If you use Arch Linux and its derivatives like Antergos or Manjaro Linux, you can easily find how long have you been without a reinstall by analyzing the pacman logs as shown below.
head -n1 /var/log/pacman.log
On Fedora, RHEL and its clones such as CentOS, Scientific Linux, Oracle Linux, you can find it using the following command:
sudo rpm -qi basesystem
Sample output from my CentOS 7 server:
Name : basesystem
Version : 10.0
Release : 7.el7.centos
Architecture: noarch
Install Date: Mon 06 Aug 2018 02:54:17 PM PDT
Group : System Environment/Base
Size : 0
License : Public Domain
Signature : RSA/SHA256, Fri 04 Jul 2014 06:16:57 AM IST, Key ID 24c6a8a7f4a80eb5
Source RPM : basesystem-10.0-7.el7.centos.src.rpm
Build Date : Fri 27 Jun 2014 04:07:10 PM IST
Build Host : worker1.bsys.centos.org
Relocations : (not relocatable)
Packager : CentOS BuildSystem http://bugs.centos.org
Vendor : CentOS
Summary : The skeleton package which defines a simple CentOS Linux system
Description :
Basesystem defines the components of a basic CentOS Linux
system (for example, the package installation order to use during
bootstrapping). Basesystem should be in every installation of a system,
and it should never be removed.