diff --git a/cartographer/mapping/internal/2d/normal_estimation_2d.cc b/cartographer/mapping/internal/2d/normal_estimation_2d.cc
new file mode 100644
index 0000000..de5550b
--- /dev/null
+++ b/cartographer/mapping/internal/2d/normal_estimation_2d.cc
@@ -0,0 +1,110 @@
+/*
+ * Copyright 2018 The Cartographer Authors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include "cartographer/mapping/internal/2d/normal_estimation_2d.h"
+
+namespace cartographer {
+namespace mapping {
+namespace {
+
+float NormalTo2DAngle(const Eigen::Vector3f& v) {
+  return std::atan2(v[1], v[0]);
+}
+
+// Estimate the normal of an estimation_point as the arithmetic mean of the the
+// normals of the vectors from estimation_point to each point in the
+// sample_window.
+float EstimateNormal(const sensor::PointCloud& returns,
+                     const size_t estimation_point_index,
+                     const size_t sample_window_begin,
+                     const size_t sample_window_end,
+                     const Eigen::Vector3f& sensor_origin) {
+  const Eigen::Vector3f& estimation_point = returns[estimation_point_index];
+  if (sample_window_end - sample_window_begin < 2) {
+    return NormalTo2DAngle(sensor_origin - estimation_point);
+  }
+  Eigen::Vector3f mean_normal = Eigen::Vector3f::Zero();
+  const Eigen::Vector3f& estimation_point_to_observation =
+      sensor_origin - estimation_point;
+  for (size_t sample_point_index = sample_window_begin;
+       sample_point_index < sample_window_end; ++sample_point_index) {
+    if (sample_point_index == estimation_point_index) continue;
+    const Eigen::Vector3f& sample_point = returns[sample_point_index];
+    const Eigen::Vector3f& tangent = estimation_point - sample_point;
+    Eigen::Vector3f sample_normal = {-tangent[1], tangent[0], 0.f};
+    constexpr float kMinNormalLength = 1e-6f;
+    if (sample_normal.norm() < kMinNormalLength) {
+      continue;
+    }
+    // Ensure sample_normal points towards 'sensor_origin'.
+    if (sample_normal.dot(estimation_point_to_observation) < 0) {
+      sample_normal = -sample_normal;
+    }
+    sample_normal.normalize();
+    mean_normal += sample_normal;
+  }
+  return NormalTo2DAngle(mean_normal);
+}
+}  // namespace
+
+proto::NormalEstimationOptions2D CreateNormalEstimationOptions2D(
+    common::LuaParameterDictionary* parameter_dictionary) {
+  proto::NormalEstimationOptions2D options;
+  options.set_num_normal_samples(
+      parameter_dictionary->GetInt("num_normal_samples"));
+  options.set_sample_radius(parameter_dictionary->GetDouble("sample_radius"));
+  CHECK_GT(options.num_normal_samples(), 0);
+  CHECK_GT(options.sample_radius(), 0.0);
+  return options;
+}
+
+// Estimates the normal for each 'return' in 'range_data'.
+// Assumes the angles in the range data returns are sorted with respect to
+// the orientation of the vector from 'origin' to 'return'.
