RULES RELATIVE TO THE CIRCLE TO FIND DIAMETER TO FIND CIRCUMFERENCE TO FIND RADIUS TO FIND SIDE OF AN INSCRIBED SQUARE TO FIND SIDE OF AN EQUAL SQUARE Multiply circumference by 0.383. Or divide circumference by 3.46. Multiply diameter by 3.46. Or divide diameter by 0.383. Multiply circumference by 0.595. Or divide circumference by 6.2838. Multiply diameter by 0.707. Or multiply circumference by 0.225. Or divide circumference by 4.4428. Multiply diameter by 0.8862. Or divide diameter by.284. Or multiply circumference by 0.282. Or divide circumference by 3.545. SQUARE A side multiplied by.442 equals diameter of its circumscribing circle. A side multiplied by 4.443 equals circumference of its circumscribing circle. A side multiplied by.28 equals diameter of an equal circle. Square inches multiplied by.273 equals circle inches of an equal circle. TO FIND THE AREA OF A CIRCLE TO FIND THE SURFACE OF A SPHERE OR GLOBE Multiply circumference by /4 of the diameter. Or multiply the square of diameter by 0.7854. Or multiply the square of circumference by 0.07958. Or multiply the square of /2 diameter by 3.46. Multiply the diameter by the circumference. Or multiply the square of diameter by 3.46. Or multiply four times the square of radius by 3.46. To find cubic inches in a globe multiply cube of diameter by 0.5236. Any circle whose diameter is double that of another contains four times the area of the other. MATERIALS REQUIRED FOR 00 SQUARE FEET OF SURFACE FOR VARYING THICKNESS OF CONCRETE OR MORTAR C. Cement in sacks. F.A. Fine Aggregate (Sand) in Cu. Ft. C.A. Coarse Aggregate (Pebbles or Broken Stone) in Cu. Ft.
UNITS OF VOLUME AND WEIGHT TROY WEIGHT 24 grains = pennyweights 20 pennyweights = ounce 2 ounces = pound (used for weighing gold, silver and jewels) APOTHECARIES WEIGHT 20 grains = scruple 3 scruples = dram 8 drams = ounce 2 ounces = pound AVOIRDUPOIS WEIGHT 27-/3 grains = dram 6 drams = ounce 6 ounces = pound 25 pounds = quarter 4 quarters = hundredweight 2,000 pounds = short ton 2,240 pounds = long ton DRY MEASURE 2 pints = quart 8 quarts = peck 4 pecks = bushel 36 bushels = chaldron LIQUID MEASURE 4 gills = pint 2 pints = quart 4 quarts = gallon 3-/2 gallons = barrel 2 barrels = hogshead TIME MEASURE 60 seconds = minute 60 minutes = hour 28, 29, 30 or 3 days = month 30 days = month (when computing interest) 365 days = year 24 hours = day 7 days = week CIRCULAR MEASURE 60 seconds = minute 60 minutes = degree 4 quadrants = 2 signs 360 degrees = circle 30 degrees = sign 90 degrees = quadrant LONG MEASURE 2 inches = foot 3 feet = yard 5-/2 yards = rod 40 rods = furlong 8 furlongs = statute mile 3 miles = league CLOTH MEASURE 2-/4 inches = nail 4 nails = quarter 4 quarters = yard MARINER S MEASURE 6 feet = fathom 20 fathoms = cable length 7-/2 cable lengths = mile 5,280 feet = statute mile 6,085 feet = nautical mile MISCELLANEOUS 3 inches = palm 4 inches = hand 6 inches = span 8 inches = cubit 2.8 inches = Biblical cubit 2-/2 feet = military step SQUARE MEASURE 44 sq. inches = sq. foot 9 sq. feet = sq. yard 30-/4 sq. yards = sq. rod 40 sq. rods = rood 4 roods = acre 640 acres = sq. mile SURVEYOR S MEASURE 7.92 inches = link 0 sq. chains, or 60 sq. rods = acre 640 acres = sq. mile 36 sq. miles (6 miles sq.) = township 25 links = rod 4 rods = chain CUBIC MEASURE,728 cu. inches = cu. foot 27 cu. feet = cu. yard 