diff --git a/doc/changelog.dox b/doc/changelog.dox
index 75474d74d..c9f746158 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -195,8 +195,9 @@ See also:
 @subsubsection changelog-latest-new-primitives Primitives library
 
 -   @ref Primitives::capsule3DSolid(), @ref Primitives::circle3DSolid(),
-    @ref Primitives::coneSolid(), @ref Primitives::cylinderSolid() and
-    @ref Primitives::uvSphereSolid() can now have tangents as well
+    @ref Primitives::coneSolid(), @ref Primitives::cylinderSolid(),
+    @ref Primitives::grid3DSolid() and @ref Primitives::uvSphereSolid() can now
+    have tangents as well
 
 @subsubsection changelog-latest-new-scenegraph SceneGraph library
 
diff --git a/src/Magnum/Primitives/Grid.cpp b/src/Magnum/Primitives/Grid.cpp
index 0fc766fdb..f02c913e3 100644
--- a/src/Magnum/Primitives/Grid.cpp
+++ b/src/Magnum/Primitives/Grid.cpp
@@ -56,16 +56,20 @@ Trade::MeshData grid3DSolid(const Vector2i& subdivisions, const GridFlags flags)
         }
     }
 
-    /* Allocate interleaved array for all vertex data */
+    /* Calculate attribute count and vertex size */
     std::size_t stride = sizeof(Vector3);
     std::size_t attributeCount = 1;
     if(flags & GridFlag::Normals) {
-        ++attributeCount;
         stride += sizeof(Vector3);
+        ++attributeCount;
     }
-    if(flags & GridFlag::TextureCoordinates) {
+    if(flags & GridFlag::Tangents) {
+        stride += sizeof(Vector4);
         ++attributeCount;
+    }
+    if(flags & GridFlag::TextureCoordinates) {
         stride += sizeof(Vector2);
+        ++attributeCount;
     }
     Containers::Array<char> vertexData{stride*vertexCount.product()};
     Containers::Array<Trade::MeshAttributeData> attributes{attributeCount};
@@ -86,8 +90,7 @@ Trade::MeshData grid3DSolid(const Vector2i& subdivisions, const GridFlags flags)
                 positions[i++] = {(Vector2(x, y)/Vector2(faceCount))*2.0f - Vector2{1.0f}, 0.0f};
     }
 
-    /* Fill normals, if any. It's always the second attribute, right after
-       positions. */
+    /* Fill normals and tangents, if any. Those are the same for all. */
     if(flags & GridFlag::Normals) {
         Containers::StridedArrayView1D<Vector3> normals{vertexData,
             reinterpret_cast<Vector3*>(vertexData.begin() + attributeOffset),
@@ -97,6 +100,15 @@ Trade::MeshData grid3DSolid(const Vector2i& subdivisions, const GridFlags flags)
         attributeOffset += sizeof(Vector3);
         for(auto&& i: normals) i = Vector3::zAxis(1.0f);
     }
+    if(flags & GridFlag::Tangents) {
+        Containers::StridedArrayView1D<Vector4> tangents{vertexData,
+            reinterpret_cast<Vector4*>(vertexData.begin() + attributeOffset),
+            std::size_t(vertexCount.product()), std::ptrdiff_t(stride)};
+        attributes[attributeIndex++] =
+            Trade::MeshAttributeData{Trade::MeshAttribute::Tangent, tangents};
+        attributeOffset += sizeof(Vector4);
+        for(auto&& i: tangents) i = {1.0f, 0.0f, 0.0f, 1.0f};
+    }
 
     if(flags & GridFlag::TextureCoordinates) {
         Containers::StridedArrayView1D<Vector2> textureCoords{vertexData,
@@ -109,8 +121,6 @@ Trade::MeshData grid3DSolid(const Vector2i& subdivisions, const GridFlags flags)
             textureCoords[i] = positions[i].xy()*0.5f + Vector2{0.5f};
     }
 
-    /* Not using a compile-time attribute array because there's way too many
-       combinations */
     return Trade::MeshData{MeshPrimitive::Triangles,
         std::move(indexData), Trade::MeshIndexData{indices},
         std::move(vertexData), std::move(attributes)};
diff --git a/src/Magnum/Primitives/Grid.h b/src/Magnum/Primitives/Grid.h
index 4dba3112b..b5846b2f0 100644
--- a/src/Magnum/Primitives/Grid.h
+++ b/src/Magnum/Primitives/Grid.h
@@ -70,8 +70,16 @@ enum class GridFlag: UnsignedByte {
      * Generate normals in positive Z direction.
      * @m_deprecated_since_latest Use @ref GridFlag::Normals instead.
      */
-    GenerateNormals CORRADE_DEPRECATED_ENUM("use Normals instead") = Normals
+    GenerateNormals CORRADE_DEPRECATED_ENUM("use Normals instead") = Normals,
     #endif
+
+    /**
+     * Generate four-component tangents. The last component can be used to
+     * reconstruct a bitangent as described in the documentation of
+     * @ref Trade::MeshAttribute::Tangent.
+     * @m_since_latest
+     */
+    Tangents = 1 << 2
 };
 
