diff --git a/pkgs/development/libraries/science/math/magma/default.nix b/pkgs/development/libraries/science/math/magma/default.nix
index b8e3999ffe8..c5960dddf51 100644
--- a/pkgs/development/libraries/science/math/magma/default.nix
+++ b/pkgs/development/libraries/science/math/magma/default.nix
@@ -1,8 +1,40 @@
 { lib, stdenv, fetchurl, cmake, gfortran, ninja, cudatoolkit, libpthreadstubs, lapack, blas }:
 
-with lib;
+assert let majorIs = lib.versions.major cudatoolkit.version;
+       in majorIs == "9" || majorIs == "10" || majorIs == "11";
 
-let version = "2.5.4";
+let
+  version = "2.5.4";
+
+  # We define a specific set of CUDA compute capabilities here,
+  # because CUDA 11 does not support compute capability 3.0. Also,
+  # we use it to enable newer capabilities that are not enabled
+  # by magma by default. The list of supported architectures
+  # can be found in magma's top-level CMakeLists.txt.
+  cudaCapabilities = rec {
+    cuda9 = [
+      "Kepler"  # 3.0, 3.5
+      "Maxwell" # 5.0
+      "Pascal"  # 6.0
+      "Volta"   # 7.0
+    ];
+
+    cuda10 = [
+      "Turing"  # 7.5
+    ] ++ cuda9;
+
+    cuda11 = [
+      "sm_35"   # sm_30 is not supported by CUDA 11
+      "Maxwell" # 5.0
+      "Pascal"  # 6.0
+      "Volta"   # 7.0
+      "Turing"  # 7.5
+      "Ampere"  # 8.0
+    ];
+  };
+
+  capabilityString = lib.strings.concatStringsSep ","
+    cudaCapabilities."cuda${lib.versions.major cudatoolkit.version}";
 
 in stdenv.mkDerivation {
   pname = "magma";
@@ -17,6 +49,8 @@ in stdenv.mkDerivation {
 
   buildInputs = [ cudatoolkit libpthreadstubs lapack blas ];
 
+  cmakeFlags = [ "-DGPU_TARGET=${capabilityString}" ];
+
   doCheck = false;
 
   preConfigure = ''