diff --git a/conan/tools/build/cpu.py b/conan/tools/build/cpu.py
index d9a6ecefab0..2de22771b73 100644
--- a/conan/tools/build/cpu.py
+++ b/conan/tools/build/cpu.py
@@ -1,5 +1,6 @@
 import math
 import multiprocessing
+import os
 
 from conans.util.files import load
 
@@ -15,8 +16,18 @@ def _cpu_count():
     try:
         try:
             # This is necessary to deduce docker cpu_count
-            cfs_quota_us = int(load("/sys/fs/cgroup/cpu/cpu.cfs_quota_us"))
-            cfs_period_us = int(load("/sys/fs/cgroup/cpu/cpu.cfs_period_us"))
+            cfs_quota_us = cfs_period_us = 0
+            # cgroup2
+            if os.path.exists("/sys/fs/cgroup/cgroup.controllers"):
+                cpu_max = load("/sys/fs/cgroup/cpu.max").split()
+                if cpu_max[0] != "max":
+                    if len(cpu_max) == 1:
+                        cfs_quota_us, cfs_period_us = int(cpu_max[0]), 100_000
+                    else:
+                        cfs_quota_us, cfs_period_us = map(int, cpu_max)
+            else:  # cgroup1
+                cfs_quota_us = int(load("/sys/fs/cgroup/cpu/cpu.cfs_quota_us"))
+                cfs_period_us = int(load("/sys/fs/cgroup/cpu/cpu.cfs_period_us"))
             if cfs_quota_us > 0 and cfs_period_us > 0:
                 return int(math.ceil(cfs_quota_us / cfs_period_us))
         except (EnvironmentError, TypeError):