The formulas for ellipses and ellipsoids plus over 170 other things are all in The Perfect Sausage
You'll find lots of formulas for getting the areas of different shapes in Desperate Measures but ellipses are just that little bit harder to work out!
Here's our way:
Put the ellipse inside the smallest rectangle you can
Work out the area of the rectangle ( by multipling the lengths of the sides together)
Divide the area of the rectangle by 4
Finally multiply by pi!
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If putting the ellipse into a rectangle looks too tough, you can just measure how long it is to get A, and then measure how fat it is to get B, then multiply the two results together. You then divide by 4 and multiply by pi. 2m2j6u
The length A is often called the "Major Axis" and B is the "Minor Axis".
Sometimes you're given the lengths of the "longest radius" (shown here as a) and the "shortest radius" (shown here as b). Obviously in our diagrams a = ½A and b = ½B in which case you get this formula:
Of course the EASIEST way to work out the area of an ellipse is to use our Area Calculator 5v621i
There's more about ellipses on our EXCELLENT ELLIPSE PAGE 5t4a1e
Thanks to JAKE CHAN who was the first person to us and ask about ellipses! 6h5q3f
The Volume of an Ellipsoid 5x6l56
In the same way that a circle turns into a solid sphere, an ellipse can become a solid "ellipsoid". 563060
There are two special types of ellipsoid. 495g42
Suppose you get a sphere and stretch it to make a longer and thinner shape (a bit like a rugby ball or a melon) this is called a PROLATE ELLIPSOID. If you chop it in half to get a circle, then the volume is the area of the circle times by 2/3rds of the major axis. (The major axis is the maximum length from one end to another.) 5s6o3n
However if you get a sphere and squash it to make a shorter fatter shape (a bit like a SMARTIE or a burger) this is called an OBLATE ELLIPSOID. If you chopped it through the middle to get a circle, then the volume is the area of the circle times by 2/3rds of the minor axis. (If your "burger" is lying flat on a table, the minor axis is the height.) 6x86r
Many thanks to "Pete" who ed us with corrections to this page in April 2005.