2,50.42 cu. inches = standard bushel 268.8 cu. inches = standard gallon cu. foot = about 4/5 of a bushel 28 cu. feet = cord (wood) 40 cu. feet = ton (shipping) METRIC EQUIVALENT LINEAR MEASURE centimeter = 0.3937 inch decimeter = 3.937 inches = 0.328 foot meter = 39.37 inches =.0936 yards dekameter =.9884 rods kilometer = 0.6237 mile inch = 2.54 centimeters foot = 3.048 decimeters yard = 0.944 meter rod = 0.5029 dekameter mile =.6093 kilometers SQUARE MEASURE sq. centimeter = 9.550 sq. inches sq. inch = 6.452 sq. centimeters sq. decimeter = 0.076 sq. foot sq. foot = 9.2903 sq. decimeters sq. meter =.96 sq. yards sq. yard = 0.836 sq. mile arc = 3.954 sq. rod sq. rod = 0.2529 arc hektar = 2.47 acres acre = 0.4047 hektar sq. kilometer = 0.386 sq. mile sq. mile = 2.59 sq. kilometers MEASURE OF VOLUME cu. centimeter = 0.06 cu. inch cu. inch = 6.39 cu. centimeters cu. decimeter = 0.0353 cu. foot cu. foot = 28.37 cu. decimeters dekaliter = 2.647 gallons gallon = 0.3785 dekaliter pk. = 0.88 dekaliter hektoliter = 2.8375 bu. bu. = 0.3524 hektoliter WEIGHTS gram = 0.3527 ounce ounce = 28.35 grams kilogram = 2.2046 pounds pound = 0.4536 kilograms metric ton = 2,200 pounds or.023 English tons English ton = 0.9072 metric ton APPROXIMATE METRIC EQUIVALENTS decimeter = 4 inches meter =. yards liter =.06 qt. (liquid) or 0.9 qt. (dry) kilometer = 5/8 mile mile =.6 kilometers hektoliter = 2-5/8 bushels kilogram = 2-/5 pounds hektar = 2-/2 acres
UNITS OF VOLUME AND WEIGHT (cont.) Area of a rectangle = length x breadth Area of a triangle = base x /2 perpendicular height Diameter of a circle = radius x 2 Circumference of a circle = diameter x 3.46 Area of a circle = square of diameter x.7854 Area of a sector of a circle = (area of circle x number of degrees in arc)/360 Area of surface of a cylinder = circumference x length area of two ends Diameter of a circle having a given area: Divide the area by.7854 and extract the square root Volume of a cylinder: Multiply the area of the section in square inches by the length in inches = the volume in cubic feet Surface of a sphere = square of diameter x 3.46 Solidity of a sphere = cube of diameter x.5236 Side of an inscribed cube = radius of a sphere x.547 Area of the base of a pyramid or cone, whether round, square or triangular multiplied by one-third of its height = the solidity Diameter x.8862 = side of an equal square Diameter x.707 = side of an inscribed square Radius x 6.2832 = circumference Circumference = 3.5446 x area of circle Diameter =.283 x area of circle Length of an arc = number of degrees x.07453 radius Degree in arc whose length equals radius = 57º 2958' Length of an arc of º = radius x.07543 Length of an arc of min. = radius x.0002909 Length of an arc of sec. = radius x.0000048 n = proportion of circumference to diameter = 3.45926 n 2 = 9.8696044 n =.7724538 Log n = 0.4975 /n =.383 /360 =.002778 360/n = 4.59 Lineal Feet x.0009 = Miles LIneal Yards x.0005 = Miles Square Inches x.007 = Square Feet Square Feet x. = Square Yards Square Yards x.0002067 = Acres Acres x 4840 = Square Yards Inches x.00058 = Feet Feet x.03704 = Yards Circular Inches x.00546 = Square Feet Cylinder Inches x.0004546 = Feet Cylinder Feet x.02909 = Yards Links x.22 = Yards Links x.66 = Feet Feet x.5 = Links Width in Chains x 8 = Acres per Mile 83346 Circ. In. = Square Foot 2200 Cylindrical In. = Foot