# Calculate coil diameter using length and thickness of the material

I'm developing a software for a stainless steel plant, and I need to calculate the diameter of steel coils so the software assigns a position inside a deposit according to the size of the coil.

I have access to a lot of data from the coil, and tried thinking of a way to calculate using the inner hole diameter and the length and thickness of the steel strip.

In a research I've found this formula:

L = 3,141[(D2/2)² - (D1/2)²]/T


Where

  L = Length of the coil

D1 = Diameter of the inner hole

D2 = Diameter of the coil

T = Thickness of the material


But in the software I have to put in this format:

D2 = (formula)


I'm no good with math, how can I "convert" the formula to suit my needs?

• $$D2=2\times\sqrt{\frac{2L}{3.141}+\left(\frac{D1}{2}\right)^2}$$ Oct 18, 2015 at 15:39
• I wrote the formula wrong, put 2 instead of T, could you post this comment (corrected with the T) in the answer section so I could accept it? Oct 18, 2015 at 16:53

What you need to do is called changing the subject of the formula. \begin{align} L = \frac{3,141\left[(D2/2)^2 + (D1/2)^2\right]}{T}\\ \\ \hline\\ \text{Multiplying by}\; \frac{T}{3,141}\; \text{on both sides}:\frac{TL}{3,141} &= \left[(D2/2)^2 + (D1/2)^2\right]\\ \text{Adding} \;(D1/2)^2 \;\text{on both sides}:\frac{TL}{3,141}+ (D1/2)^2 &= \left[(D2/2)^2 \right]\\ \text{Taking square roots on both sides}:\sqrt{\frac{TL}{3,141}+ (D1/2)^2 }&= \sqrt{\left[(D2/2)^2 \right]}=D2/2\\ \text{Multiplying both sides by}\; 2:2\times\sqrt{\frac{TL}{3,141}+ (D1/2)^2 }&=D2\\ \end{align}