So the following is where I think the problem lies in my code:

public void actionPerformed(ActionEvent i) { 
	int temp;
	double newtemp = 0;
	String inputString;
	inputString = infield.getText();//pulls the number that was entered in the input field
	temp = Integer.parseInt(inputString);// makes a new variable to handle the input
	//tells the output how to calculate the input based on the button that was pressed
	if(i.getSource() == button) {
		newtemp = (5/9) * (temp - 32);//Fahrenheit to Celsius equation
	}
	else if(i.getSource() == button2) {
		newtemp = (5/9) * (temp - 32) + 273;//Fahrenheit to Kelvin equation
	}
	else if(i.getSource() == button3) {
		newtemp = temp + 273;//Celsius to Kelvin equation
	}
	else if(i.getSource() == button4) {
		newtemp = ((9/5) * temp) + 32;//Celsius to Fahrenheit equation
	}
	else if(i.getSource() == button5) {
		newtemp = temp - 273;//Kelvin to Celsius equation
	}
	else {
		newtemp = ((temp - 273) * (9/5)) + 32;//Kelvin to Fahrenheit equation
	}
	outfield.setText(" "+ three.format(newtemp));
	}
	}

The following is where the code fits in as a whole:

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import java.text.DecimalFormat;

@SuppressWarnings("serial")
public class ConvertTemp extends JFrame
implements ActionListener {
private JButton button, button2, button3, button4, button5, button6;
@SuppressWarnings("unused")
private JPanel panel;
@SuppressWarnings("unused")
private JFrame frame;
@SuppressWarnings("unused")
private JTextField Text;
@SuppressWarnings("unused")
private JLabel label;
private JTextField infield = new JTextField(10);
private JTextField outfield = new JTextField(10);
private JLabel inlabel = new JLabel("Temperature Value:");
private JLabel outlabel = new JLabel("Converted Temperature Value:");

DecimalFormat three = new DecimalFormat("0.000");//sets up the 3 Decimal places for use on the output

public static void main(String[] args) {
	ConvertTemp frame = new ConvertTemp();
	frame.createFrame();
	frame.createButton1();
	frame.createButton2();
	frame.createButton3();
	frame.createButton4();
	frame.createButton5();
	frame.createButton6();
	frame.addLabels();
	}

public void createFrame() {
	Container window = getContentPane();
	window.setLayout(new FlowLayout() ); //using the FlowLayout manager
	setSize(400, 200); //setting the size of the initial box
	setVisible(true); //allows for manual size changing of the box
	setTitle("Temperature Converter"); 
	setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); 
	panel = new JPanel(new GridLayout());
	add(new JLabel("Temperature Conversions" + "   C: Celsius" + "   F: Farhrenheit"+ "   K: Kelvin")); 
	}

public void createButton1() {
	//this is to create the Fahrenheit to Celsius button
	button = new JButton("F to C");
	add(button);
	button.addActionListener((ActionListener) this);//this allows an action to be performed when the button is pressed
	}

public void createButton2() {
	//this is to create the Fahrenheit to Kelvin button
	button2 = new JButton("F to K");
	add(button2); 
	button2.addActionListener((ActionListener) this);//this allows an action to be performed when the button is pressed
	}

public void createButton3() {
	//this is to create the Celsius to Kelvin button
	button3 = new JButton("C to K");
	add(button3); 
	button.addActionListener((ActionListener) this);//this allows an action to be performed when the button is pressed
	}

public void createButton4() {
	//this is to create the Celsius to Fahrenheit button
	button4 = new JButton("C to F");
	add(button4); 
	button4.addActionListener((ActionListener) this);//this allows an action to be performed when the button is pressed
	}

public void createButton5() {
	//this is to create the Kelvin to Celsius button
	button5 = new JButton("K to C");
	add(button5); 
	button5.addActionListener((ActionListener) this);//this allows an action to be performed when the button is pressed
	}

public void createButton6() {
	//this is to create the Kelvin to Fahrenheit button
	button6 = new JButton("K to F");
	add(button6);
	button6.addActionListener((ActionListener) this);//this allows an action to be performed when the button is pressed
	}

public void addLabels() {
	add(inlabel);
	add(infield);
	add(outlabel);
	add(outfield);
	outfield.setEditable(false);//removes ability to enter a value in the output field
	}

public void actionPerformed(ActionEvent i) { 
	int temp;
	double newtemp = 0;
	String inputString;
	inputString = infield.getText();//pulls the number that was entered in the input field
	temp = Integer.parseInt(inputString);// makes a new variable to handle the input
	//tells the output how to calculate the input based on the button that was pressed
	if(i.getSource() == button) {
		newtemp = (5/9) * (temp - 32);//Fahrenheit to Celsius equation
	}
	else if(i.getSource() == button2) {
		newtemp = (5/9) * (temp - 32) + 273;//Fahrenheit to Kelvin equation
	}
	else if(i.getSource() == button3) {
		newtemp = temp + 273;//Celsius to Kelvin equation
	}
	else if(i.getSource() == button4) {
		newtemp = ((9/5) * temp) + 32;//Celsius to Fahrenheit equation
	}
	else if(i.getSource() == button5) {
		newtemp = temp - 273;//Kelvin to Celsius equation
	}
	else {
		newtemp = ((temp - 273) * (9/5)) + 32;//Kelvin to Fahrenheit equation
	}
	outfield.setText(" "+ three.format(newtemp));
	}
	}

The correct values are not coming out. I am pretty sure the problem lies in the IF statements but I am lost as to how. Any help would be appreciated.

So after going over this a few times I found that the issue was with the 5/9 and 9/5. For some reason Java was not calculating them correctly so I had to input the decimal equivalents instead.

So after going over this a few times I found that the issue was with the 5/9 and 9/5. For some reason Java was not calculating them correctly so I had to input the decimal equivalents instead.

You were right ti out the decimal equivalents, but java was calculating them correctly:

9 is an int
5 is an int
When you divide 2 ints, another int must be the result.
So the result should be:
int/int = int
9/5 = 1

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