Domesday weights and measures can rarely, if ever, be regarded as exact quantities; the word 'measure' should always be treated as though it were in inverted commas. Since most early units of measurement ultimately derive from parts of the human body or the pulling power of the ox on soils of varying quality, this is unsurprising. How long is a foot or an arm? What is a day's work for an ox? Standards will clearly vary from area to area. Nationally defined and enforced measures lay in the future in 1086. In Domesday England, as Maitland observed, there was 'little real, though much nominal uniformity'.
Lack of even elementary standards may also be partially explained by the comparatively recent emergence of a unified kingdom of England from many independent political units. Despite efforts by government to impose some standards from the late Anglo-Saxon period onwards, it would take centuries to achieve even a modest degree of standardisation. Henry I is reported to have made the length of his own arm the standard for measuring cloth (William of Malmesbury, Gesta regum Anglorum, vol. 1, pages 742-43); but most efforts at standardisation were made only from the late twelfth century onwards. In earlier centuries, there can be little certainty, and scarcely ever any precision, about 'measures'.
This is particularly true of measures of land, which were not even fully standardised by the nineteenth century. The major units would have varied in size from area to area, sometimes even within the same locality. Moreover, it is often unclear whether a particular unit was a linear or an areal measure, what constituted an 'areal' measure, or whether units employed were based upon a decimal hundred (100) or the 'long' duodecimal hundred (120), called 'the English reckoning' in one Domesday entry (LIN C19). All this uncertainty could be compounded by royal grants. The king could, and often did, deem some units to be smaller than they actually were, in order to reduce their tax burden. The Conqueror practised this 'beneficial hidation' on a grand scale, circuit 1 in particular recording hundreds of such reductions.
With these qualifications in mind, the normal relationship of the common Domesday measures of length or area to each other, and their approximate - very approximate - size, would in modern terms be:
1 rod/perch = 5.5 yards
1 furlong = 40 perches
1 mile = 8 furlongs
1 league = 12 furlongs
1 acre = 40 * 4 perches
1 bovate = 15 acres
1 virgate = 30 acres
1 yoke = 60 acres
1 hide = 120 acres
1 carucate = 120 acres
1 sulung = 240 acres
But Domesday Book itself records exceptions to this general scale of measures and relationships.
Of the measures of capacity commonly used in the early middle ages - amber, bushel, modius, pint, and sester - Domesday Book records only the amber, modius, and sester. Most other liquid or dry measures in Domesday are either unknown or uncertain quantities: cartloads of lead; blooms or dickers of iron; measures (Latin: ferlingl, mensura, modium, vasculum) of corn or wheat; packloads (summa) of salt; sticks (stica) of eels, etc.
For more detail, see F.W. Maitland, Domesday Book and beyond (1897); Philip Grierson, English linear measures: an essay in origins (1972); and Philip Grierson, 'Weights and measures', Domesday Book: studies, edited by Ann Williams and R.W.H. Erskine (1987), pages 80-85. A dictionary of English weights and measures from Anglo-Saxon times to the nineteenth century, edited by Ronald E. Zupko (1968), is a compilation of references, mainly useful for later periods.