ABSTRACT
Millimetre mm 1 in = 25.4 mm 1 mm = 0.0394 in Centimetre cm 1 in = 2.54 cm 1 cm = 0.3937 in Metre m 1 ft = 0.3048 m 1 m = 3.2808 ft
1 yd = 0.9144 m = 1.0936 yd Kilometre km 1 mile = 1.6093 km 1km = 0.6214 mile
Note: 1 cm = 10 mm 1 ft = 12 in 1 m = 1 000 mm 1 yd = 3 ft 1 km = 1 000 m 1 mile = 1 760 yd
Area Unit Conversion factors
Square Millimetre mm2 1 in2 = 645.2 mm2 1 mm2 = 0.0016 in2
Square Centimetre cm2 1 in2 = 6.4516 cm2 1 cm2 = 1.1550 in2
Square Metre m2 1 ft2 = 0.0929 m2 1 m2 = 10.764 ft2
1 yd2 = 0.8361 m2 1 m2 = 1.1960 yd2
Square Kilometre km2 1 mile2 = 2.590 km2 1 km2 = 0.3861 mile2
Note: 1 cm2 = 100 mm2 1 ft2 = 144 in2
1 m2 = 10 000 cm2 1 yd2 = 9 ft2
1 km2 = 100 hectares 1 acre = 4 840 yd2
1 mile2 = 640 acres
Volume Unit Conversion factors
Cubic Centimetre cm3 1 cm3 = 0.0610 in3 1 in3 = 16.387 cm3
Cubic Decimetre dm3 1 dm3 = 0.0353 ft3 1 ft3 = 28.329 dm3
Cubic Metre m3 1 m3 = 35.3147 ft3 1 ft3 = 0.0283 m3
1 m3 = 1.3080 yd3 1 yd3 = 0.7646 m3
Litre l 1 l = 1.76 pint 1 pint = 0.5683 l = 2.113 US pt = 0.4733 US l
Note: 1 dm3 = 1 000 cm3 1 ft3 = 1 728 in3 1 pint = 20 fl oz 1 m3 = 1 000 dm3 1 yd3 = 27 ft3 1 gal = 8 pints 1 l = 1 dm3
Mass Unit Conversion factors
Milligram mg 1 mg = 0.0154 grain 1 grain = 64.935 mg Gram g 1 g = 0.0353 oz 1 oz = 28.35 g Kilogram kg 1 kg = 2.2046 lb 1 lb = 0.4536 kg Tonne t 1 t = 0.9842 ton 1 ton = 1.016 t
Note: 1 g = 1000 mg 1 oz = 437.5 grains 1 cwt = 112 lb 1 kg = 1000 g 1 lb = 16 oz 1 ton = 20 cwt 1 t = 1000 kg 1 stone = 14 lb
Force Unit Conversion factors
Newton N 1 lbf = 4.448 N 1 kgf = 9.807 N Kilonewton kN 1 lbf = 0.004448 kN 1 ton f = 9.964 kN Meganewton MN 100 tonf = 0.9964 MN
Pressure and stress Unit Conversion factors
Kilonewton per square metre kN/m2 1 lbf/in2 = 6.895 kN/m2
1 bar = 100 kN/m2
Meganewton per square metre MN/m2 1 tonf/ft2 = 107.3 kN/m2 = 0.1073 MN/m2
1 kgf/cm2 = 98.07 kN/m2
1 lbf/ft2 = 0.04788 kN/m2
Coefficient of consolidation (Cv) or swelling
Unit Conversion factors
Square metre per year m2/year 1 cm2/s = 3 154 m2/year 1 ft2/year = 0.0929 m2/year
Coefficient of permeability Unit Conversion factors
Metre per second m/s 1 cm/s = 0.01 m/s Metre per year m/year 1 ft/year = 0.3048 m/year
= 0.9651 × (10)8m/s
Temperature Unit Conversion factors
Degree Celsius °C °C = 5/9 × (°F − 32) °F = (9 × °C)/ 5 + 32
Power Unit Conversion factors
Kilowatt kW 1kW = 1.341HP Horsepower HP 1HP = 0.746 kW
km/h m/min mph fpm
1 16.7 0.6 54.7 2 33.3 1.2 109.4 3 50.0 1.9 164.0 4 66.7 2.5 218.7 5 83.3 3.1 273.4
6 100.0 3.7 328.1 7 116.7 4.3 382.8 8 133.3 5.0 437.4 9 150.0 5.6 492.1
10 166.7 6.2 546.8
11 183.3 6.8 601.5 12 200.0 7.5 656.2 13 216.7 8.1 710.8 14 233.3 8.7 765.5 15 250.0 9.3 820.2
16 266.7 9.9 874.9 17 283.3 10.6 929.6 18 300.0 11.2 984.3 19 316.7 11.8 1038.9 20 333.3 12.4 1093.6
