WEIGHTS & MEASURES

Linear measure

  12 inches        =  1 foot (ft)
  3 feet           =  1 yard (yd)
  5.5 yards        =  1 rod (rd), pole or perch (16.5 ft)
  40 rods          =  1 furlong (fur) = 220 yds = 660 ft
  8 furlongs       =  1 statute mile (ml) = 1760 yds  =  5280 ft
  3 lands miles    =  1 league
  5280 feet        =  1 statute or land mile
  6076.11549 feet  =  1 nautical mile

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Area Measure

  144 square inches  =  1 sq ft
  9 square feet      =  1 sq yd = 1296 sq in
  30.25 square yards =  1 sq rd = 272.25 sq ft
  160 square rods    =  1 acre = 4840 sq yds = 43450 sq ft
  640 acres          =  1 sq ml
  1 mile square      =  1 section (of land)
  6 miles square     =  1 township = 36 sections = 36 sq ml

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Cubic Measure

  1728 cubic inches  =  1 cu ft
  27 cubic feet      =  1 cu yd

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Circular Measure

  Second = 1/60 minute
  Minute = 60 seconds
  Degree = 60 minutes

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Liquid Measure

  4 gills  = 1 pint (pt) =28.875 cu in
  2 pints  = 1 quart (qt) 57.75 cu in
  4 quarts = 1 gallon (gal) = 231 cu in = 8 pts = 32 gills

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Apothecaries Fluid Measure

  60 minums        = 1 fluid dram (fl dr) = 9.2256 cu in
  8 fluid drams    = 1 fluid ounce (fl oz) 1.8047 cu in
  16 fluid ounces  = 1 pt = 28.875 cu in = 128 fl drs
  2 pints = 1 qt   = 57.75 cu in = 32 fl oz = 256 fl drs
  4 qts = 1 gal    = 231 cu in = 128 fl oz = 1024 fl drs

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Dry Measure

  2 pints  = 1 qt (67.2006 cubic inches)
  8 quarts = 1 peck (pk) = 537.605 cu in = 16 pts
  4 pecks  = 1 bushel (bu) = 2150.42 cu in = 32 qts

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Gunter's or Surveyors Chain Measure

  7.92 inches = 1 link (li)
  100 links   = 1 chain (ch) = 4 rods = 66 feet
  80 chains   = 1 statute mile = 320 rods = 5280 feet

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Troy Weight

  24 grains       = 1 pennyweight (dwt)
  20 pennyweights = 1 ounce troy (ox t) = 480 grains
  12 ounces troy  = 1 pound troy (lb t) = 240 pennyweights = 5760 grains

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Apothecaries Weight

  20 grains     = 1 scruple (s ap)
  3 scruples    = 1 dram apothecaries (dr ap) = grains
  8 drams ap    = 1 ounce apothecaries (oz ap) = 23 sc ap = 480 grains
  12 ounces ap  = 1 pound ap (lb ap) = 96 dr ap = 240 sc ap = 5760 grains

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GEOMETRIC FORMULAE

Circle

  area                    = 1/2 diameter x 1/2 circumference
  area of sector          = length of arc x 1/2 radius
  area of segment thats
  greater than semicircle = area of sector of equal radius + area of triangle
  area of segment thats
  less than semicircle    = area of sector of equal radius - area of triangle
  circumference           = diameter x 3.1416 (PI)
                          = radius x 6.283185 (PIx2)
  diameter                = circumference x .3183
  radius                  = circumference x .0159155

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  Cylinder or Prism
  surface                 = (area of both ends + length) x circumference

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  Ellipse
  area                    = product of the two diameters x .7854

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  Parabola
  area                    = 2/3 altitude x base

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  Parallelogram
  area                    = altitude x base

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  Regular Polygon
  area                    = sum of sides x perpendicular from centre to
                            one of sides - 2

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  Pyramid or Cone
  surface                 = circumference of base x 1/2 slant height
                            + area of base
  contents                = 1/3 altitude x area of base

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  Sphere
  circumference           = cube root of solidity x 3.8978
                          = square root of surface x 1.772454
  contents                = diameter x .5236
  contents of segment     = (height squared + three times the square of
                             radius of base) x (height x .5236)
  diameter                = square root of surface x .56419
                          = cube root of solidity x 1.2407
  surface                 = circumference  x diameter
  volume                  = surface x 1/6 diameter
                          = diameter cubed x .5236
                          = radius cubed x 4.1888
                          = circumference cubed x .016887

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  Square or rectangle
  area                    = length x width

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  Trapezium
  area                    = divide trapezium into 2 triangles, add areas

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  Trapezoid
  area                    = altitude x 1/2 sum of parallel sides

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  Triangle
  area                    = 1/2 altitude x base

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  Wedge
  contents                = 1/2 altitude x area of base

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