 /**
@@ -89,8 +97,8 @@ CORRADE_ENUMSET_OPERATORS(GridFlags)
 2x2 grid in the XY plane with normals in positive Z direction.
 @ref MeshPrimitive::Triangles with @ref MeshIndexType::UnsignedInt indices,
 interleaved @ref VertexFormat::Vector3 positions, optional
-@ref VertexFormat::Vector3 normals and @ref VertexFormat::Vector2 texture
-coordinates.
+@ref VertexFormat::Vector3 normals, optional @ref VertexFormat::Vector4
+tangents and optional @ref VertexFormat::Vector2 texture coordinates.
 
 @image html primitives-grid3dsolid.png width=256px
 
diff --git a/src/Magnum/Primitives/Test/GridTest.cpp b/src/Magnum/Primitives/Test/GridTest.cpp
index 1db60af6c..8696fc7f9 100644
--- a/src/Magnum/Primitives/Test/GridTest.cpp
+++ b/src/Magnum/Primitives/Test/GridTest.cpp
@@ -26,7 +26,7 @@
 #include <Corrade/TestSuite/Tester.h>
 #include <Corrade/TestSuite/Compare/Container.h>
 
-#include "Magnum/Math/Vector3.h"
+#include "Magnum/Math/Vector4.h"
 #include "Magnum/Primitives/Grid.h"
 #include "Magnum/Trade/MeshData.h"
 
@@ -35,103 +35,37 @@ namespace Magnum { namespace Primitives { namespace Test { namespace {
 struct GridTest: TestSuite::Tester {
     explicit GridTest();
 
-    void solid3DWithoutAnything();
-    void solid3DWithNormalsAndTextureCoords();
+    void solid3D();
     void wireframe3D();
 };
 
-GridTest::GridTest() {
-    addTests({&GridTest::solid3DWithoutAnything,
-              &GridTest::solid3DWithNormalsAndTextureCoords,
-              &GridTest::wireframe3D});
-}
-
-void GridTest::solid3DWithoutAnything() {
-    Trade::MeshData grid = grid3DSolid({5, 3}, {});
-
-    CORRADE_COMPARE(grid.primitive(), MeshPrimitive::Triangles);
-    CORRADE_VERIFY(grid.isIndexed());
-    CORRADE_COMPARE(grid.attributeCount(), 1);
-
-    CORRADE_COMPARE_AS(grid.attribute<Vector3>(Trade::MeshAttribute::Position), Containers::arrayView<Vector3>({
-        {-1.0f, -1.0f, 0.0f},
-        {-0.666667f, -1.0f, 0.0f},
-        {-0.333333f, -1.0f, 0.0f},
-        {0.0f, -1.0f, 0.0f},
-        {0.333333f, -1.0f, 0.0f},
-        {0.666667f, -1.0f, 0.0f},
-        {1.0f, -1.0f, 0.0f},
-
-        {-1.0f, -0.5f, 0.0f},
-        {-0.666667f, -0.5f, 0.0f},
-        {-0.333333f, -0.5f, 0.0f},
-        {0.0f, -0.5f, 0.0f},
-        {0.333333f, -0.5f, 0.0f},
-        {0.666667f, -0.5f, 0.0f},
-        {1.0f, -0.5f, 0.0f},
-
-        {-1.0f, 0.0f, 0.0f},
-        {-0.666667f, 0.0f, 0.0f},
-        {-0.333333f, 0.0f, 0.0f},
-        {0.0f, 0.0f, 0.0f},
-        {0.333333f, 0.0f, 0.0f},
-        {0.666667f, 0.0f, 0.0f},
-        {1.0f, 0.0f, 0.0f},
-
-        {-1.0f, 0.5f, 0.0f},
-        {-0.666667f, 0.5f, 0.0f},
-        {-0.333333f, 0.5f, 0.0f},
-        {0.0f, 0.5f, 0.0f},
-        {0.333333f, 0.5f, 0.0f},
-        {0.666667f, 0.5f, 0.0f},
-        {1.0f, 0.5f, 0.0f},
-
-        {-1.0f, 1.0f, 0.0f},
-        {-0.666667f, 1.0f, 0.0f},
-        {-0.333333f, 1.0f, 0.0f},
-        {0.0f, 1.0f, 0.0f},
-        {0.333333f, 1.0f, 0.0f},
-        {0.666667f, 1.0f, 0.0f},
-        {1.0f, 1.0f, 0.0f}
-    }), TestSuite::Compare::Container);
-
-    CORRADE_COMPARE_AS(grid.indices<UnsignedInt>(), Containers::arrayView<UnsignedInt>({
-        0, 8, 7, 0, 1, 8,
-        1, 9, 8, 1, 2, 9,
-        2, 10, 9, 2, 3, 10,
-        3, 11, 10, 3, 4, 11,
-        4, 12, 11, 4, 5, 12,
-        5, 13, 12, 5, 6, 13,
-
-        7, 15, 14, 7, 8, 15,
-        8, 16, 15, 8, 9, 16,
-        9, 17, 16, 9, 10, 17,
-        10, 18, 17, 10, 11, 18,
-        11, 19, 18, 11, 12, 19,
-        12, 20, 19, 12, 13, 20,
+constexpr struct {
+    const char* name;
+    GridFlags flags;
+} Solid3DData[] {
+    {"", GridFlags{}},
+    {"normals", GridFlag::Normals},
+    {"texture coordinates", GridFlag::TextureCoordinates},
+    {"tangents", GridFlag::Tangents},
+    {"normals + tangents", GridFlag::Normals|GridFlag::Tangents},
+    {"all", GridFlag::TextureCoordinates|GridFlag::Normals|GridFlag::Tangents}
+};
 
