From Handbook of Machining and Metalworking Calculations


Mensuration is the mathematical name for calculating the areas, volumes, length of sides, and other geometric parts of standard geometric shapes such as circles, spheres, polygons, prisms, cylinders, cones, etc., through the use of mathematical equations or formulas. Included here are the most frequently used and important mensuration formulas for the common geometric figures, both plane and solid. (See Figs. 2.1 through 2.36.)




a, b, etc.


A, B, C



height perpendicular to base b


length of side or edge




number of sides






surface area

Figure 2.1: Oblique triangle.

Figure 2.2: Oblique triangle.

Figure 2.3: Rectangle.

Figure 2.4: Parallelogram.

Figure 2.5: Rhombus.

Figure 2.6: Trapezoid.

Figure 2.7: Polyhedra.

Figure 2.8: Trapezium.

Figure 2.9: Regular polygon.

Figure 2.10: Inscribed circle.

Figure 2.11: Circumscribed circle.

Figure 2.12: Inscribed polygon.

Figure 2.13: Circumscribed polygon.

Figure 2.14: Circle circumference.

Figure 2.15: Circle area.

Figure 2.16: Length of arc.

Figure 2.17: Chord and sector.

Figure 2.18: Segment of a circle.

Figure 2.19: Ring.

Figure 2.20: Ellipse.

Figure 2.21: Pyramid.

Figure 2.22: Sphere.

Figure 2.23: Cylinder.

Figure 2.24: Cone.

Figure 2.25: Spherical segment.

Figure 2.26: Frustum of a cone.

Figure 2.27: Truncated cylinder.

Figure 2.28: Spherical zone.

Figure 2.29: Spherical wedge.

Figure 2.30: Paraboloid.

Figure 2.31: Spherical sector.

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Hydraulic cylinders are actuation devices that utilize pressurized hydraulic fluid to produce linear motion and force.
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Surface metrology equipment is used to measure the surface finish and/or geometry of engineering components. Surface texture and topology characteristics include surface roughness, contour, form, waviness, and defects.

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