It's impossible with wings of any size - as far as scientists know up to now.

However, there was a flying dinosaur called quetzalcoatlus that probably weighed 75-100 kilograms, like an adult male human. It had a wingspan of up to 15 metres. But even with these huge wings scientists suppose it was not able to actively fly or start, only to soar. They think so because in order to actively fly, it would need chest muscles of one metre in diameter.

So, to fly we would need not only a pair of wings but also a completely different chest. and probably a tail, to steer, and something to do with our inconveniently heavy legs. We couldn't hold them outstretched to the back all the time, but dangling down they would endanger the balance, or we would fly very slowly.

To soar, though... how big is the span of a hang-glider?

Not only are we too heavy, we don't have the necessary anatomy or physiology. Not for this planet and this stage of our evolution anyway.

The adaptations of the really spectacular fliers, the vultures, swifts, albatrosses, bar-headed geese, gannets, hummingbirds, dragonflies, spiders, bats (and bats, and bats), fairy flies, even pigeons, bustards and falcons, are so breathtaking as nearly to bring me to tears. Albatrosses for example have massive support tendons that permit them to keep their wings spread almost without muscular exertion, much as our leg tendons enable us to stand erect without much exertion. Even domestic fowl have the massive muscles and keeled bones that we lack, and we would desperately need some similar equipment for flight.

Do not despair.  With some fairly modest genetic engineering we could develop decent flying capability without losing either our humanity, our virtues in politics, commerce, education, constraint or compassion. We might even do without feathers, although they represent a stunning field of biological technology. Pterodactyl wings seem to be a very promising alternative, though insect wings offer certain advantages.

And by reducing our size to that of say, a smallish goose, we not only could fly well, but you could fit say, four times as many of us on the planet, and we could roost in trees, leaving more room for agriculture, and we could participate in battery farming with a human face.

But, for the squeamish and hide-bound, there are other fields of biological engineering that might work well without our having to improve our anatomies.  Develop tissue culture to grow super-flying attachments that we could strap on to make good our lack of wings and breastbones etc. The device had better include a good brain and eyes however, to prevent incompetent human fliers from doing stupid things like flying into power cables or candle flames. When we take it off again, we need only attach it to a wall connection to maintain its metabolic and excretory needs.

Come Xmas time we could recycle last year's steed for the feast, and to make room for the new Trick-aerobatic model that we had been saving up for.

Wing size? No problem. Laptop-size winglets should work fine, as long as you flap them supersonically.  

What's that? Can't hear you over the sound of my wings. (Ooops! There goes another window.) Virtual reality?  Who said virtual reality???  

Jon      

If you make a scale model of a goose twice as long, its wings have twice the surface area and can lift twice the weight, but its weight is 8 times as much, so an 80 kg human would need 256 times the wing area of a 5 kg goose.  You'd also need a novel metabolism and bone structure.  Birds have already pushed the strength-to-weight of their fuselage and the power-to-weight ratio of their muscles close to the theoretical limit, so you'd need non-biological structural materials for the wings and the power unit.  If you wanted to fly like a hummingbird, your engineering difficulties would be even greater.

Human unpowered flight is achieved daily by people with hangliding or paragliding equipment.

My paraglider wing is approximately 26 square metres in area, and is about 11 metres from tip to tip. It weighs about 5kg.

With it, I can run off a steep slope and take to the air. If I pick a good day, I can soar in updrafts just like a seagull, eagle (or a pterodactyl if you like).  People have flown hundreds of kilometres using thermals to gain height. The only "power" used is the force of gravity.

To answer your question - for a human to beable to fly, with wings, they would need a wingspan of about 15-17m and they would need to flap as often as a hummingbird. This is just to even lift off the ground.