<Window x:Class="WpfAppChildWidthInPercent.MainWindow"
          xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
          xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
          xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
          xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
          xmlns:local="clr-namespace:WpfAppChildWidthInPercent"
          mc:Ignorable="d"
          Title="MainWindow" Height="450" Width="800">

     <!-- my width converter -->
     <Window.Resources>
          <local:PercentageConverter x:Key="percentageConverter"/>
     </Window.Resources>
    
     <!-- stackpanel -->
     <StackPanel x:Name="my1">
         
          <!-- button -->
          <Button Content="Hello!"
                    HorizontalAlignment="Left"
                    Width="{Binding
                         Converter={StaticResource percentageConverter},
                         ElementName=my1,
                         Path=ActualWidth,
                         ConverterParameter=0.4}"> <!-- 0.4 это значит что будет 40% от всего экрана, расчет написан в классе PercentageConverter -->
          </Button>
         
     </StackPanel>
</Window>

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;

namespace WpfAppChildWidthInPercent
{
     /// <summary>
     /// Interaction logic for MainWindow.xaml
     /// </summary>
     public partial class MainWindow : Window
     {
          public MainWindow()
          {
               InitializeComponent();
          }
     }

     // my converter
     public class PercentageConverter : IValueConverter
     {
          public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
          {
               return System.Convert.ToDouble(value) * System.Convert.ToDouble(parameter);
          }

          public object ConvertBack(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
          {
               throw new NotImplementedException();
          }
     }
}