How to estimate the number of components on a tape reel?

Question

I have a partial reel of tape with components. The label says 2500 pieces. Counting the outermost layer (60 pieces) and multiplying it with the number of turns (15) gives 900 pieces. But the inner turns will have fewer components.

The spool has an indicator like a ruler which goes from 1 to 11. The belt ends at ~3.5. But I have no idea how full it may have been originally.

As a hobbyist I don't have a counting machine or similar. Is there a known approach to get a better estimate except counting manually? If you do math, please mention the formula, since I have many other reels like this with different number of turns, diameters etc.

Here’s how my reel(s) look like:

The component is ST72F324BK6T3.

Answer 1

An interesting geometry problem. It is easiest to understand in Excel. Doing it in calculus would be cool, but I am rusty.

The radius measurements are in arbitrary units, it doesn't matter (I measured with a ruler in Photoshop). The bold numbers are the inputs.

Answer 2

CompuPhase has a reel quantity estimate calculator available online.

It works by the basic geometry calculations and gives results in number of components remaining:

Answer 3

The length will be

$$L = \frac {A_{spiral}} t $$ where \$ A \$ is the area of the spriral and \$t\$ the thickness of a layer.

$$L = \frac {A_{spiral}} t = \frac {\pi R^2 - \pi r^2} t$$

where \$R\$ is the outer radius and \$r\$ is the inner radius.

The number of pieces is given by $$ \frac L p $$ where \$p\$ is the pitch of the components.

Answer 4

You need to measure the inside and outside diameters of the spiral. From the circumference of the outermost turn you know the components per cm (or inch). There is an online spiral length calculator here.
The calculation is then trivial multiplication.

Using Mattman944's numbers (thanks Mattman944) the length of the spiral is 74.4 units and the count per length is 9.5 giving a total count of 707. Which is in complete agreement with Mattman944's answer, but doesn't require Excel.

Answer 5

You can get the average length of all loops by taking the average of the outermost and innermost loops. Then you can multiply the average you get with the number of loops you can see, and you get the total length, which you can use to calculate the number of components in the reel.

You can do the simplification I mentioned (outside length + inside length)/2 because the relationship between the length of the loop and the radius is linear.

Answer 6

Another way of calculating it is just from the 3 diameters

• The spool's OD (when full and containing 2500 units) D
• The diameter of the remaining units spiral S
• The inner diameter of the spool, the hub. d The number of items is proportional to the area.
  Then \$2500 ∝ D^2 - d^2\$ (the area of the full spool omitting pi)
  remaining units \$∝ S^2 - d^2\$
  thus remaining units = \$2500 * (S^2 - d^2) / (D^2 - d^2)\$
  No need to know the units per length.