diff --git a/changelog.d/forbid-randomness-in-formulas.added.md b/changelog.d/forbid-randomness-in-formulas.added.md
new file mode 100644
index 00000000..e651efdc
--- /dev/null
+++ b/changelog.d/forbid-randomness-in-formulas.added.md
@@ -0,0 +1 @@
+Forbid random number generation inside variable formulas. A rules-engine formula must be a pure, deterministic function of its inputs, so any call to `numpy.random` or the standard library `random` module while a formula runs now raises `NonDeterministicFormulaError`. Stochastic inputs must be precomputed deterministically when building the dataset. Removes the per-variable `np.random.seed` previously applied before each calculation, which existed only to make formula-level randomness reproducible.
diff --git a/policyengine_core/simulations/randomness_guard.py b/policyengine_core/simulations/randomness_guard.py
new file mode 100644
index 00000000..3514b184
--- /dev/null
+++ b/policyengine_core/simulations/randomness_guard.py
@@ -0,0 +1,132 @@
+"""Forbid non-deterministic randomness inside variable formulas.
+
+A rules engine must be a pure function of its inputs: identical inputs must
+always produce identical outputs. Calling a random number generator inside a
+formula breaks that contract — the same household can get different results on
+different runs — and makes whole datasets non-reproducible.
+
+While a formula is executing, this guard replaces the callables exposed by
+``numpy.random`` and the standard library ``random`` module with functions that
+raise :class:`NonDeterministicFormulaError`. This includes the RNG constructors
+``np.random.default_rng``/``Generator``/``RandomState``, so *building* a
+generator inside a formula — even a seeded one — also raises. Seeding does not
+make randomness acceptable in a formula: stochastic inputs belong in the dataset
+(computed once, deterministically, and stored), not in the formula. The guard is
+re-entrant, so nested formula evaluation is handled correctly, and it restores
+the originals once the outermost guarded formula returns.
+
+Known limitations (pinned by tests in ``test_randomness_guard`` so they cannot
+drift silently):
+
+* A ``Generator``/``RandomState`` instance built *before* the formula runs
+  (e.g. ``rng = np.random.default_rng(0)`` at module scope) is not intercepted
+  when its methods are called inside the formula. ``numpy``'s generator classes
+  are immutable C extension types, so their bound methods cannot be patched.
+* A *bare drawing function* bound into another module's namespace before the
+  guard installs (e.g. ``from numpy.random import random``) is not intercepted,
+  because the guard patches the ``numpy.random`` module attribute, not every
+  rebinding of it.
+
+Both require deliberately hoisting randomness out of the ``np.random.<fn>`` form;
+use ``np.random.<fn>(...)`` or construct the generator inside the formula (both
+caught) rather than importing or pre-building drawing callables.
+"""
+
+from __future__ import annotations
+
+import random as _stdlib_random
+from typing import Callable
+
+import numpy as np
+
+
+class NonDeterministicFormulaError(RuntimeError):
+    """Raised when a formula invokes a random number generator."""
+
+
+# Public callables exposed by each randomness namespace, captured once at
+# import so the per-formula swap is a cheap dict iteration rather than a
+# fresh ``dir()`` scan.
+def _public_callables(module) -> dict[str, Callable]:
+    return {
+        name: getattr(module, name)
+        for name in dir(module)
+        if not name.startswith("_") and callable(getattr(module, name))
+    }
+
+
+_GUARDED_NAMESPACES = (
+    ("numpy.random", np.random, _public_callables(np.random)),
+    ("random", _stdlib_random, _public_callables(_stdlib_random)),
+)
+
+# Re-entrancy bookkeeping: only the outermost guarded formula installs and
+# removes the patches; the active variable name is tracked as a stack so the
+# error message always names the formula that actually made the call.
+_depth = 0
+_variable_stack: list[str] = []
+
+
+def _make_raiser(namespace: str, attribute: str) -> Callable:
+    qualified = f"{namespace}.{attribute}"
+
+    def _raise(*args, **kwargs):
+        variable = _variable_stack[-1] if _variable_stack else "<unknown>"
+        raise NonDeterministicFormulaError(
+            f"The formula for '{variable}' called {qualified}(), but rules-engine "
+            f"formulas must be deterministic functions of their inputs. Remove the "
+            f"random call. If you need a stochastic input, compute it once when "
+            f"building the dataset (with a seeded generator) and store it as an "
+            f"input variable instead."
+        )
+
+    return _raise
+
+
+# Pre-build the raisers once per (namespace, attribute).
+_RAISERS = {
+    id(module): {name: _make_raiser(namespace, name) for name in originals}
+    for namespace, module, originals in _GUARDED_NAMESPACES
+}
+
+
+def _install() -> None:
+    for _namespace, module, originals in _GUARDED_NAMESPACES:
+        raisers = _RAISERS[id(module)]
+        for name in originals:
+            setattr(module, name, raisers[name])
+
+
+def _restore() -> None:
+    for _namespace, module, originals in _GUARDED_NAMESPACES:
+        for name, original in originals.items():
+            setattr(module, name, original)
+
+
+class forbid_randomness:
+    """Context manager that bans RNG use while a formula runs.
+
+    Re-entrant: nested formulas reuse the single installed patch set and only
+    the outermost context restores the originals.
+    """
+
+    __slots__ = ("variable_name",)
+
+    def __init__(self, variable_name: str):
+        self.variable_name = variable_name
+
+    def __enter__(self) -> "forbid_randomness":
+        global _depth
+        if _depth == 0:
+            _install()
+        _depth += 1
+        _variable_stack.append(self.variable_name)
+        return self
+
+    def __exit__(self, exc_type, exc_value, traceback) -> bool:
+        global _depth
+        _variable_stack.pop()
+        _depth -= 1
+        if _depth == 0:
+            _restore()
+        return False
diff --git a/policyengine_core/simulations/simulation.py b/policyengine_core/simulations/simulation.py
index c655106c..3864a5dc 100644
--- a/policyengine_core/simulations/simulation.py
+++ b/policyengine_core/simulations/simulation.py
@@ -14,6 +14,7 @@
 from policyengine_core.entities.entity import Entity
 from policyengine_core.enums import Enum, EnumArray
 from policyengine_core.errors import CycleError, SpiralError
+from policyengine_core.simulations.randomness_guard import forbid_randomness
 from policyengine_core.holders.holder import Holder
 from policyengine_core.periods import Period
 from policyengine_core.periods.config import ETERNITY, MONTH, YEAR
@@ -591,7 +592,9 @@ def calculate(
 
