calculand - Formula collection, page 1

Area Formulas

Annulus
Circle [π·r²]Circle [¼·π·d²]
Circular Sector
Circular Segment
Cone
Cube
Cuboctahedron
Cuboid
Decagon
Dodecagon [3·(2+√3)·a²]Dodecagon [12·(2-√3)·r²]Dodecagon [3·R²]Dodecagon [3·a²·cot(180°/12)]
Dodecahedron
Ellipse
Event Horizon
Heptagon [¼·7·a²·cot(180°/7)]Heptagon [½·7·R²·sin(360°/7)]Heptagon [7·r²·tan(180°/7)]
Hexagon [½·3·√3·a²]Hexagon [3·R·r]Hexagon [2·√3·r²]Hexagon [½·√3·d²]Hexagon [3/4·D·d]
Icosagon [5·(1+√5+√(5+2·√5))·a²]Icosagon [½·5·(√5-1)·R²]
Icosahedron
Nonagon [¼·9·a²·cot(180°/9)]Nonagon [½·9·R²·sin(360°/9)]Nonagon [9·r²·tan(180°/9)]
Octagon [(2+2·√2)·a²]Octagon [2·√2·R²]Octagon [8·(√2-1)·r²]
Octahedron
Parallelogram
Pentagon [¼·√(25+10·√5)·a²]Pentagon [¼·5·√((5+√5)/2)·R²]
Permeability
Planck Area
Polygon [¼·n·a²·cot(180°/n)]Polygon [n·r²·tan(180°/n)]Polygon [½·n·R²·sin(360°/n)]
Rectangle
Rhombus [½·e·f]Rhombus [2·a·r]
Sphere
Spherical Cap
Spheroid [oblate: 2·π·a·(a+c²/√(a²-c²)·arsinh(√(a²-c²)/c))]Spheroid [prolate: 2·π·a·(a+c²/√(c²-a²)·arcsin(√(c²-a²)/c))]
Square
Tetragon [¼·√(4·e²·f²(b²+d²a²-c²))]Tetragon [½·e·f·sinθ]
Tetrahedron
Tetrakis hexahedron
Thomson Cross Section [⅓·8·π·rₑ²]Thomson Cross Section [⅙·e⁴/(π·εₒ²·mₑ²·c⁴)]Thomson Cross Section [⅓·8·π·(α·ħ/(mₑ·c))²]
Torus
Trapezoid
Triangle [½·l·h]Triangle [½·a·b·sinγ]Triangle [√(½·P·(½·P-a)·(½·P-b)·(½·P-c))]

© 2010 - 2018 Norbert Schneider