 Online Calculators

# Geometric Shapes

### Capsule

Capsule Calculator
• Volume = πr2((4/3)r + a)
• Surface Area = 2πr(2r + a)
• Circumference = 2πr

Also called a stadium of revolution.

### Circular Cone

Circular Cone Calculator
• Volume = (1/3)πr2h
• Slant Height = √(r2 + h2)
• Lateral Surface Area = πrs = πr√(r2 + h2)
• Base Surface Area = πr2
• Total Surface Area
= L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

### Circular Cylinder

Circular Cylinder Calculator
• Volume = πr2h
• Lateral Surface Area = 2πrh
• Top Surface Area = πr2
• Bottom Surface Area = πr2
• Total Surface Area
= L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

### Conical Frustum

Conical Frustum Calculator
• Volume = (1/3)πh (r12 + r22 + (r1 * r2))
• Slant Height = √((r1 - r2)2 + h2)
• Lateral Surface Area
= π(r1 + r2)s = π(r1 + r2)√((r1 - r2)2 + h2)
• Top Surface Area = πr12
• Base Surface Area = πr22
• Total Surface Area
= π(r12 + r22 + (r1 + r2) * s)
= π[ r12 + r22 + (r1 + r2) * √((r1 - r2)2 + h2) ]

### Cube

Cube Calculator
• Volume = a3
• Surface Area = 6a2
• Face Diagonal (f) = a√2
• Diagonal (d) = a√3

### Hemisphere

Hemisphere Calculator
• Volume = (2/3)πr3
• Circumference = 2πr
• Curved Surface Area = 2πr2
• Base Surface Area = πr2
• Total Surface Area= (2πr2) + (πr2) = 3πr2

### Pyramid : Square

Pyramid Calculator
• Volume = (1/3)a2h
• Slant Height (s) = √(h2 + (1/4)a2)
• Lateral Surface Area = a√(a2 + 4h2)
• Base Surface Area = a2
• Total Surface Area
= L + B = a2 + a√(a2 + 4h2))
= a(a + √(a2 + 4h2))

### Rectangular Prism

Rectangular Prism Calculator
• Volume = lwh
• Surface Area = 2(lw + lh + wh)
• Diagonal (d) = √(l2 + w2 + h2)

### Sphere

Sphere Calculator
• Volume = (4/3)πr3
• Circumference = 2πr
• Surface Area = 4πr2

### Spherical Cap

Spherical Cap Formulas
• Volume
= (1/6)πh(3a2 + h2)
= (1/3)πh2(3R - h)
• Radius Base Circle = √h(2R - h)
• Circumference Base Circle = 2π√h(2R - h)
• Surface Area = 2πRh = π(a2 + h2)

### Spherical Segment

Spherical Segment Formulas
• Volume = (1/6)πh(3a2 + 3b2 + h2)
• Top Surface Area = πb2
• Bottom Surface Area = πa2
• Lateral Surface Area = 2πRh
• Where R = sphere radius and
• R = √{ [ [(a-b)2 + h2] [(a+b)2 + h2] ] / 4h2 }

### Triangular Prism

Triangular Prism Formulas
• Volume = (1/4)h √[(a+b+c)(b+c-a)(c+a-b)(a+b-c)]
• Top Surface Area = (1/4) √[(a+b+c)(b+c-a)(c+a-b)(a+b-c)]
• Bottom Surface Area = (1/4) √[(a+b+c)(b+c-a)(c+a-b)(a+b-c)]
• Lateral Surface Area = h(a+b+c)
• Total Surface Area = Top Surface Area + Bottom Surface Area + Lateral Surface Area

### Tube

Tube Calculator (Hollow Cylinder)
• Circumference, C:
• C1 = 2πr1
• C2 = 2πr2
• Lateral Surface Area, L, for a cylinder:
• L1 = 2πr1h, the external surface area
• L2 = 2πr2h, the internal surface area
• Area, A, for the end cross section of the tube:
• A1 = πr12 for the area enclosed by C1
• A2 = πr22 for the area enclosed by C2
• A = A1 - A2 = π(r12 - r22) for the area of the solid cross section of the tube, the end, an annulus.
• Volume, V, (using volume for a cylinder):
• V1 = πr12h for the volume enclosed by C1
• V2 = πr22h for the volume enclosed by C2
• V = V1 - V2 = π(r12 - r22)h for the volume of the solid, the tube.
• Thickness of the tube wall, t:
• t = r1 - r2

Cite this content, page or calculator as:

Furey, Edward "Geometric Shapes and Formulas in Solid Geometry" at https://www.calculatorsoup.com/calculators/geometry-solids/geometricshapes.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: October 4, 2023