+std::vector<float> EstimateNormals(
+    const sensor::RangeData& range_data,
+    const proto::NormalEstimationOptions2D& normal_estimation_options) {
+  std::vector<float> normals;
+  normals.reserve(range_data.returns.size());
+  const size_t max_num_samples = normal_estimation_options.num_normal_samples();
+  const float sample_radius = normal_estimation_options.sample_radius();
+  for (size_t current_point = 0; current_point < range_data.returns.size();
+       ++current_point) {
+    const Eigen::Vector3f& hit = range_data.returns[current_point];
+    size_t sample_window_begin = current_point;
+    for (; sample_window_begin > 0 &&
+           current_point - sample_window_begin < max_num_samples / 2 &&
+           (hit - range_data.returns[sample_window_begin - 1]).norm() <
+               sample_radius;
+         --sample_window_begin) {
+    }
+    size_t sample_window_end = current_point;
+    for (;
+         sample_window_end < range_data.returns.size() &&
+         sample_window_end - current_point < ceil(max_num_samples / 2.0) + 1 &&
+         (hit - range_data.returns[sample_window_end]).norm() < sample_radius;
+         ++sample_window_end) {
+    }
+    const float normal_estimate =
+        EstimateNormal(range_data.returns, current_point, sample_window_begin,
+                       sample_window_end, range_data.origin);
+    normals.push_back(normal_estimate);
+  }
+  return normals;
+}
+
+}  // namespace mapping
+}  // namespace cartographer
diff --git a/cartographer/mapping/internal/2d/normal_estimation_2d.h b/cartographer/mapping/internal/2d/normal_estimation_2d.h
new file mode 100644
index 0000000..f3d937d
--- /dev/null
+++ b/cartographer/mapping/internal/2d/normal_estimation_2d.h
@@ -0,0 +1,42 @@
+/*
+ * Copyright 2018 The Cartographer Authors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef CARTOGRAPHER_MAPPING_INTERNAL_NORMAL_ESTIMATION_2D_H_
+#define CARTOGRAPHER_MAPPING_INTERNAL_NORMAL_ESTIMATION_2D_H_
+
+#include <vector>
+#include "cartographer/mapping/proto/2d/normal_estimation_options_2d.pb.h"
+#include "cartographer/sensor/point_cloud.h"
+#include "cartographer/sensor/range_data.h"
+#include "cartographer/transform/transform.h"
+
+namespace cartographer {
+namespace mapping {
+
+proto::NormalEstimationOptions2D CreateNormalEstimationOptions2D(
+    common::LuaParameterDictionary* parameter_dictionary);
+
+// Estimates the normal for each 'return' in 'range_data'.
+// Assumes the angles in the range data returns are sorted with respect to
+// the orientation of the vector from 'origin' to 'return'.
+std::vector<float> EstimateNormals(
+    const sensor::RangeData& range_data,
+    const proto::NormalEstimationOptions2D& normal_estimation_options);
+
+}  // namespace mapping
+}  // namespace cartographer
+
+#endif  // CARTOGRAPHER_MAPPING_INTERNAL_NORMAL_ESTIMATION_2D_H_
diff --git a/cartographer/mapping/internal/2d/normal_estimation_2d_test.cc b/cartographer/mapping/internal/2d/normal_estimation_2d_test.cc
new file mode 100644
index 0000000..889d6a2
--- /dev/null
+++ b/cartographer/mapping/internal/2d/normal_estimation_2d_test.cc
@@ -0,0 +1,144 @@
+/*
+ * Copyright 2018 The Cartographer Authors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include "cartographer/mapping/internal/2d/normal_estimation_2d.h"
+
+#include "cartographer/common/lua_parameter_dictionary.h"
+#include "cartographer/common/lua_parameter_dictionary_test_helpers.h"
+#include "cartographer/common/math.h"
+#include "gmock/gmock.h"
+#include "gtest/gtest.h"
+
+namespace cartographer {
+namespace mapping {
+namespace {
+
+using ::testing::TestWithParam;
+using ::testing::Values;
+
+TEST(NormalEstimation2DTest, SinglePoint) {
+  const auto parameter_dictionary = common::MakeDictionary(
+      "return { "
+      "num_normal_samples = 2, "
+      "sample_radius = 10.0, "
+      "}");
+  const proto::NormalEstimationOptions2D options =
+      CreateNormalEstimationOptions2D(parameter_dictionary.get());
+  sensor::RangeData range_data;
+  const size_t num_angles = 100;
+  range_data.origin.x() = 0.f;
+  range_data.origin.y() = 0.f;
+  for (size_t angle_idx = 0; angle_idx < num_angles; ++angle_idx) {
+    const double angle = static_cast<double>(angle_idx) /
+                             static_cast<double>(num_angles) * 2. * M_PI -
