I'm trying to center a JButton in a JPanel using the default FlowLayout. Here is my code:
import javax.swing.*;
import java.awt.*;
public class CoinFlip {
    public static void main(String[] args) {
        JFrame frame = new JFrame("Coin Flip");
        frame.setSize(500, 500);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        JButton coinFlipButton = new JButton("Flip Coin");
        coinFlipButton.setSize(100, 100);
        JPanel coinFlipPanel = new JPanel();
        coinFlipPanel.setSize(500, 100);
        coinFlipPanel.setBackground(Color.GRAY);
        coinFlipPanel.add(coinFlipButton);
        JTextArea coinFlipResults = new JTextArea();
        coinFlipResults.setSize(500, 200);
        frame.getContentPane().add(coinFlipPanel);
        frame.getContentPane().add(coinFlipResults);
        frame.setVisible(true);
    }
}
How can I center the JButton (coinFlipButton) in the JPanel (coinFlipPanel)? I've tried using FlowLayout.CENTER but that makes the button increase in size so that it takes up all the space.
 
     
     
    