<SampledDouble>>(node, "averages");
+
+    updateAccumulatedData();
+}
\ No newline at end of file
diff --git a/src/math/histogram2D.h b/src/math/histogram2D.h
index 81072a8e64..98106b9888 100644
--- a/src/math/histogram2D.h
+++ b/src/math/histogram2D.h
@@ -8,7 +8,7 @@
 #include "templates/array2D.h"
 
 // Two-Dimensional Histogram
-class Histogram2D
+class Histogram2D : public Serialisable
 {
     public:
     Histogram2D();
@@ -53,6 +53,10 @@ class Histogram2D
     // Accumulated data
     Data2D accumulatedData_;
 
+    private:
+    // Update accumulated data
+    void updateAccumulatedData();
+
     public:
     // Initialise with specified bin range
     void initialise(double xMinimum, double xMaximum, double xBinWidth, double yMinimum, double yMaximum, double yBinWidth);
@@ -105,4 +109,8 @@ class Histogram2D
     bool deserialise(LineParser &parser);
     // Write data through specified LineParser
     bool serialise(LineParser &parser) const;
+    // Express as a serialisable value
+    void serialise(std::string tag, SerialisedValue &target) const override;
+    // Read values from a serialisable value
+    void deserialise(const SerialisedValue &node) override;
 };
diff --git a/src/math/histogram3D.cpp b/src/math/histogram3D.cpp
index 713c01b241..d2f8761517 100644
--- a/src/math/histogram3D.cpp
+++ b/src/math/histogram3D.cpp
@@ -278,3 +278,30 @@ bool Histogram3D::serialise(LineParser &parser) const
 
     return true;
 }
+
+// Express as a serialisable value
+void Histogram3D::serialise(std::string tag, SerialisedValue &target) const
+{
+    target[tag] = {{"xMinimum", xMinimum_}, {"xMaximum", xMaximum_}, {"xBinWidth", xBinWidth_},
+                   {"yMinimum", yMinimum_}, {"yMaximum", yMaximum_}, {"yBinWidth", yBinWidth_},
+                   {"zMinimum", zMinimum_}, {"zMaximum", zMaximum_}, {"zBinWidth", zBinWidth_},
+                   {"nBinned", nBinned_},   {"nMissed", nMissed_},   {"averages", averages_.linearArray()}};
+}
+
+// Read values from a serialisable value
+void Histogram3D::deserialise(const SerialisedValue &node)
+{
+    clear();
+
+    initialise(
+        toml::find<double>(node, "xMinimum"), toml::find<double>(node, "xMaximum"), toml::find<double>(node, "yBinWidth"),
+        toml::find<double>(node, "yMinimum"), toml::find<double>(node, "yMaximum"), toml::find<double>(node, "yBinWidth"),
+        toml::find<double>(node, "zMinimum"), toml::find<double>(node, "zMaximum"), toml::find<double>(node, "zBinWidth"));
+
+    nBinned_ = toml::find<long>(node, "nBinned");
+    nMissed_ = toml::find<long>(node, "nMissed");
+
+    averages_.linearArray() = toml::find<std::vector<SampledDouble>>(node, "averages");
+
+    updateAccumulatedData();
+}
\ No newline at end of file
diff --git a/src/math/histogram3D.h b/src/math/histogram3D.h
index 638cff0484..72fe2840aa 100644
--- a/src/math/histogram3D.h
+++ b/src/math/histogram3D.h
@@ -7,8 +7,7 @@
 #include "math/sampledDouble.h"
 #include "templates/array3D.h"
 
-// Three-Dimensional Histogram
-class Histogram3D
+class Histogram3D : public Serialisable
 {
     public:
     Histogram3D();
@@ -132,4 +131,8 @@ class Histogram3D
     bool deserialise(LineParser &parser);
     // Write data through specified LineParser
     bool serialise(LineParser &parser) const;
+    // Express as a serialisable value
+    void serialise(std::string tag, SerialisedValue &target) const override;
+    // Read values from a serialisable value
+    void deserialise(const SerialisedValue &node) override;
 };
diff --git a/src/math/integerHistogram1D.cpp b/src/math/integerHistogram1D.cpp
index 4b4a8d324d..94d8b02b7f 100644
--- a/src/math/integerHistogram1D.cpp
+++ b/src/math/integerHistogram1D.cpp
@@ -212,3 +212,33 @@ bool IntegerHistogram1D::serialise(LineParser &parser) const
 
     return true;
 }
+
+// Express as a serialisable value
+void IntegerHistogram1D::serialise(std::string tag, SerialisedValue &target) const
+{
+    target[tag] = {{"zeroCounter", zeroCounter_}, {"nBinned", nBinned_}, {"nMissed", nMissed_}};
+
+    if (minimum_)
+        target[tag]["minimum"] = *minimum_;
+    if (maximum_)
+        target[tag]["maximum"] = *maximum_;
+
+    fromMap(averages_, "averages", target);
+}
+
+// Read values from a serialisable value
+void IntegerHistogram1D::deserialise(const SerialisedValue &node)
+{
+    clear();
+
+    getIfPresent<int>(node, "minimum", minimum_);
+    getIfPresent<int>(node, "maximum", maximum_);
+
+    nBinned_ = toml::find<long>(node, "nBinned");
+    nMissed_ = toml::find<long>(node, "nMissed");
+    zeroCounter_ = toml::find<SampledDouble>(node, "nMissed");
+
+    toMap(node, "averages", [&](const auto &key, const auto &value) { averages_[std::stoi(key)].deserialise(value); });
+
+    updateAccumulatedData();
+}
diff --git a/src/math/integerHistogram1D.h b/src/math/integerHistogram1D.h
index bc72d60eaa..87c000b87c 100644
--- a/src/math/integerHistogram1D.h
+++ b/src/math/integerHistogram1D.h
@@ -8,8 +8,7 @@
 #include "math/sampledDouble.h"
 #include <map>
 
-// Pure Integer Histogram
-class IntegerHistogram1D
+class IntegerHistogram1D : public Serialisable
 {
     public:
     IntegerHistogram1D();
@@ -74,4 +73,8 @@ class IntegerHistogram1D
     bool deserialise(LineParser &parser);
     // Write data through specified LineParser
     bool serialise(LineParser &parser) const;
+    // Express as a serialisable value
+    void serialise(std::string tag, SerialisedValue &target) const override;
+    // Read values from a serialisable value
+    void deserialise(const SerialisedValue &node) override;
 };