Feet x 7.48 = U.S. Gallons Inches x.004329 = U.S. Gallons U.S. Gallons x.3367 = Feet U.S. Gallons x 23 = Inches Feet x.8036 = U.S. Bushel Inches x.000466 = U.S. Bushel Cylind. Ft. of Water x 6 = U.S. Gallons Pounds Avoirdupois x.009 = Hundredweights (2) Pounds Avoirdupois x.00045 = Tons (2240) Ft. of Water x 62.5 = Pounds Avoirdupois In. of Water x.0367 = Pounds Avoirdupois Cylind. Ft. of Water x 49. = Pounds Avoirdupois Cylind. In. of Water x.02842 = Pounds Avoirdupois 3.44 U.S. Gallons of Water = Hundredweight 268.8 U.S. Gallons of Water = Ton.8 Feet of Water = Hundredweight 35.88 Feet of Water = Ton Column of Water, 2 inches high and inch in diameter =.34 lbs. U.S. Bushel x.0495 = Yards U.S. Bushel x.2446 = Feet U.S. Bushel x 250.42 = Inches
CONVERSION TABLE MILLIMETERS AND FRACTIONS OF MILLIMETERS TO INCHES IN DECIMALS /00B = 0.0003937 inches /50 =.00079 2/50 =.0057 3/50 =.00236 4/50 =.0035 5/50 =.00394 6/50 =.00472 7/50 =.0055 8/50 =.00630 9/50 =.00709 0/50 =.00787 /50 =.00866 2/50 =.00945 3/50 =.0024 4/50 =.002 5/50 =.08 6/50 =.0260 7/50 =.0339 8/50 =.047 9/50 =.0496 20/50 =.0575 2/50 =.0654 22/50 =.0732 23/50 =.08 24/50 =.0890 25/50 =.0969 26/50 =.02047 27/50 =.0226 28/50 =.02205 29/50 =.02283 30/50 =.02362 3/50 =.0244 32/50 =.02520 33/50 =.02598 34/50 =.02677 35/50 =.02756 36/50 =.02835 37/50 =.0293 38/50 =.02992 39/50 =.0307 40/50 =.0350 4/50 =.03228 42/50 =.03307 43/50 =.03386 44/50 =.03465 45/50 =.03543 46/50 =.03622 47/50 =.0370 48/50 =.03780 49/50 =.03858 =.03937 2 =.07874 3 =.8 4 =.5748 5 =.9685 6 =.23622 7 =.27559 8 =.3496 9 =.35433 0 =.39370 =.43307 2 =.47244 3 =.58 4 =.558 5 =.59055 6 =.62992 7 =.66929 8 =.70866 9 =.74803 20 =.78740 2 =.82677 22 =.8664 23 =.9055 24 =.94488 25 =.98425 26 =.02362 27 =.06299 28 =.0236 29 =.473 30 =.80 3 =.22047 32 =.25984 33 =.2992 34 =.33858 35 =.37795 36 =.4732 37 =.45669 38 =.49606 39 =.53543 40 =.57480 4 =.647 42 =.65354 43 =.6929 44 =.73228 45 =.7765 46 =.802 47 =.85039 48 =.88976 49 =.9293 50 =.96850 5 = 2.00787 52 = 2.04724 53 = 2.0866 54 = 2.2598 55 = 2.6536 56 = 2.20472 57 = 2.24409 58 = 2.28346 59 = 2.32283 60 = 2.36220 6 = 2.4057 62 = 2.44094 63 = 2.4803 64 = 2.5968 65 = 2.55905 66 = 2.59842 67 = 2.63779 68 = 2.6776 69 = 2.7653 70 = 2.75590 7 = 2.79527 72 = 2.83464 73 = 2.8740 74 = 2.9338 75 = 2.95275 76 = 2.9922 77 = 3.0349 78 = 3.07986 79 = 3.023 80 = 3.4960 8 = 3.8897 82 = 3.22834 83 = 3.2677 84 = 3.30708 85 = 3.34645 86 = 3.38582 87 = 3.4259 88 = 3.46456 89 = 3.50393 90 = 3.54330 9 = 3.58267 92 = 3.62204 93 = 3.664 94 = 3.70078 95 = 3.7405 96 = 3.77952 97 = 3.8889 98 = 3.85826 99 = 3.89763 00 = 3.93700 0 millimeters = centimeter = 0.3937 inch 0 decimeters = meter = 39.37 inches 0 centimeters = decimeter = 3.937 inches 25.4 millimeters = inch DECIMAL CONVERSION TABLE EIGHTHS, SIXTEENTHS, THIRTY-SECONDS AND SIXTY-FOURTHS Eighths /8 =.25 /4 =.250 3/8 =.375 /2 =.500 5/8 =.625 3/4 =.750 7/8 =.875 Sixteenths /6 =.0625 3/6 =.875 5/6 =.325 7/6 =.4375 9/6 =.5625 /6 =.6875 3/6 =.825 5/6 =.9375 Thirty-Seconds /32 =.0325 3/32 =.09375 5/32 =.5625 7/32 =.2875 9/32 =.2825 /32 =.34375 3/32 =.40625 5/32 =.46875 7/32 =.5325 9/32 =.59375 2/32 =.65625 23/32 =.785 25/32 =.7825 27/32 =.84375 29/32 =.90625 3/32 =.96875 Sixty-Fourths /64 =.05625 3/64 =.046875 5/64 =.07825 7/64 =.09375 9/64 =.40625 /64 =.7875 3/64 =.20325 5/64 =.234375 7/64 =.265625 9/64 =.296875 2/64 =.32825 23/64 =.359375 25/64 =.390625 27/64 =.42875 29/64 =.45325 3/64 =.484375 33/64 =.55625 35/64 =.546875 37/64 =.57825 39/64 =.609375 4/64 =.640625 43/64 =.67875 45/64 =.70325 47/64 =.734375 49/64 =.765625 5/64 =.796875 53/64 =.82825 55/64 =.859375 57/64 =.890625 59/64 =.92875 6/64 =.95325 63/64 =.985375
