If you're
really bored (or simply curious), and you want to do this calculation by hand, here's how:
(Using the numbers from the original post.)
So my 67mm pistons in my CB750 stroke of 63mm = 888cc.
Since we want cubic centimeters (cc) as the final unit, we can either convert mm to cm first, or convert cubic-mm to cc last. I prefer to convert first in this case.
There are 10 mm in 1 cm:
bore (piston dia.):--> 67 mm = 6.7 cm
stroke:--> 63 mm = 6.3 cm
We want the volume of the displacement. This is the volume of a cylinder, the formula for which is
volume = piston cross-sectional area * stroke.
("*" means "times")
The cross-sectional area of the piston is the area of a circle:
Area = pi * radius-squared, or A = 3.1415 * r
2.
Putting it all together gives
displacement = 3.1415 * (bore/2)2 * stroke * number of cylinders.
Example:
Using the above numbers, we get
displacement = 3.1415 * [(6.7 cm)/2]
2 * 6.3 cm * 4
= 3.1415 * [3.35 cm]
2 * 6.3 cm * 4
= 3.1415 * 11.2225 cm
2 * 6.3 cm * 4
= 222.1160 cm
3 * 4
= 888.46 cm
3 (or cc's).
Good old geometry.
Notice the units work out correctly. This is one trick to doing calculations; carry the units throughout the calculation, and if the final units aren't what they should be, then you know to look for a mistake.