-        14, 22, 21, 14, 15, 22,
-        15, 23, 22, 15, 16, 23,
-        16, 24, 23, 16, 17, 24,
-        17, 25, 24, 17, 18, 25,
-        18, 26, 25, 18, 19, 26,
-        19, 27, 26, 19, 20, 27,
+GridTest::GridTest() {
+    addInstancedTests({&GridTest::solid3D},
+        Containers::arraySize(Solid3DData));
 
-        21, 29, 28, 21, 22, 29,
-        22, 30, 29, 22, 23, 30,
-        23, 31, 30, 23, 24, 31,
-        24, 32, 31, 24, 25, 32,
-        25, 33, 32, 25, 26, 33,
-        26, 34, 33, 26, 27, 34
-    }), TestSuite::Compare::Container);
+    addTests({&GridTest::wireframe3D});
 }
 
-void GridTest::solid3DWithNormalsAndTextureCoords() {
-    Trade::MeshData grid = grid3DSolid({5, 3}, GridFlag::Normals|GridFlag::TextureCoordinates);
+void GridTest::solid3D() {
+    auto&& data = Solid3DData[testCaseInstanceId()];
+    setTestCaseDescription(data.name);
+
+    Trade::MeshData grid = grid3DSolid({5, 3}, data.flags);
 
     CORRADE_COMPARE(grid.primitive(), MeshPrimitive::Triangles);
     CORRADE_VERIFY(grid.isIndexed());
-    CORRADE_COMPARE(grid.attributeCount(), 3);
 
     CORRADE_COMPARE_AS(grid.attribute<Vector3>(Trade::MeshAttribute::Position), Containers::arrayView<Vector3>({
         {-1.0f, -1.0f, 0.0f},
@@ -175,89 +109,150 @@ void GridTest::solid3DWithNormalsAndTextureCoords() {
         {1.0f, 1.0f, 0.0f}
     }), TestSuite::Compare::Container);
 
