Take a closer look at your first subroutine. Make sure that you declare your variables. So, fixed:

sub button3_sub {
    my $mh = ( 35 + ( 29 - 1 ) * 6 );
    my $cur = $mh;
}
[download]

As for the rest, I couldn't reproduce your problem. This worked for me.

#!/usr/bin/perl

use strict;
use autodie;
use warnings;

use Tk;
use Tk::Table;
use Tk::Gauge;

my $mw = MainWindow->new;
$mw->geometry("75x75");
$mw->title("Gauge testing");

my $button =
  $mw->Button( -text => "Null", -command => \&button3_sub )
  ->pack( -anchor => 'center' );

my ( $alpha, $alphaone, $beta, $betaone, $mh, $output_text, $gaugevar,
+ $cur );

sub button3_sub {
    my $mh = ( 35 + ( 29 - 1 ) * 6 );
    my $cur = $mh;

    my $hw = $mw->Toplevel;
    $hw->geometry("650x450");
    $hw->title('Health Track (!!!WARNING:DO NOT EXIT THIS WINDOW UNTIL
+ DONE)');

    my $hf =
      $hw->Frame( -background => 'white' )
      ->pack( -ipadx => 250, -fill => 'both', -expand => 'yes' );
    my $left_frame =
      $hf->Frame( -background => 'white' )
      ->pack( -side => 'left', -fill => 'y' );
    my $right_frame =
      $hf->Frame( -background => 'white' )
      ->pack( -ipadx => 150, -fill => 'y', -anchor => 'n', -expand => 
+1 );
    $betaone =
      $left_frame->Entry( -background => "green", )->pack( -anchor => 
+'nw' );
    my $beta_button =
      $left_frame->Button( -text => "Alpha Null", -command => \&update
+_output )
      ->pack( -anchor => 'nw' );
    $alphaone =
      $left_frame->Entry( -background => "red", )->pack( -anchor => 'n
+w' );
    my $alpha_button =
      $left_frame->Button( -text => "Alpha Null", -command => \&update
+_output )
      ->pack( -anchor => 'nw' );
    $output_text =
      $left_frame->Text( -height => 5, -width => 15 )->pack( -expand =
+> 0, );

    my $gauge = $right_frame->Gauge(
        -background => 'white',
        -bands      => [
            {
                -piecolor => 'green',
                -minimum  => 50,
                -maximum  => 100,
                -tag      => 'Healthy',
            },
            {
                -piecolor => 'yellow',
                -minimum  => 25,
                -maximum  => 50,
                -tag      => 'Bloodied',
            },
            {
                -piecolor => 'red',
                -minimum  => 0,
                -maximum  => 25,
                -tag      => 'Critical',
            }
        ],
        -bandplace           => 'underticks',
        -bandstyle           => 'pieslice',
        -bandwidth           => 0,
        -caption             => 'Current Value',
        -captioncolor        => 'black',
        -extent              => -180,
        -from                => 0,
        -hubcolor            => 'black',
        -huboutline          => 'blue',
        -hubradius           => 15,
        -majortickinterval   => 10,
        -majorticklabelplace => 'outside',
        -finetickinterval    => 1,
        -minortickinterval   => 5,
        -margin              => 40,
        -needles             => [
            {
                -arrowshape => [ 12, 23, 6 ],
                -color      => 'black',
                -command    => undef,
                -format     => '%d',
                -radius     => 196,
                -showvalue  => 1,
                -tag        => 'null',
                -title      => 'null',
                -titlecolor => 'white',
                -titlefont  => 'Helvetica-12',
                -titleplace => 'south',
                -variable   => \$gaugevar,
                -width      => 5,
            }
        ],
        -start => 180,
        -to    => 100,
    )->pack( -fill => 'both', -expand => 1 );
}

sub gaugebutton1_sub {
    $gaugevar = ( $cur / $mh ) * 100;
}

sub update_output {
    my $beta  = $betaone->get();
    my $alpja = $alphaone->get();
    if ( $alpha eq "" ) { $alpha = 0; }
    if ( $beta  eq "" ) { $beta  = 0; }
    $cur = $cur + $beta - $alpha;
    if ( $cur gt $mh ) { $cur = $mh; }
    if ( $cur lt 0 )   { $cur = 0; }

    my $output = "Current value:\n$cur";
    $output_text->delete( '0.0', 'end' );
    $output_text->insert( "end", $output );
    $betaone->delete( '0.0', 'end' );
    $alphaone->delete( '0.0', 'end' );
    $gaugevar = ( $cur / $mh ) * 100;
}

MainLoop;
[download]

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