Instead of hard coding $pi twice, I'd put near the top of the file:

my $PI = 2 * atan2(1, 0);
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I use capitals to indicate the variable plays the role of a constant - it shouldn't be assigned to. Some people will suggest using use constant PI => 2 * atan2(1, 0), but that style gives constants that are harder to interpolate, so I tend to shy away from them.

I also note that both subroutines are almost the same. I would use just one subroutine, and an extra parameter. Something like:

my $PI = 2 * atan2(1, 0);
my $A = 1.18;
my $C = 0.28e6;
my $HWM = 2e-5;
my $SCALE = 1e-6;

sub sigma;

my (@rads, @sigs);
for (my $i = 1; $i <= 100; $i += 2)) {
    my $r = $i * 1e-6;
    push @rads, $r;
    push @sigs, sigma($r, $r >= $HWM)
}
print "radii: @rads\n";
print "sigmas: @sigs\n";
    
sub sigma {
    my ($rad, $high) = @_;
    $PI * $rad ** 2 * ($high ? 2 : $A * (1 - exp(-$C * $rad)));
}
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I didn't run or even compiled the code above, so it may be full of typos.