-    CORRADE_COMPARE_AS(grid.attribute<Vector3>(Trade::MeshAttribute::Normal), Containers::arrayView<Vector3>({
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f},
-    }), TestSuite::Compare::Container);
-
-    CORRADE_COMPARE_AS(grid.attribute<Vector2>(Trade::MeshAttribute::TextureCoordinates), Containers::arrayView<Vector2>({
-        {0.0f, 0.0f},
-        {0.166667f, 0.0f},
-        {0.333333f, 0.0f},
-        {0.5f, 0.0f},
-        {0.666667f, 0.0f},
-        {0.833333f, 0.0f},
-        {1.0f, 0.0f},
-
-        {0.0f, 0.25f},
-        {0.166667f, 0.25f},
-        {0.333333f, 0.25f},
-        {0.5f, 0.25f},
-        {0.666667f, 0.25f},
-        {0.833333f, 0.25f},
-        {1.0f, 0.25f},
-
-        {0.0f, 0.5f},
-        {0.166667f, 0.5f},
-        {0.333333f, 0.5f},
-        {0.5f, 0.5f},
-        {0.666667f, 0.5f},
-        {0.833333f, 0.5f},
-        {1.0f, 0.5f},
-
-        {0.0f, 0.75f},
-        {0.166667f, 0.75f},
-        {0.333333f, 0.75f},
-        {0.5f, 0.75f},
-        {0.666667f, 0.75f},
-        {0.833333f, 0.75f},
-        {1.0f, 0.75f},
-
-        {0.0f, 1.0f},
-        {0.166667f, 1.0f},
-        {0.333333f, 1.0f},
-        {0.5f, 1.0f},
-        {0.666667f, 1.0f},
-        {0.833333f, 1.0f},
-        {1.0f, 1.0f}
-    }), TestSuite::Compare::Container);
+    if(data.flags & GridFlag::Tangents) {
+        CORRADE_COMPARE_AS(grid.attribute<Vector4>(Trade::MeshAttribute::Tangent), Containers::arrayView<Vector4>({
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+            {1.0f, 0.0f, 0.0f, 1.0f},
+        }), TestSuite::Compare::Container);
+    } else CORRADE_VERIFY(!grid.hasAttribute(Trade::MeshAttribute::Tangent));
+
+    if(data.flags & GridFlag::Normals) {
+        CORRADE_COMPARE_AS(grid.attribute<Vector3>(Trade::MeshAttribute::Normal), Containers::arrayView<Vector3>({
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+            {0.0f, 0.0f, 1.0f},
+        }), TestSuite::Compare::Container);
+    } else CORRADE_VERIFY(!grid.hasAttribute(Trade::MeshAttribute::Normal));
+
+    if(data.flags & GridFlag::TextureCoordinates) {
+        CORRADE_COMPARE_AS(grid.attribute<Vector2>(Trade::MeshAttribute::TextureCoordinates), Containers::arrayView<Vector2>({
+            {0.0f, 0.0f},
+            {0.166667f, 0.0f},
+            {0.333333f, 0.0f},
+            {0.5f, 0.0f},
+            {0.666667f, 0.0f},
+            {0.833333f, 0.0f},
+            {1.0f, 0.0f},
+
+            {0.0f, 0.25f},
+            {0.166667f, 0.25f},
+            {0.333333f, 0.25f},
+            {0.5f, 0.25f},
+            {0.666667f, 0.25f},
+            {0.833333f, 0.25f},
+            {1.0f, 0.25f},
+
+            {0.0f, 0.5f},
+            {0.166667f, 0.5f},
+            {0.333333f, 0.5f},
+            {0.5f, 0.5f},
+            {0.666667f, 0.5f},
+            {0.833333f, 0.5f},
+            {1.0f, 0.5f},
+
+            {0.0f, 0.75f},
+            {0.166667f, 0.75f},
+            {0.333333f, 0.75f},
+            {0.5f, 0.75f},
+            {0.666667f, 0.75f},
+            {0.833333f, 0.75f},
+            {1.0f, 0.75f},
+
+            {0.0f, 1.0f},
+            {0.166667f, 1.0f},
+            {0.333333f, 1.0f},
+            {0.5f, 1.0f},
+            {0.666667f, 1.0f},
+            {0.833333f, 1.0f},
+            {1.0f, 1.0f}
+        }), TestSuite::Compare::Container);
+    } else CORRADE_VERIFY(!grid.hasAttribute(Trade::MeshAttribute::TextureCoordinates));
+
+    if(data.flags >= (GridFlag::Tangents|GridFlag::Normals)) {
+        auto tangents = grid.attribute<Vector4>(Trade::MeshAttribute::Tangent);
+        auto normals = grid.attribute<Vector3>(Trade::MeshAttribute::Normal);
+        for(std::size_t i = 0; i != tangents.size(); ++i) {
+            CORRADE_ITERATION(i);
+            CORRADE_ITERATION(tangents[i]);
+            CORRADE_ITERATION(normals[i]);
+            CORRADE_VERIFY(tangents[i].xyz().isNormalized());
+            CORRADE_VERIFY(normals[i].isNormalized());
+            CORRADE_COMPARE(Math::dot(tangents[i].xyz(), normals[i]), 0.0f);
+        }
+    }
 
     CORRADE_COMPARE_AS(grid.indices<UnsignedInt>(), Containers::arrayView<UnsignedInt>({
         0, 8, 7, 0, 1, 8,