diff --git a/explorer/interpreter/interpreter.cpp b/explorer/interpreter/interpreter.cpp
index e143c259f22b..14d346a7c0ee 100644
--- a/explorer/interpreter/interpreter.cpp
+++ b/explorer/interpreter/interpreter.cpp
@@ -28,6 +28,7 @@
 #include "explorer/interpreter/action_stack.h"
 #include "explorer/interpreter/stack.h"
 #include "explorer/interpreter/stack_fragment.h"
+#include "llvm/ADT/APInt.h"
 #include "llvm/ADT/StringExtras.h"
 #include "llvm/Support/Casting.h"
 #include "llvm/Support/Error.h"
@@ -210,23 +211,34 @@ auto Interpreter::EvalPrim(Operator op, Nonnull<const Value*> /*static_type*/,
     -> ErrorOr<Nonnull<const Value*>> {
   switch (op) {
     case Operator::Neg:
-      return arena_->New<IntValue>(-cast<IntValue>(*args[0]).value());
     case Operator::Add:
-      return arena_->New<IntValue>(cast<IntValue>(*args[0]).value() +
-                                   cast<IntValue>(*args[1]).value());
     case Operator::Sub:
-      return arena_->New<IntValue>(cast<IntValue>(*args[0]).value() -
-                                   cast<IntValue>(*args[1]).value());
-    case Operator::Mul:
-      return arena_->New<IntValue>(cast<IntValue>(*args[0]).value() *
-                                   cast<IntValue>(*args[1]).value());
-    case Operator::Div: {
-      const auto& lhs = cast<IntValue>(*args[0]).value();
-      const auto& rhs = cast<IntValue>(*args[1]).value();
-      if (rhs == 0) {
-        return ProgramError(source_loc) << "division by zero";
+    case Operator::Div:
+    case Operator::Mul: {
+      llvm::APInt op0(64, cast<IntValue>(*args[0]).value());
+      llvm::APInt result;
+      if (op == Operator::Neg) {
+        result = -op0;
+      } else {
+        llvm::APInt op1(64, cast<IntValue>(*args[1]).value());
+        if (op == Operator::Add) {
+          result = op0 + op1;
+        } else if (op == Operator::Sub) {
+          result = op0 - op1;
+        } else if (op == Operator::Mul) {
+          result = op0 * op1;
+        } else if (op == Operator::Div) {
+          if (op1.getSExtValue() == 0) {
+            return ProgramError(source_loc) << "division by zero";
+          }
+          result = op0.sdiv(op1);
+        }
+      }
+      if (result.isSignedIntN(32)) {
+        return arena_->New<IntValue>(result.getSExtValue());
+      } else {
+        return ProgramError(source_loc) << "integer overflow";
       }
-      return arena_->New<IntValue>(lhs / rhs);
     }
     case Operator::Mod: {
       const auto& lhs = cast<IntValue>(*args[0]).value();
diff --git a/explorer/testdata/operators/fail_overflow_add.carbon b/explorer/testdata/operators/fail_overflow_add.carbon
new file mode 100644
index 000000000000..b02f636a248c
--- /dev/null
+++ b/explorer/testdata/operators/fail_overflow_add.carbon
@@ -0,0 +1,15 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+// AUTOUPDATE
+// RUN: %{not} %{explorer-run}
+// RUN: %{not} %{explorer-run-trace}
+
+package ExplorerTest api;
+
+fn Main() -> i32 {
+  // CHECK:STDERR: RUNTIME ERROR: {{.*}}/explorer/testdata/operators/fail_overflow_add.carbon:[[@LINE+1]]: integer overflow
+  var a: auto = 2147483647 + 1;
+  return 0;
+}
diff --git a/explorer/testdata/operators/fail_overflow_div.carbon b/explorer/testdata/operators/fail_overflow_div.carbon
new file mode 100644
index 000000000000..a17bba3c9aa9
--- /dev/null
+++ b/explorer/testdata/operators/fail_overflow_div.carbon
@@ -0,0 +1,15 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+// AUTOUPDATE
+// RUN: %{not} %{explorer-run}
+// RUN: %{not} %{explorer-run-trace}
+
+package ExplorerTest api;
+
+fn Main() -> i32 {
+  // CHECK:STDERR: RUNTIME ERROR: {{.*}}/explorer/testdata/operators/fail_overflow_div.carbon:[[@LINE+1]]: integer overflow
+  var a: auto = (-2147483647 -1) /-1;
+  return 0;
+}
diff --git a/explorer/testdata/operators/fail_overflow_multiply.carbon b/explorer/testdata/operators/fail_overflow_multiply.carbon
new file mode 100644
index 000000000000..6cba1ee1e8e5
--- /dev/null
+++ b/explorer/testdata/operators/fail_overflow_multiply.carbon
@@ -0,0 +1,15 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+// AUTOUPDATE
+// RUN: %{not} %{explorer-run}
+// RUN: %{not} %{explorer-run-trace}
+
+package ExplorerTest api;
+
+fn Main() -> i32 {
+  // CHECK:STDERR: RUNTIME ERROR: {{.*}}/explorer/testdata/operators/fail_overflow_multiply.carbon:[[@LINE+1]]: integer overflow
+  var a: auto = 1000000000 * 1000000000;
+  return 0;
+}
diff --git a/explorer/testdata/operators/fail_overflow_sub.carbon b/explorer/testdata/operators/fail_overflow_sub.carbon
new file mode 100644
index 000000000000..be3ce2d6772b
--- /dev/null
+++ b/explorer/testdata/operators/fail_overflow_sub.carbon
@@ -0,0 +1,15 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+// AUTOUPDATE
+// RUN: %{not} %{explorer-run}
+// RUN: %{not} %{explorer-run-trace}
+
+package ExplorerTest api;
+
+fn Main() -> i32 {
+  // CHECK:STDERR: RUNTIME ERROR: {{.*}}/explorer/testdata/operators/fail_overflow_sub.carbon:[[@LINE+1]]: integer overflow
+  var a: auto = -2147483647 - 2;
+  return 0;
+}