diff --git a/changelog.d/746.md b/changelog.d/746.md
new file mode 100644
index 000000000..1d14c4190
--- /dev/null
+++ b/changelog.d/746.md
@@ -0,0 +1 @@
+- Expand the National Insurance documentation page with a per-class computation section, add Class 3 (voluntary) to the modelling table, link the underlying variables, and add a references section; also fix the boolean-chain warning in the rates chart.
diff --git a/docs/book/programs/gov/hmrc/national-insurance.ipynb b/docs/book/programs/gov/hmrc/national-insurance.ipynb
index 8bdb55af3..71841820c 100644
--- a/docs/book/programs/gov/hmrc/national-insurance.ipynb
+++ b/docs/book/programs/gov/hmrc/national-insurance.ipynb
@@ -133,30 +133,33 @@
    "source": [
     "# @title\n",
     "import pandas as pd\n",
-    "from tabulate import tabulate\n",
     "\n",
     "\n",
     "data = {\n",
-    "    \"Class\": [\"Class 1\", \"Class 2\", \"Class 4\"],\n",
+    "    \"Class\": [\"Class 1\", \"Class 2\", \"Class 3\", \"Class 4\"],\n",
     "    \"Methodology & Basis\": [\n",
     "        \"Based on employment income. \\n- Monthly and annual calculations.\",\n",
     "        \"Based on self-employment income. \\n- Weekly flat rate.\",\n",
+    "        \"Voluntary contributions for those filling gaps in their NI record. \\n- Weekly flat rate.\",\n",
     "        \"Derived from self-employment income minus Class 1 employee NI.\",\n",
     "    ],\n",
     "    \"Thresholds & Limits\": [\n",
     "        \"Primary Threshold, Upper Earnings Limit\",\n",
     "        \"Small Profits Threshold\",\n",
+    "        \"None (voluntary)\",\n",
     "        \"Lower Profits Limit, Upper Profits Limit\",\n",
     "    ],\n",
     "    \"Rate Application\": [\n",
     "        \"Main and Additional rates\",\n",
     "        \"Flat rate\",\n",
+    "        \"Flat rate\",\n",
     "        \"Main and Additional rates\",\n",
     "    ],\n",
     "    \"Reference\": [\n",
     "        \"Social Security Contributions and Benefits Act 1992 s. 8\",\n",
-    "        \"Social Security and Benefits Act 1992 s. 11\",\n",
-    "        \"Social Security and Benefits Act 1992 s. 15\",\n",
+    "        \"Social Security Contributions and Benefits Act 1992 s. 11\",\n",
+    "        \"Social Security Contributions and Benefits Act 1992 s. 13\",\n",
+    "        \"Social Security Contributions and Benefits Act 1992 s. 15\",\n",
     "    ],\n",
     "}\n",
     "\n",
@@ -164,6 +167,11 @@
     "df"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": "## How PolicyEngine computes National Insurance liability\n\nFor each person, PolicyEngine computes NI contributions class-by-class:\n\n- **Class 1 employee** (`ni_class_1_employee`): the sum of `ni_class_1_employee_primary` (main rate on earnings between the Primary Threshold and the Upper Earnings Limit) and `ni_class_1_employee_additional` (additional rate on earnings above the UEL).\n- **Class 1 employer** (`ni_class_1_employer`): paid on earnings above the Secondary Threshold; surfaced through the `ni_employer` variable.\n- **Class 2** (`ni_class_2`): a flat weekly rate paid by the self-employed with profits above the Small Profits Threshold.\n- **Class 3** (`ni_class_3`): a voluntary flat weekly rate; the variable is exposed but defaults to zero unless explicitly set.\n- **Class 4** (`ni_class_4`): main rate between the Lower and Upper Profits Limits plus additional rate above the UPL, capped at the published Class 4 maximum.\n\nThe individual total `national_insurance` sums the four employee and self-employed components directly — `ni_class_1_employee + ni_class_2 + ni_class_3 + ni_class_4` — so voluntary Class 3 contributions are included in the household-side liability. The convenience aggregates `ni_employee` (Class 1 employee only) and `ni_self_employed` (Class 2 + Class 4) are also exposed for reporting. The Class 1 *employer* charge (`ni_class_1_employer`, surfaced as `ni_employer`) is an employer-side cost rather than part of the individual's `national_insurance`, so it is tracked separately and feeds the government revenue aggregates on its own.\n\nParameters live in `policyengine_uk/parameters/gov/hmrc/national_insurance/` and the per-class formulas in `policyengine_uk/variables/gov/hmrc/national_insurance/`."
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -1529,16 +1537,6 @@
     ]
    },
    "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/8f/pgfhysmd5ls3jnxb_5j7yy340000gn/T/ipykernel_41381/4247299465.py:2: UserWarning:\n",
-      "\n",
-      "Boolean Series key will be reindexed to match DataFrame index.\n",
-      "\n"
-     ]
-    },
     {
      "data": {
       "application/vnd.plotly.v1+json": {
@@ -2688,7 +2686,7 @@
    ],
    "source": [
     "fig = px.line(\n",
-    "    df[df[\"Threshold\"] == False][df.Value < 1],  # Don't plot the flat rate,\n",
+    "    df[(df[\"Threshold\"] == False) & (df[\"Value\"] < 1)],  # Don't plot the flat rate,\n",
     "    x=\"Instant\",\n",
     "    y=\"Value\",\n",
     "    color=\"Label\",\n",
@@ -2714,6 +2712,17 @@
     "fig = format_fig(fig)\n",
     "fig"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References\n",
+    "\n",
+    "- [Social Security Contributions and Benefits Act 1992](https://www.legislation.gov.uk/ukpga/1992/4/contents) — primary statute defining each NI class.\n",
+    "- HMRC, [Rates and allowances: National Insurance contributions](https://www.gov.uk/government/publications/rates-and-allowances-national-insurance-contributions).\n",
+    "- HMRC, [National Insurance contributions outturn statistics](https://www.gov.uk/government/collections/income-tax-statistics-and-distributions)."
+   ]
   }
  ],
  "metadata": {
@@ -2739,4 +2748,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 0
-}
+}
\ No newline at end of file