METRIC AND ENGLISH OR U.S. EQUIVALENT MEASURES MEASURES OF LENGTH meter = 39.3 inches 3.28083 feet.0936 yards centimeter =.3937 inch millimeter =.03937 inch, or ca. /25 inch kilometer = 0.6237 mile foot =.3048 meter inch = 2.54 centimeters 25.4 millimeters MEASURES OF WEIGHT gram = 5.432 grains kilogram = 2.2046 pounds metric ton =.9842 ton of 2.240 pounds 9.68 hundredweights 2,204.6 pounds grain = 0.648 gram ounce avoirdupois = 28.35 grams pound =.4536 kilogram ton of 2,240 pounds =.06 metric tons 06 kilograms MEASURES OF VOLUME AND CAPACITY cubic meter = 35.34 cubic feet 264.2 U.S. gallons (23 cu. in.).308 cubic yards cubic decimeter = 6.023 cubic inches.0353 cubic feet cubic centimeter =.06 cubic inch liter = cubic decimeter 6.023 cubic inches.0353 cubic foot.0567 quarts (U.S.).2642 gallon (U.S.) 2.202 lbs. of water at 62º F. cubic yard =.7645 cubic meter cubic foot =.02832 cubic meter 28.37 cubic decimeters 28.37 liters cubic inch = 6.383 cubic centimeters gallon (British) = 4.543 liters gallon (U.S.) = 3.785 liters MEASURES OF SURFACE square meter = 0.764 square feet.96 square yards square centimeter =.55 square inch square millimeter =.0055 square inch square yard =.836 square meter square foot =.0929 square meter square inch = 6.452 square centimeters 645.2 square millimeters MISCELLANEOUS kilogram per meter =.6720 pounds per foot gram per square millimeter =.422 pounds per square inch kilogram per square meter =.20482 per square foot kilogram per cubic meter =.06243 per cubic foot degree centigrade =.8 degrees fahrenheit pound per foot =.4882 kilograms per meter
GEOMETRIC FORMULAE Area of a square = length x breadth or height Area of a rectangle = length x breadth or height Area of a triangle = base x /2 altitude Area of a parallelogram = base x altitude Area of a trapezoid = altitude x /2 the sum of parallel sides Area of a trapezium = divide into two triangles, total their areas Circumference of a circle = diameter x 3.46 Circumference of a circle = radius x 6.28385 Diameter of a circle = circumference x.383 Diameter of a circle = square root of area x.2838 Radius of a circle = circumference x.05955 Area of a circle = half diameter x half circumference Area of a circle = square of diameter x.7854 Area of a circle = square of circumference x.07958 Area of a sector of a circle = length of arc x /2 radius Area of a segment of a circle = area of sector of equal radius-area of triangle, when the segment is less, and plus area of triangle when segment is greater than the semi-circle Area or circular ring = sum of the diameter of the two circles x difference of the diameter of the two circles and that product x.7854 Side of a square that shall equal area of a circle = diameter x.8862 Side of a square that shall equal area of a circle = circumference x.282 Diameter of a circle that shall contain area of a given square = side of square x.284 Side of an inscribed equilateral triangle = diameter x.86 Side of an inscribed square = diameter x.707 Side of an inscribed square = circumference x.225 Area of an