It's not a real easy question for me to answer as there area lot of factors involved. Some of them have been mentioned above, some haven't. You might follow the link in my signature to get some of my thoughts on it, Some of those will not apply to you but some will.
Climate is a big factor, but so is how you manage them. Will they be confined to the coop only for extended periods because you like to sleep in occasionally or will they have access to a predator proof run 24/7? Where will you feed and water? Can you fit roosts, nests (you could get by with one but I'd prefer two), food, and water in the coop without them pooping on them from the roosts? That's a potential problem with square feet per bird numbers for small numbers of chickens, you may not have room for practical things.
Are you buying a prefab coop, building it yourself, or repurposing something else? Most prefab coops only hold about 1/3 to 1/2 the number of birds they advertise and are often poorly designed or built. Still, many people use them for a very small number of birds in certain climates and circumstances, often with some modifications.
If you are building it yourself and are buying the materials new, most building materials come in 4' or 8' dimensions, at least in the USA. A 6' dimension isn't horrible, the cut-offs can often be used for nests and other things. If you take these dimensions into account you can often minimize cutting and waste. Don't make the mistake of making it too short either, you need to stack things a bit like nests, roosts, and ventilation. How much may depend on your climate.
If you are refurbishing something there may be some natural dimensions that make it easier.
For three Orpington hens in a nice climate my minimum coop would be 4' x 4' with a 4' height. In some climates a 4' x 6' might work better. In many climates I'd be OK with a coop elevated a couple of feet off the ground, the area underneath can provide shade or a dry place to feed. In some climates you might be better off with a coop on the ground as long as it stays dry. If you ever plan to integrate new chickens in the future, additional space can be quite valuable.
For the run I'd look at how you want to build it. I absolutely want a run I can stand in, to me that is very important. If your coop is 4' wide and you are going to use standard lumber, I'd probably make it 8' long x 4' wide. If you are using a post and wire construction I'd look at how much wire is on the roll, how many posts you would need, well it gets a little more complicated to efficiently use materials but you actually have more freedom in the dimensions.
The roof complicates it a bit. You want a sloped roof so rainwater runs off. You do not want a flat roof, standing water leaks or corrodes. If you are in a heavy snow area you might want a fairly steep roof, on the run also if you put a solid roof on the run. I really like an overhang on the coop roof, that gives you great options for ventilation without letting rain or snow in. Since it is sloped it will be wider than the standard 4' width to start with. You can go with a wooden, shingle, metal, or plastic roof. Lots of options.
If your run roof is open wire instead of solid you may still collect snow, ice, or leaf load on it. If you have a roof on your run it may need to be strong enough for those.
It sounds a lot more complicated than it should be. If your weather and management techniques will have them outside in the run most of their waking hours a 4x4 coop should work. If they are going to be locked in the coop section only a lot I'd go with a 4x6. That should take care of 99% of the cases.
