Oak hardwood floors have a rich, warm feel. Also, since the wood colour is naturally neutral, it lends itself to a wealth of colour combinations. Although from a colour theory point of view, you could pair the oak with just about any colour walls, there are some standard pairings that are more likely to produce a pleasing combination. Stick with warmth and neutrals for best results.
White is always an option for a neutral -- being a colour without character itself, it can be matched up with anything else on the colour wheel. To be a little more interesting, though, try light neutrals. Sand and light taupe are colours that will keep light in the room. You could match them with white trim if brightness is desired. Khaki is another choice with a bit more depth. Cooler neutrals, like those in the green range, will contrast the warmth of the oak, but may be good matches for cool-coloured upholstery or drapes. Sage or a light olive neutral are in this category.
For a rich, smoky feel that matches darker stone like you might find in a fireplace, try dark neutral colours. These colours will produce a den-like feel, but can be edgy too. Sienna, a natural red-brown, is a warm colour that has a bit more saturation than other neutrals. Saddle brown has less red but the same deep value and is close to oak in colour characteristics. Cooler neutrals like burnt umber or Bohemian green umber are contrasting choices that are not so full of colour they will compete with the oak hardwood.
Any colours in the warm range of the colour wheel (from red, through orange and to yellow) will match oak, it just depends on how intense a colour you want. At the darker end is maroon. This will remove a lot of light from the room but give a classic touch. Brighter options like tangerine are powerful, but may be over the edge, unless you really enjoy eye-opening effects. Pastels like lemon chiffon or pale orange are less vibrant but still formidable. A warm colour rooted in a neutral like brick red or coral is a solid compromise between intensity and balance.
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