7696 Route 31, Lyons, NY 14489
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www.caswellplating.com [email protected]
Calculating Surface Areas for Electroplating Purposes
In order to apply the correct amount of current to the work piece, we need to have a good idea of
the total surface area being plated.
Caswell plating solutions have fairly precise current requirements and using too much or
too little power can seriously affect the end result.
Excessive power will result in a rough, dark finish, with poor adhesion properties.
Insufficient current will result in only areas nearest to the anodes being plated.
Most parts being plated are awkward shapes, which, at first glance, could mean much time is
spent calculating the surface area. This would, of course, be unproductive, so we need to define
the degree of accuracy needed here.
As there are several other variables which affect the current, such as bath temperature, distance
from the anode, and rectifier fine-tuning, we do not need 100% accuracy with our calculations. In
fact, a 10-15% error factor is quite acceptable. This tolerant operating range greatly simplifies our
calculations.
Lets begin with FLAT surfaces and the calculations needed for these. Once we have established
the flat surfaces, we can go onto the more complicated calculations of three-dimensional objects.
Here are several basic shapes with their formulae and an example calculation.
We have substituted π or pi (pronounced ‘pie’) for 3.14. (pi is used in circle/ellipse calculations)
h= height
l= length
r = radius
b = base
w = width
Square
Rectangle
Circle
Ellipse
Triangle
h x l” =
hxl=
r x r x 3.14=
r1 x r2 x 3.14 =
bxh ÷2=
2” x 2” =4sq”
2” x 3” = 6sq”
2” x 2” x 3.14
= 12.56sq”
2” x 3” x 3.14
=18.84sq”
3” x 2.5” ÷
3.75sq”
2 =
To effectively work out a complex surface area, as
shown left, simply place an imaginary grid of 1”
squares over the part, and count the whole squares.
Then go around the perimeter and add up all the
squares that are more than ½ full. Divide the total by
2 and add this to your total of completely filled
squares.
CALCULATING AREA OF THREE DIMENSIONAL OBJECTS
Cube
Brick
Sphere
Egg
Pyramid
hxlx6=
(2 x h x l) + (2 x l x w) +
(2 x h x w) =
4 x r x r x
3.14=
4 x r1 x r2 x 3.14
=
Calculate each side
like a triangle, add all
sides together. Add
base
2” x 2” x 6 =
24sq”
(2 x 2” x 3”) + (2 x 3” x
1”) + (2 x 2” x 1”) = 12 +
6 + 4= 22 sq”
4 x 2” x 2” x
3.14
= 50.24sq”
4” x 2” x 3” x
3.14 =75.36sq”
Hollow Tube
(Inside & Outside)
Solid Rod
2 x 3.14 x 0.5 x d x h =
(2 x 3.14 x r x r) +
(2 x 3.14 x r x h)
2 x 3.14 x 0.5 x 4”x 4” =
50.24sq”
(2 x 3.14 x 2” x
2”) + (2 x 3.14 x
2” x 4”) = 25.12 +
50.24= 75.36 sq”
CALCULATING THE SURFACE AREA OF IRREGULAR SHAPED THREE DIMENSIONAL
OBJECTS
When calculating surface area of an item, we are basically working out the area of the object if it
has been totally flattened out.
To work out the area of irregular shaped items, cover the entire part in one layer of newspaper or
tinfoil. Make sure every part is covered, and try not to overlap the newspaper.
Once the part is covered, remove the newspaper and arrange it into a shape as close to a
rectangle as possible. You may need to tear it into smaller parts to get it into a rectangle shape.
Then simply multiply the Length x Width of the rectangle to get your surface area.
CALCULATING THE SURFACE AREA OF BOLTS
There are 3 dimensions we need to calculate on a bolt. In this exercise, ignore the threads, and
consider this area to be a cylinder
1. The shank.
2. The flats or sides of the head
3. The top of the head.
To calculate the shank of the bolt: regard it as a tube. Therefore 2 x 3.14 x r x L
above)
(see tube
In this example, there are 4 sides, or ‘flats’ to the head of the bolt.
(Some bolts have 6 sides, so, in that situation, you need to use D x H x 6)
Measure each ‘flat’s’ surface area and multiply that answer by the number of flats.
Therefore D x H x 4
To quickly calculate the surface area of the head, the bottom of the bolt and the underside of the
head, calculate the area of the top as a square, multiply by two and then subtract the area of the
bottom of the shank.
(F x F x 2) – (3.14 x r x r)
Your final total calculations are:
D x H x 4 + (F x F x 2) – (3.14 x r x r) + 2 x 3.14 x r x L = total surface area of bolt
These figures are only guides, designed for approximate, quick calculations.