21 350.0 13.0 1148.3 22 366.7 13.7 1203.0 23 383.3 14.3 1257.7 24 400.0 14.9 1312.3 25 416.7 15.5 1367.0
26 433.3 16.2 1421.7 27 450.0 16.8 1476.4 28 466.7 17.4 1531.1 29 483.3 18.0 1585.7 30 500.0 18.6 1640.4
31 516.7 19.3 1695.1 32 533.3 19.9 1749.8 33 550.0 20.5 1804.5 34 566.7 21.1 1859.1 35 583.3 21.7 1913.8
36 600.0 22.4 1968.5 37 616.7 23.0 2023.2 38 633.3 23.6 2077.9 39 650.0 24.2 2132.5 40 666.7 24.9 2187.2
41 683.3 25.5 2241.9 42 700.0 26.1 2296.6 43 716.7 26.7 2351.3 44 733.3 27.3 2405.9 45 750.0 28.0 2460.6
km/h m/min mph fpm
46 766.7 28.6 2515.3 47 783.3 29.2 2570.0 48 800.0 29.8 2624.7 49 816.7 30.4 2679.4 50 833.3 31.1 2734.0
Figure Diagram of figure Surface area Perimeter
Square a2 4a
Rectangle ab 2ðaþ bÞ
Triangle 12 ch aþ bþ c
where 2r ¼ d
2r d
Parallelogram ah 2ðaþ bÞ
Trapezium 12 hðaþ bÞ aþ bþ cþ d
Ellipse Approximately ab
ðaþ bÞ
Hexagon 2:6 a2
Figure Diagram of figure Surface area Perimeter
Octagon 4:83 a2 6a
Sector of a circle
note b ¼ angle q360 2r
Segment of a circle
S T where S = area of sector,
T = area of triangle
Figure Diagram of figure Surface area Volume
Cube 6a2 a3
Cuboid/ rectangular block
2ðabþ acþ bcÞ abc
Prism/ triangular block
bdþ hcþ dcþ ad 12 hcd
Cylinder 2r2 þ 2h r2h 1 4d
Segment of sphere
2ð3R HÞ
Pyramid ðaþ bÞIþ ab 13 abh
Figure Diagram of figure Surface area Volume
Frustum of a pyramid
Iðaþ bþ cþ dÞ þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðabþ cdÞp [rectangular figure only]
ffiffiffiffiffiffiffiffiffiffiffi abcd
p Þ
Cone rl (excluding base)
rlþ r2 (including base)
Frustum of a cone
r2 þ R2 þ lðRþ rÞ 13ðR2 þ Rr þ r2Þ
Formula Description
Pythagoras theorem A2 = B2 + C2
where A is the hypotenuse of a right-angled triangle and B and C are the two adjacent sides
Simpsons Rule The Area is divided into an even number of strips of equal width, and therefore has an odd number of ordinates at the division points
area = SðAþ 2Bþ 4CÞ
where S = common interval (strip width) A = sum of first and last ordinates B = sum of remaining odd ordinates C = sum of the even ordinates
The Volume can be calculated by the same formula, but by substituting the area of each coordinate rather than its length
Trapezoidal Rule A given trench is divided into two equal sections, giving three ordinates, the first, the middle and the last
volume = S ðAþ Bþ 2CÞ
where S = width of the strips A = area of the first section B = area of the last section C = area of the rest of the sections
Prismoidal Rule A given trench is divided into two equal sections, giving three ordinates, the first, the middle and the last
volume = L ðAþ 4Bþ CÞ
where L = total length of trench A = area of the first section B = area of the middle section C = area of the last section
Material kg/m³ lb/cu yd
Adobe 1914 3230 Ashes 610 1030 Asphalt, rock 2400 4050 Basalt 2933 4950 Bauxite: alum ore 2619 4420
Borax 1730 2920 Caliche 1440 2430 Carnotite 2459 4150 Cement 1600 2700 Chalk (hard) 2406 4060
Cinders 759 1280 Clay: dry 1908 3220 Clay: wet 1985 3350 Coal: bituminous 1351 2280 Coke 510 860
Conglomerate 2204 3720 Dolomite 2886 4870 Earth: dry 1796 3030 Earth: moist 1997 3370 Earth: wet 1742 2940
Feldspar 2613 4410 Felsite 2495 4210 Fluorite 3093 5220 Gabbro 3093 5220 Gneiss 2696 4550
Granite 2690 4540 Gravel, dry 1790 3020 Gypsum 2418 4080 Hardcore (consolidated) 1928 120 Lignite broken 1244 2100
Limestone 2596 4380 Magnesite, magnesium ore 2993 5050 Marble 2679 4520 Marl 2216 3740 Peat 700 1180
Potash 2193 3700 Pumice 640 1080 Quarry waste 1438 90 Quartz 2584 4360 Rhyolite 2400 4050
Material kg/m³ lb/cu yd
Sand: dry 1707 2880 Sand: wet 1831 3090 Sand and gravel – dry 1790 3020
– wet 2092 3530 Sandstone 2412 4070
Schist 2684 4530 Shale 2637 4450 Slag (blast) 2868 4840 Slate 2667 4500 Snow – dry 130 220
– wet 510 860
Taconite 3182 5370 Topsoil 1440 2430 Trachyte 2400 4050 Traprock 2791 4710 Water 1000 62
Type of vehicle Capacity of vehicle
Payload Heaped capacity
Wheelbarrow 150 0.10 1 tonne dumper 1250 1.00 2.5 tonne dumper 4000 2.50 Articulated dump truck (Volvo A20 6 × 4) 18500 11.00 Articulated dump truck (Volvo A35 6 × 6) 32000 19.00 Large capacity rear dumper (Euclid R35) 35000 22.00 Large capacity rear dumper (Euclid R85) 85000 50.00
Machine type Cycles per minute Volume per minute (m3)
1.5 tonne excavator 1 0.04 2 0.08 3 0.12
3 tonne excavator 1 0.13 2 0.26 3 0.39
5 tonne excavator 1 0.28 2 0.56 3 0.84
7 tonne excavator 1 0.28 2 0.56 3 0.84
21 tonne excavator 1 1.21 2 2.42 3 3.63
Backhoe loader JCB3CX excavator 1 0.28 Rear bucket capacity 0.28m3 2 0.56
3 0.84
Backhoe loader JCB3CX loading 1 1.00 Front bucket capacity 1.00m3 2 2.00
Machine type Loads per hour Volume per hour (m3)
1 tonne high tip skip loader 5 2.43 Volume 0.485m3 7 3.40
10 4.85
3 tonne dumper 4 7.60 Max volume 2.40m3 5 9.50 Available volume 1.9m3 7 13.30
10 19.00
6 tonne dumper 4 15.08 Max volume 3.40m3 5 18.85 Available volume 3.77m3 7 26.39
10 37.70
Type of soil Approximate bulking of 1m3 after excavation
Vegetable soil and loam 25-30% Soft clay 30-40% Stiff clay 10-20% Gravel 20-25% Sand 40-50% Chalk 40-50% Rock, weathered 30-40% Rock, unweathered 50-60%
Type of soil Approximate bulking of 1m3 after excavation
Clay 10% Gravel 8% Gravel and sand 9% Loam and light sandy soils 12% Loose vegetable soils 15%
Material m3 of voids/m3
Alluvium 0.37 River grit 0.29 Quarry sand 0.24 Shingle 0.37 Gravel 0.39 Broken stone 0.45 Broken bricks 0.42
Type of soil Degrees
Clay – dry 30 – damp, well drained 45 – wet 15-20
Earth – dry 30 – damp 45
Gravel – moist 48 Sand – dry or moist 35
– wet 25 Loam 40
Ratio of base to height Angle in degrees
5:1 11 4:1 14 3:1 18 2:1 27 1½:1 34 1:1 45 1:1½ 56 1:2 63 1:3 72 1:4 76 1:5 79
Degrees Percent Degrees Percent
1 1.8 24 44.5 2 3.5 25 46.6 3 5.2 26 48.8 4 7.0 27 51.0 5 8.8 28 53.2 6 10.5 29 55.4 7 12.3 30 57.7 8 14.0 31 60.0 9 15.8 32 62.5
10 17.6 33 64.9 11 19.4 34 67.4 12 21.3 35 70.0 13 23.1 36 72.7 14 24.9 37 75.4 15 26.8 38 78.1 16 28.7 39 81.0 17 30.6 40 83.9 18 32.5 41 86.9 19 34.4 42 90.0 20 36.4 43 93.3 21 38.4 44 96.6 22 40.4 45 100.0
Ground conditions Bearing power
kg/m2 lb/in2 Metric t/m2
Rock, broken 483 70 50 solid 2415 350 240
Clay, dry or hard 380 55 40 medium dry 190 27 20 soft or wet 100 14 10
Gravel, cemented 760 110 80
Sand, compacted 380 55 40 clean dry 190 27 20
Swamp and alluvial soils 48 7 5
Ground conditions Feet (ft) Metres (m)
Compact soil 12 3.66 Drained loam 6 1.83 Dry sand 1 0.3 Gravelly earth 2 0.61 Ordinary earth 3 0.91 Stiff clay 10 3.05
Type of material kg/m³ lb/cu ft
Ordinary concrete (dense aggregates)
Non-reinforced plain or mass concrete Nominal weight 2305 144 Aggregate – limestone 2162 to 2407 135 to 150
– gravel 2244 to 2407 140 to 150 – broken brick 2000 (av) 125 (av) – other crushed stone 2326 to 2489 145 to 155
Reinforced concrete Nominal weight 2407 150 Reinforcement – 1% 2305 to 2468 144 to 154
– 2% 2356 to 2519 147 to 157 – 4% 2448 to 2703 153 to 163
Special concretes
Heavy concrete Aggregates – barytes, magnetite 3210 (min) 200 (min)
– steel shot, punchings 5280 330
Lean mixes Dry-lean (gravel aggregate) 2244 140 Soil-cement (normal mix) 1601 100
Type of material kg/m2 lb/sq ft per mm thick per inch thick
Ordinary concrete (dense aggregates)
Solid slabs (floors, walls etc.) Thickness: 75mm or 3 in 184 37.5
100mm or 4 in 245 50 150mm or 6 in 378 75 250mm or 10 in 612 125 300mm or 12 in 734 150
Ribbed slabs Thickness: 125mm or 5 in 204 42
150mm or 6 in 219 45 225mm or 9 in 281 57 300mm or 12 in 342 70
Special concretes
Finishes etc. Rendering, screed etc. Granolithic, terrazzo 1928 to 2401 10 to 12.5
Glass-block (hollow) concrete
1734 (approx) 9 (approx)
Prestressed concrete Weights as for reinforced concrete (upper limits)
Air-entrained concrete Weights as for plain or reinforced concrete
Materials Voids % Weight kg/m3
Sand 39 1660 Gravel 10-20mm 45 1440 Gravel 35-75mm 42 1555 Crushed stone 50 1330 Crushed granite (over 15mm) 50 1345 (n.e. 15mm) 47 1440 'All-in' ballast 32 1800-2000
Material kg/m³ lb/cu yd
Vermiculite (aggregate) 64-80 108-135
All-in aggregate 1999 125
Recommended mix
Class of work suitable for Cement Sand Coarse aggregate
Nr 25 kg bags cement per
m3 of combined aggregate
(kg) (kg) (kg)
1:3:6 Roughest type of mass concrete such as footings, road haunching over 300mm thick
208 905 1509 8.30
1:2.5:5 Mass concrete of better class than 1:3:6 such as bases for machinery, walls below ground etc.