Door hinge sizes are an issue when purchasing new hinges. You will only want to do this if they need replacing.
It is more likely that your door is out of adjustment, see 'Adjusting Interior Doors' or 'Adjusting Exterior Doors' for more information.
See 'Door Repair' for a complete listing of door topics.
The size and weight of the door will determine the size and number of hinges. Usually, you will replace the old ones with the same size and quantity.
A valid question. Most residential doors are between an 1 3/8" and 1 3/4" thick. So the normal size hinges for a residential door are 3" x 3" or 3 1/2" x 3 1/2". Your entrance doors might have 4" x 4" hinges, since the doors are heavier and usually thicker than the interior ones.
Measuring Door Hinge Sizes – You measure a door hinge when it is open and lying flat. The height is one dimension and the distance across both leaves is the other dimension. Butt door hinges are often the same size each way, but they don't have to be. It is possible to have hinges that are taller than they are wide. So it is a good idea to measure them both ways.
Is the hinge still on the door? Then you will have trouble getting a good measurement. You can also measure one side of the hinge from the edge of the hinge to the center of the pin. Take this dimension and double it to get the correct size.
Checking the Corners – There are more options, with different types of hinges, when it comes to the corners on the hinge. They might be square or they could have a radius. The square ones are easy, they are square. Both square and round corners are available with different door hinge sizes.
Radius corners are a more of a problem. They can be different radius's. The two common sizes for a radius on a door hinge is either 1/4" or 5/8". You should be able to use a tape measure to determine which size you have.
You may be wondering about the corners, why the difference? Rounded corners are made to fit into mortises that are cut with a router. Hinge jigs and commercial mortising machine use a round cutting head to cut out the mortise. So round corners are easier. They do have machinery that will cut square corners, but it involves another step.
Square corners are better when you are cutting the mortises with a chisel. Round corners are hard to do with a chisel. So there you have it, depending on the tooling you have, you may prefer, square or round corners. When replacing hinges, it makes things much easier to get the same size and style of hinge. Then you don't have to mess with the mortises at all.
So you have two things with the size that you need to make a note of. First the size of the hinges, height x width. Next the type and size of the corners on the hinge. When shopping for different types of hinges the best thing to do is take one of the old ones with you. Match them up at the store and you can't go wrong.
Purchasing Door Hinges
For a door hinge installation or replacement, you want hinges that are the same size and type as the one you have. The best practice is to take an old hinge with you when looking for replacements.
Even among hinges that are the same size, styles can vary. Spring loaded and ball bearing hinges are a couple of examples. See the article 'Types of Door Hinges', for an explanation of the various types and sizes of hinges.
Color and metal type are also important. A door with brass hardware, will likely have brass hinges. You may find stainless steel hinges that are the right size. It would be best to keep looking until you find the right metal finish.
Door hinges are measured by the dimensions when the hinge is open and lying flat. A 3 1/2" x 3 1/2" hinge will be 3 1/2" high, have a center pin and two plates that are approximately 1 1/2" wide. The common sizes for door residential door hinges are 3" and 3 1/2". They can come with both square and rounded corners. Most hardware stores and home supply stores will have a selection and stock the common sizes.
WARNING!! Doors Are Heavy, GET HELP When Removing a Door. Chisels Are Sharp, Use Caution!!! WARNING!!!
Summary
As you can see door hinges come in a number of sizes. See the articles, 'Adjusting Door Hinges', 'Replacing Door Hinges' and 'Squeaky Door Hinges' for related information.