+                         M_PI;
+    range_data.returns.clear();
+    range_data.returns.emplace_back(std::cos(angle), std::sin(angle), 0.f);
+    std::vector<float> normals;
+    normals = EstimateNormals(range_data, options);
+    EXPECT_NEAR(common::NormalizeAngleDifference(angle - normals[0] - M_PI),
+                0.0, 2.0 * M_PI / num_angles + 1e-4);
+  }
+}
+
+TEST(NormalEstimation2DTest, StraightLineGeometry) {
+  const auto parameter_dictionary = common::MakeDictionary(
+      "return { "
+      "num_normal_samples = 2, "
+      "sample_radius = 10.0, "
+      "}");
+  const proto::NormalEstimationOptions2D options =
+      CreateNormalEstimationOptions2D(parameter_dictionary.get());
+  sensor::RangeData range_data;
+  range_data.returns.emplace_back(-1.f, 1.f, 0.f);
+  range_data.returns.emplace_back(0.f, 1.f, 0.f);
+  range_data.returns.emplace_back(1.f, 1.f, 0.f);
+  range_data.origin.x() = 0.f;
+  range_data.origin.y() = 0.f;
+  std::vector<float> normals;
+  normals = EstimateNormals(range_data, options);
+  for (const float normal : normals) {
+    EXPECT_NEAR(normal, -M_PI_2, 1e-4);
+  }
+  normals.clear();
+  range_data.returns.clear();
+  range_data.returns.emplace_back(1.f, 1.f, 0.f);
+  range_data.returns.emplace_back(1.f, 0.f, 0.f);
+  range_data.returns.emplace_back(1.f, -1.f, 0.f);
+  normals = EstimateNormals(range_data, options);
+  for (const float normal : normals) {
+    EXPECT_NEAR(std::abs(normal), M_PI, 1e-4);
+  }
+
+  normals.clear();
+  range_data.returns.clear();
+  range_data.returns.emplace_back(1.f, -1.f, 0.f);
+  range_data.returns.emplace_back(0.f, -1.f, 0.f);
+  range_data.returns.emplace_back(-1.f, -1.f, 0.f);
+  normals = EstimateNormals(range_data, options);
+  for (const float normal : normals) {
+    EXPECT_NEAR(normal, M_PI_2, 1e-4);
+  }
+
+  normals.clear();
+  range_data.returns.clear();
+  range_data.returns.emplace_back(-1.f, -1.f, 0.f);
+  range_data.returns.emplace_back(-1.f, 0.f, 0.f);
+  range_data.returns.emplace_back(-1.f, 1.f, 0.f);
+  normals = EstimateNormals(range_data, options);
+  for (const float normal : normals) {
+    EXPECT_NEAR(normal, 0, 1e-4);
+  }
+}
+
+class CircularGeometry2DTest : public TestWithParam<int> {};
+
+TEST_P(CircularGeometry2DTest, NumSamplesPerNormal) {
+  const auto parameter_dictionary = common::MakeDictionary(
+      "return { "
+      "num_normal_samples = " +
+      std::to_string(GetParam()) +
+      ", "
+      "sample_radius = 10.0, "
+      "}");
+  const proto::NormalEstimationOptions2D options =
+      CreateNormalEstimationOptions2D(parameter_dictionary.get());
+  sensor::RangeData range_data;
+  const size_t num_angles = 100;
+  for (size_t angle_idx = 0; angle_idx < num_angles; ++angle_idx) {
+    const double angle = static_cast<double>(angle_idx) /
+                             static_cast<double>(num_angles) * 2. * M_PI -
+                         M_PI;
+    range_data.returns.emplace_back(std::cos(angle), std::sin(angle), 0.f);
+  }
+  range_data.origin.x() = 0.f;
+  range_data.origin.y() = 0.f;
+  std::vector<float> normals;
+  normals = EstimateNormals(range_data, options);
+  for (size_t angle_idx = 0; angle_idx < num_angles; ++angle_idx) {
+    const double angle = static_cast<double>(angle_idx) /
+                         static_cast<double>(num_angles) * 2. * M_PI;
+    EXPECT_NEAR(common::NormalizeAngleDifference(normals[angle_idx] - angle),
+                0.0, 2.0 * M_PI / num_angles * GetParam() / 2.0 + 1e-4);
+  }
+}
+
+INSTANTIATE_TEST_CASE_P(InstantiationName, CircularGeometry2DTest,
+                        ::testing::Values(1, 2, 4, 5, 8));
+
+}  // namespace
+}  // namespace mapping
+}  // namespace cartographer
diff --git a/cartographer/mapping/proto/2d/normal_estimation_options_2d.proto b/cartographer/mapping/proto/2d/normal_estimation_options_2d.proto
new file mode 100644
index 0000000..dc88368
--- /dev/null
+++ b/cartographer/mapping/proto/2d/normal_estimation_options_2d.proto
@@ -0,0 +1,22 @@
+// Copyright 2018 The Cartographer Authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+syntax = "proto3";
+
+package cartographer.mapping.proto;
+
+message NormalEstimationOptions2D {
+  int32 num_normal_samples = 1;
+  float sample_radius = 2;
+}