The surface area of a geometric shape can be calculated from key measurements. This can be used to determine the surface area of cells, organs or lesions.

Shape |
Formula for Total Surface |
Variables |

cube |
6 * a^2 |
a = length of side |

box |
2 * ((a * b) + (b * c) + (c * a)) |
a, b, c = lengths of sides |

cylinder |
2π * R * (R + h) |
R = radius of base h = height |

cone |
π * R * (R + SQRT((R^2) + (h^2))) |
R = radius of base h = height |

sphere |
4 * π * (R^2) |
R = radius |

torus |
(π^2) * a * b |
a = radius from center of inner space to innermost edge; b = radius from center of inner space to outermost edge |

where:

• Cylinders and cones also have a "lateral surface" which is total surface without the circular end(s)..

Shape |
Formula for Lateral Surface |
Variables |

zone and segment of sphere with 1 base |
2 * π * R * h |
r = radius of the sphere h = distance to top |

zone and segment of sphere with 2 bases |
2 * π * R * h |
R = radius of the sphere h = distance between planes |

lune (surface segment on sphere) |
2 * R * (angle in radians) |
R = radius of sphere; angle = angle subtended perpendicular to the central axis |

where:

• The equation for the zone and segment of sphere with 2 bases looks a little funny to me. This would mean that the surface area for a zone near the equator would be the same for a zone of the same height near the pole.