This is the most often-used historical definition of the Labyrinth, by Herodotus. Nothing we have seen indeed, refutes any of his descriptions, though some degree of inaccuracy in both description and geographical detail must be assigned to the understanding of the times. It is possible, be reading these descriptions, to arrive at a detailed understanding concerning the size and grandure of the Labyrinth and temple compound built in connection with the pyramid.
Extract from the diaries of Karl Oskar Eklund.
Herodotus Book 2: Euterpe 
The History of Herodotus, parallel English/Greek, tr. G. C. Macaulay, .
147. but I will now recount that which other nations also tell, and the Egyptians in agreement with the others, of that which happened in this land: and there will be added to this also something of that which I have myself seen. Being set free after the reign of the priest of Hephaistos, the Egyptians, since they could not live any time without a king, set up over them twelve kings, having divided all Egypt into twelve parts. These made intermarriages with one another and reigned, making agreement that they would not put down one another by force, nor seek to get an advantage over one another, but would live in perfect friendship: and the reason why they made these agreements, guarding them very strongly from violation, was this, namely that an oracle had been given to them at first when they began to exercise their rule, that he of them who should pour a libation with a bronze cup in the temple of Hephaistos, should be king of all Egypt (for they used to assemble together in all the temples).
148. Moreover they resolved to join all together and leave a memorial of themselves; and having so resolved they caused to be made a labyrinth, situated a little above the lake of Moiris and nearly opposite to that which is called the City of Crocodiles. This I saw myself, and I found it greater than words can say. For if one should put together and reckon up all the buildings and all the great works produced by the Hellenes, they would prove to be inferior in labour and expense to this labyrinth, though it is true that both the temple at Ephesos and that at Samos are works worthy of note. The pyramids also were greater than words can say, and each one of them is equal to many works of the Hellenes, great as they may be; but the labyrinth surpasses even the pyramids. It has twelve courts covered in, with gates facing one another, six upon the North side and six upon the South, joining on one to another, and the same wall surrounds them all outside; and there are in it two kinds of chambers, the one kind below the ground and the other above upon these, three thousand in number, of each kind fifteen hundred. The upper set of chambers we ourselves saw, going through them, and we tell of them having looked upon them with our own eyes; but the chambers under ground we heard about only; for the Egyptians who had charge of them were not willing on any account to show them, saying that here were the sepulchres of the kings who had first built this labyrinth and of the sacred crocodiles. Accordingly we speak of the chambers below by what we received from hearsay, while those above we saw ourselves and found them to be works of more than human greatness. For the passages through the chambers, and the goings this way and that way through the courts, which were admirably adorned, afforded endless matter for marvel, as we went through from a court to the chambers beyond it, and from the chambers to colonnades, and from the colonnades to other rooms, and then from the chambers again to other courts. Over the whole of these is a roof made of stone like the walls; and the walls are covered with figures carved upon them, each court being surrounded with pillars of white stone fitted together most perfectly; and at the end of the labyrinth, by the corner of it, there is a pyramid of forty fathoms, upon which large figures are carved, and to this there is a way made under ground.
149. Such is this labyrinth; but a cause for marvel even greater than this is afforded by the lake, which is called the lake of Moiris, along the side of which this labyrinth is built. The measure of its circuit is three thousand six hundred furlongs (being sixty schoines), and this is the same number of furlongs as the extent of Egypt itself along the sea. The lake lies extended lengthwise from North to South, and in depth where it is deepest it is fifty fathoms. That this lake is artificial and formed by digging is self-evident, for about in the middle of the lake stand two pyramids, each rising above the water to a height of fifty fathoms, the part which is built below the water being of just the same height; and upon each is placed a colossal statue of stone sitting upon a chair. Thus the pyramids are a hundred fathoms high; and these hundred fathoms are equal to a furlong of six hundred feet, the fathom being measured as six feet or four cubits, the feet being four palms each, and the cubits six. The water in the lake does not come from the place where it is, for the country there is very deficient in water, but it has been brought thither from the Nile by a canal: and for six months the water flows into the lake, and for six months out into the Nile again; and whenever it flows out, then for the six months it brings into the royal treasury a talent of silver a day from the fish which are caught, and twenty pounds when the water comes in.
Herodotus Book 2: Euterpe 
150. The natives of the place moreover said that this lake had an outlet under ground to the Syrtis which is in Libya, turning towards the interior of the continent upon the Western side and running along by the mountain which is above Memphis. Now since I did not see anywhere existing the earth dug out of this excavation (for that was a matter which drew my attention), I asked those who dwelt nearest to the lake where the earth was which had been dug out. These told me to what place it had been carried away; and I readily believed them, for I knew by report that a similar thing had been done at Nineveh, the city of the Assyrians. There certain thieves formed a design once to carry away the wealth of Sardanapallos son of Ninos, the king, which wealth was very great and was kept in treasure-houses under the earth. Accordingly they began from their own dwelling, and making estimate of their direction they dug under ground towards the king’s palace; and the earth which was brought out of the excavation they used to carry away, when night came on, to the river Tigris which flows by the city of Nineveh, until at last they accomplished that which they desired. Similarly, as I heard, the digging of the lake in Egypt was effected, except that it was done not by night but during the day; for as they dug the Egyptians carried to the Nile the earth which was dug out; and the river, when it received it, would naturally bear it away and disperse it. Thus is this lake said to have been dug out.