diff --git a/src/api/l_graphics.c b/src/api/l_graphics.c
index bb8d8d33..e8ba7e8e 100644
--- a/src/api/l_graphics.c
+++ b/src/api/l_graphics.c
@@ -451,6 +451,14 @@ static int l_lovrGraphicsGetLimits(lua_State* L) {
   lua_setfield(L, -2, "anisotropy");
   lua_pushinteger(L, limits->blockSize);
   lua_setfield(L, -2, "blocksize");
+  lua_createtable(L, 3, 0);
+  lua_pushinteger(L, limits->compute[0]);
+  lua_rawseti(L, -2, 1);
+  lua_pushinteger(L, limits->compute[1]);
+  lua_rawseti(L, -2, 2);
+  lua_pushinteger(L, limits->compute[2]);
+  lua_rawseti(L, -2, 3);
+  lua_setfield(L, -2, "compute");
   return 1;
 }
 
diff --git a/src/modules/graphics/graphics.h b/src/modules/graphics/graphics.h
index 468fad91..ea21f347 100644
--- a/src/modules/graphics/graphics.h
+++ b/src/modules/graphics/graphics.h
@@ -189,13 +189,13 @@ typedef struct {
 } GpuFeatures;
 
 typedef struct {
-  bool initialized;
   float pointSizes[2];
   int textureSize;
   int textureMSAA;
   float textureAnisotropy;
   int blockSize;
   int blockAlign;
+  int compute[3];
 } GpuLimits;
 
 typedef struct {
diff --git a/src/modules/graphics/opengl.c b/src/modules/graphics/opengl.c
index b52f9823..64e49ed5 100644
--- a/src/modules/graphics/opengl.c
+++ b/src/modules/graphics/opengl.c
@@ -1263,6 +1263,12 @@ void lovrGpuInit(void* (*getProcAddress)(const char*), bool debug) {
 #endif
   glGetFloatv(GL_POINT_SIZE_RANGE, state.limits.pointSizes);
 
+  if (state.features.compute) {
+    glGetIntegeri_v(GL_MAX_COMPUTE_WORK_GROUP_COUNT, 0, &state.limits.compute[0]);
+    glGetIntegeri_v(GL_MAX_COMPUTE_WORK_GROUP_COUNT, 1, &state.limits.compute[1]);
+    glGetIntegeri_v(GL_MAX_COMPUTE_WORK_GROUP_COUNT, 2, &state.limits.compute[2]);
+  }
+
   if (state.features.multiview) {
     state.singlepass = MULTIVIEW;
   } else if (state.features.instancedStereo) {
@@ -1395,6 +1401,9 @@ void lovrGpuCompute(Shader* shader, int x, int y, int z) {
 #else
   lovrAssert(state.features.compute, "Compute shaders are not supported on this system");
   lovrAssert(shader->type == SHADER_COMPUTE, "Attempt to use a non-compute shader for a compute operation");
+  lovrAssert(x <= state.limits.compute[0], "Compute x size %d exceeds the maximum of %d", state.limits.compute[0]);
+  lovrAssert(y <= state.limits.compute[1], "Compute y size %d exceeds the maximum of %d", state.limits.compute[1]);
+  lovrAssert(z <= state.limits.compute[2], "Compute z size %d exceeds the maximum of %d", state.limits.compute[2]);
   lovrGraphicsFlush();
   lovrGpuBindShader(shader);
   glDispatchCompute(x, y, z);