         self.tracer.record_calculation_start(variable_name, period, self.branch_name)
 
-        np.random.seed(_stable_hash_to_seed(variable_name + str(period)))
+        # No per-variable RNG seeding: formulas may not use randomness at all
+        # (enforced by forbid_randomness in _run_formula), so there is nothing
+        # to make reproducible here.
 
         try:
             result = self._calculate(variable_name, period)
@@ -1102,10 +1105,14 @@ def _run_formula(
             self.tax_benefit_system.parameters.tracer = self.tracer
         parameters_at = self.tax_benefit_system.parameters
 
-        if formula.__code__.co_argcount == 2:
-            array = formula(population, period)
-        else:
-            array = formula(population, period, parameters_at)
+        # A rules-engine formula must be a pure, deterministic function of its
+        # inputs. Forbid any random number generation while it runs so the same
+        # inputs always produce the same outputs.
+        with forbid_randomness(variable.name):
+            if formula.__code__.co_argcount == 2:
+                array = formula(population, period)
+            else:
+                array = formula(population, period, parameters_at)
 
         return array
 
diff --git a/tests/core/test_randomness_guard.py b/tests/core/test_randomness_guard.py
new file mode 100644
index 00000000..f96443a2
--- /dev/null
+++ b/tests/core/test_randomness_guard.py
@@ -0,0 +1,189 @@
+"""A variable formula must not invoke a random number generator.
+
+Rules-engine formulas have to be deterministic functions of their inputs, so
+calling ``numpy.random`` or the stdlib ``random`` module inside a formula raises
+:class:`NonDeterministicFormulaError`. These tests pin that behaviour and verify
+the guard restores the randomness namespaces afterwards.
+"""
+
+import random
+from numpy.random import random as _bare_random_import
+
+import numpy as np
+import pytest
+
+# A generator hoisted to module scope, built before any formula runs. Its bound
+# methods cannot be patched (numpy generator classes are immutable C types), so
+# using it inside a formula is a known, pinned gap in the guard.
+_PREBUILT_RNG = np.random.default_rng(0)
+
+from policyengine_core import periods
+from policyengine_core.country_template import CountryTaxBenefitSystem, entities
+from policyengine_core.simulations import SimulationBuilder
+from policyengine_core.simulations.randomness_guard import (
+    NonDeterministicFormulaError,
+    forbid_randomness,
+)
+from policyengine_core.variables import Variable
+
+PERIOD = "2013-01"
+
+
+def _simulation_with(*variable_classes):
+    system = CountryTaxBenefitSystem()
+    system.add_variables(*variable_classes)
+    return SimulationBuilder().build_default_simulation(system)
+
+
+class uses_numpy_random(Variable):
+    value_type = float
+    entity = entities.Person
+    definition_period = periods.MONTH
+    label = "formula that draws from numpy.random"
+
+    def formula(person, period):
+        return np.random.random(person.count)
+
+
+class uses_stdlib_random(Variable):
+    value_type = float
+    entity = entities.Person
+    definition_period = periods.MONTH
+    label = "formula that draws from the random module"
+
+    def formula(person, period):
+        return random.random()
+
+
+class uses_seeded_generator(Variable):
+    value_type = float
+    entity = entities.Person
+    definition_period = periods.MONTH
+    label = "formula that builds a seeded generator"
+
+    def formula(person, period):
+        # Seeding does not make randomness acceptable inside a formula.
+        return np.random.default_rng(0).random(person.count)
+
+
+class deterministic(Variable):
+    value_type = int
+    entity = entities.Person
+    definition_period = periods.MONTH
+    label = "deterministic formula"
+
+    def formula(person, period):
+        return person.count
+
+
+class raises_value_error(Variable):
+    value_type = float
+    entity = entities.Person
+    definition_period = periods.MONTH
+    label = "formula that raises a non-RNG exception"
+
+    def formula(person, period):
+        raise ValueError("boom")
+
+
+class uses_prebuilt_generator(Variable):
