Why doesn't the buttons align up properly?

The problem is that the button is literally too small to take up 2 columns, and tkinter doesn't stretch them up automatically. You'd have to configure the stretching manually using sticky property so it knows the direction(s) of the stretch: button_clear.grid(row=4,column=1,columnspan=2, sticky='we'). Here is your full code fixed:

from tkinter import *root = Tk()display = Entry(root,width=48,borderwidth=5)display.grid(row=0,column=0,columnspan=3)button_1 = Button(root, text="1",width=16,height=3)button_2 = Button(root, text="2",width=16,height=3)button_3 = Button(root, text="3",width=16,height=3)button_4 = Button(root, text="4",width=16,height=3)button_5 = Button(root, text="5",width=16,height=3)button_6 = Button(root, text="6",width=16,height=3)button_7 = Button(root, text="7",width=16,height=3)button_8 = Button(root, text="8",width=16,height=3)button_9 = Button(root, text="9",width=16,height=3)button_0 = Button(root, text="0",width=16,height=3)button_clear = Button(root, text="Clear",width=32,height=3)button_plus = Button(root, text="+",width=16,height=3)button_equal = Button(root, text="=",width=32,height=3)button_1.grid(row=3,column=0)button_2.grid(row=3,column=1)button_3.grid(row=3,column=2)button_4.grid(row=2,column=0)button_5.grid(row=2,column=1)button_6.grid(row=2,column=2)button_7.grid(row=1,column=0)button_8.grid(row=1,column=1)button_9.grid(row=1,column=2)button_0.grid(row=4,column=0)button_clear.grid(row=4,column=1,columnspan=2, sticky='we')button_plus.grid(row=5,column=0)button_equal.grid(row=5,column=1,columnspan=2, sticky='we')root.mainloop()

Hope that's helpful!

I have made some changes according to above and also made it look-good.

Try this:

from tkinter import *root = Tk()display = Entry(root,width=33,borderwidth=5, font = ('Helvetica',15, 'bold'))display.grid(row=0,column=0,columnspan=3,  ipady =10)button_1 = Button(root, text="1",width=16,height=3, bd =5)button_2 = Button(root, text="2",width=16,height=3, bd =5)button_3 = Button(root, text="3",width=16,height=3, bd =5)button_4 = Button(root, text="4",width=16,height=3, bd =5)button_5 = Button(root, text="5",width=16,height=3, bd =5)button_6 = Button(root, text="6",width=16,height=3, bd =5)button_7 = Button(root, text="7",width=16,height=3, bd =5)button_8 = Button(root, text="8",width=16,height=3, bd =5)button_9 = Button(root, text="9",width=16,height=3, bd =5)button_0 = Button(root, text="0",width=16,height=3, bd =5)button_clear = Button(root, text="Clear",width=32,height=3, bd =5)button_plus = Button(root, text="+",width=16,height=3, bd =5)button_equal = Button(root, text="=",width=32,height=3, bd =5)button_1.grid(row=3,column=0)button_2.grid(row=3,column=1)button_3.grid(row=3,column=2)button_4.grid(row=2,column=0)button_5.grid(row=2,column=1)button_6.grid(row=2,column=2)button_7.grid(row=1,column=0)button_8.grid(row=1,column=1)button_9.grid(row=1,column=2)button_0.grid(row=4,column=0)button_clear.grid(row=4,column=1,columnspan=2, sticky = 'we')button_plus.grid(row=5,column=0)button_equal.grid(row=5,column=1,columnspan=2, sticky = 'we')root.mainloop()

Output: