Formulae

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

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

Square metre per year m2/year 1 cm2/s = 3 154 m2/year 1 ft2/year = 0.0929 m2/year

Coefficient of permeability

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 x (10)8m/s

Temperature

Degree Celsius °C °C = 5/9 x (°F - 32) °F = (9 x °C)/ 5 + 32

FORMULAE

Two dimensional figures

Figure Area

Square (side)2

Rectangle Length x breadth

Triangle ½ (base x height) or √(s(s - a)(s-b)(s-c)) where a, b and c are the lengths of the three sides, and s = (a + b + c)/ 2

or a2 = b2 + c2 - (2b ccosA) where A is the angle opposite side a

Hexagon 2.6 x (side)2

Octagon 4.83 x (side)2

Trapezoid height x ½ (base + top)

Circle 3.142 x radius2 or 0.7854 x diameter2 (circumference = 2 x 3.142 x radius or 3.142 x diameter)

Two dimensional figures

Figure Area

Sector of a circle ½ x length of arc x radius

Segment of a circle area of sector - area of triangle

Ellipse 3.142 x AB (where A = ½ x height and B = ½ x length)

Bellmouth 3/14 x radius2

Three dimensional figures

Figure Volume Surface Area

Prism Area of base x height circumference of base x height

Cube (side)3 6 x (side)2

Cylinder 3.142 x radius2 x height 2 x 3.142 x radius x (height - radius)

Sphere 4/3 x 3.142 x radius3 4 x 3.142 x radius2

Segment of a sphere ((3.142 x h) x (3 x r2 + h2))/6 2 x 3.142 x r x h

Pyramid 1/3 of area of base x height ½ x circumference of base x slant height

Cone 1/3 x 3.142 x radius2 x h 3.142 x radius x slant height

Frustrum of a pyramid 1/3 x height [A + B + √(AB)] ½ x mean circumference x slant height where A is the area of the large end and B is the area of the small end

Frustrum of a cone (1/3 x 3.142 x height (R2 + r2 + R x r)) 3.142 x slant height x (R + r) where R is the radius of the large end and r is the radius of the small end

Other formulae

Formula Description

Pythagoras’ theorum A2 = B2 + C2 where A is the hypotenuse of a right-angled triangle and B and C are the two adjacent sides

Simpson’s Rule Volume = x/3 [(y1 + yn) + 2(y3 + y5) + 4(y2 + y4)] The volume to be measured must be represented by an odd number of cross-sections (y1 -yn) taken at fixed intervals (x), the sum of the areas at even numbered intermediate crosssections (y2, y4, etc.) is multiplied by 4 and the sum of the areas at odd numbered intermediate cross-sections (y3, y5, etc.) is multiplied by 2, and the end cross-sections (y1 and yn) taken once only. The resulting weighted average of these areas is multiplied by 1/3 of the distance between the cross-sections (x) to give the total volume.