+    value_type = float
+    entity = entities.Person
+    definition_period = periods.MONTH
+    label = "formula that uses a module-scope generator (known gap)"
+
+    def formula(person, period):
+        return _PREBUILT_RNG.random(person.count)
+
+
+class uses_bare_imported_function(Variable):
+    value_type = float
+    entity = entities.Person
+    definition_period = periods.MONTH
+    label = "formula that uses a by-name imported drawing function (known gap)"
+
+    def formula(person, period):
+        return _bare_random_import()
+
+
+def test_numpy_random_in_formula_raises():
+    simulation = _simulation_with(uses_numpy_random)
+    with pytest.raises(NonDeterministicFormulaError, match="uses_numpy_random"):
+        simulation.calculate("uses_numpy_random", PERIOD)
+
+
+def test_stdlib_random_in_formula_raises():
+    simulation = _simulation_with(uses_stdlib_random)
+    with pytest.raises(NonDeterministicFormulaError, match="random"):
+        simulation.calculate("uses_stdlib_random", PERIOD)
+
+
+def test_seeded_generator_in_formula_still_raises():
+    simulation = _simulation_with(uses_seeded_generator)
+    with pytest.raises(NonDeterministicFormulaError):
+        simulation.calculate("uses_seeded_generator", PERIOD)
+
+
+def test_deterministic_formula_is_unaffected():
+    simulation = _simulation_with(deterministic)
+    result = simulation.calculate("deterministic", PERIOD)
+    assert (result == 1).all()
+
+
+def test_randomness_restored_after_guarded_formula():
+    simulation = _simulation_with(uses_numpy_random)
+    with pytest.raises(NonDeterministicFormulaError):
+        simulation.calculate("uses_numpy_random", PERIOD)
+    # Outside any formula, numpy and stdlib randomness work normally again.
+    assert isinstance(float(np.random.random()), float)
+    assert isinstance(random.random(), float)
+
+
+def test_randomness_restored_after_non_rng_exception_in_formula():
+    # If a formula raises a normal exception, _run_formula's guarded block must
+    # still restore the randomness namespaces (no leak of the patched state).
+    simulation = _simulation_with(raises_value_error)
+    with pytest.raises(ValueError, match="boom"):
+        simulation.calculate("raises_value_error", PERIOD)
+    assert isinstance(float(np.random.random()), float)
+    assert isinstance(random.random(), float)
+
+
+def test_constructing_generator_inside_formula_is_caught():
+    # Building a generator inside the formula hits the patched np.random
+    # constructor, so even this seeded form raises (covered by
+    # uses_seeded_generator too; kept explicit for the boundary).
+    simulation = _simulation_with(uses_seeded_generator)
+    with pytest.raises(NonDeterministicFormulaError):
+        simulation.calculate("uses_seeded_generator", PERIOD)
+
+
+def test_prebuilt_generator_is_a_known_gap():
+    # Documented limitation: a generator built before the formula runs cannot be
+    # intercepted (numpy generator classes are immutable). Pin the behaviour so a
+    # future change to it is noticed.
+    simulation = _simulation_with(uses_prebuilt_generator)
+    result = simulation.calculate("uses_prebuilt_generator", PERIOD)
+    assert result is not None
+
+
+def test_by_name_imported_function_is_a_known_gap():
+    # Documented limitation: a drawing function imported by name before the guard
+    # installs is not intercepted. Pin the behaviour.
+    simulation = _simulation_with(uses_bare_imported_function)
+    result = simulation.calculate("uses_bare_imported_function", PERIOD)
+    assert result is not None
+
+
+def test_guard_is_reentrant():
+    # Entering twice and leaving the inner context must not restore the
+    # originals while the outer context is still active.
+    with forbid_randomness("outer"):
+        with forbid_randomness("inner"):
+            with pytest.raises(NonDeterministicFormulaError, match="inner"):
+                np.random.random()
+        # Still guarded: the outer context owns the patch.
+        with pytest.raises(NonDeterministicFormulaError, match="outer"):
+            np.random.random()
+    # Fully restored once the outermost context exits.
+    assert isinstance(float(np.random.random()), float)