ellipse = product of the two diameters x.7854 Area of a parabola = base x 2/3 of altitude Area of a regular polygon = sum of its sides x perpendicular from its center to one of its sides divided by 2 Surface of a sphere = diameter x circumference Solidity of a sphere = surface x /6 diameter Solidity of a sphere = cube of diameter x.5236 Solidity of a sphere = cube of radius x 4.888 Solidity of a sphere = cube of circumference x.06887 Diameter of a sphere = cube root of solidity x.2407 Diameter of a sphere = square root of surface x.5649 Circumference of a sphere = square root of surface x.772454 Circumference of a sphere = cube root of solidity x 3.8978 Contents of a segment of a sphere = (height squared plus three times the square of radius of base) x (height x.5236) Contents of a sphere = diameter x.5236 Side of an inscribed cube of a sphere = radius x.547 Side of an inscribed cube of a sphere = square root of diameter Surface of a pyramid or cone = circumference of base x /2 of the slant height plus area of base Contents of a pyramid or cone = area of base x /3 altitude Contents of frustrum of a pyramid or cone = sum of circumference at both ends x /2 slant height plus area of both ends Contents of frustrum of a pyramid or cone = multiply areas of two ends together and extract square root. Add to this root the two areas and x /3 altitude Contents of a wedge = area of base x /2 altitude
UNITS OF MEASUREMENT UNITS OF VOLUME AND WEIGHT Water in small tanks, cisterns and sumps is usually measured in gallons. Water in large tanks and small reservoirs is usually measured in cubic feet or gallons Water in large reservoirs is most commonly measured in acre-feet. Units U.S. Gallons Imperial Gallons Inches Feet Acre- Feet Pounds* Meters Liters U.S. Gallon = Imperial Gallon = Inch = Foot = Acre Foot = Pound = Meter = Liter =.20.00433 7.48 325,850 20 264.8.2642.833.00360 6.23 27,335.0998 220.220 23 277.4 728 27.7 6,023 6.023.337.605.000579 43,560.060 35.34.0353.00000307.00000369.0000230.0008 8.35 0.02.036 62.4 2204 2.2046.003785.004546.02832 233.5 3.785 4.546.064 28.32.454 000 *Weights shown are based on maximum density of fresh water at 39º F. UNITS OF FLOW foot per second, also written second-foot, is the unit of flow in the English system used to express rate of flow in large pumps, ditches and canals. Flow in pipe lines, from pumps and wells is commonly measured in gallons per minute. Rates of water consumption and measurement of municipal water supply are ordinarily made in million gallons per day. The Miner s Inch is still used in some localities for irrigation and hydaulic mining, but not suitable for general use. Units U.S. Gallons/ Minute Million U.S. Gallons/ Day Feet/ Second Meters/ Hour Liter/ Second Miner s Inch As Set By State Laws I II III U.S. Gallon/Minute (U.S. G.P.M.) = Million U.S. Gallons/ Day (M.GD) = Foot/Second = 694.5 448.8.00440.646.00223.547.2270 57.73 0.9.063 43.8 28.32.089 6.9 40.4 77.4 50.0856 59.4 38.4 Meter/Hour = Liter/Second = Miner s Inch (M.I.) I II III IV 4.403 5.85.22 8.98.69 2.58.00634.0228.068.0294.0682.08.0098.0353.0250.0200.0260.0280 3.60.2778 Ariz. Calif. Mont. Oreg. * Idaho Neb. Nev. N. Mex. Utah Kans. N. Dak. S. Dak. Colo. IV. A Miner s Inch legally set by British Columbia, 35.7 M.I. = Second-Foot *Usual practice in Southern California, 50 M.I. = Second-Foot = 448.8 G.P.M.