The size of a staircase is usually indicated by **4 dimensions**; The **Horizontal Diameter** **or Radius of the railing**, the **Total Height** of the staircase, the **Total Arc (in degrees)** of the staircase and last but certainly not least, the **Direction of Rise (clockwise or counterclockwise).**

The **height of the staircase will be 120”** and its **radius at the rail will be 48”**. The railing will be going up in a **counter-clockwise** direction. In order to make a spiral, all this information is needed although it may come in different forms. For instance, the rise and run of a step, the number of steps, might replace the total height and the total arc of the staircase, but this is less desirable.

The first step in determining a rolling radius to find the **horizontal circumference** of the portion of a circle being used by the staircase, in this case **270deg.**. **NOTE:** A triangle will best illustrate each of the following steps. The horizontal circumference is represented by the Base Line of the triangle.

## Step #1 – Base Line of Triangle

**48” x ∏(3.14159) = 150.8”**. Now **x 270 =** then **÷ 180 = 226.2”**. This is the base of our triangle. With a **total height** of **120”** we will now figure the length of the hypotenuse of our triangle, which will represent the **Arc Length** of your work-piece.

## Step #2 – Figuring the Arc Length.

**120 ² + 226.2 ² = 65566.44,** now **√***(square-root)*, you get **256.05”**.

This number represents the amount of material **(Arc Length)** required to do the project.

## Step #3 – Figuring the Rolling Radius.

**256.05” ÷ 226.2” = 1.132**. Now **1.132²**, you get **1.2814** now** x 48” = 61.508”**. Your **rolling radius is 61.5”**.

**In short:**

**Step #1:** **Radius x ∏(3.14)=___ x Arc of staircase =___ ÷ 180 = Base line.**

**Step #2:** **Height² + Base line² =___ √***(**square-root)*** =Arc Length.**

**Step #3:** **Arc length ÷ Base line =___² x Radius = Rolling Radius.**

**Note:**Any size spiral can be figured using the above method.