Spiral Staircase Calculator (2024)

🙋 You would not need a stair carpet for your spiral staircases. But if you're interested in stair carpet installation, you may find our stair carpet calculator helpful.

The basics of how to build a spiral staircase

How to calculate tread measurements and spiral staircase dimensions

$$\footnotesize\begin{gather*}\rm number\\[-5px]\rm of\ steps \end{gather*} = \rm \frac{total\ rise}{riser\ rise}$$numberofsteps​=riserrisetotalrise​

Let's say we want to install a spiral staircase to get to the second floor 10 feet high (total rise), and we want our steps to be 8 inches away from each other (the building code suggests a riser rise that is not greater than 9.5 inches). Using our formula above, we get the following:

$$\footnotesize\begin{align*}\begin{gather*}\rm number\\[-5px]\rm of\ steps \end{gather*} &=\rm \frac{total\ rise}{riser\ rise}\\\\&=\rm \frac{120\ inches}{8\ inches}\\\\&=\rm 15\ steps\end{align*}$$numberofsteps​​=riserrisetotalrise​=8inches120inches​=15steps​

Since we got an exact value for our number of steps, we can already use that. If we obtained an answer with decimals, we round that value to the next whole number and then calculate the new actual riser rise using this equation:

$$\footnotesize\begin{align*}\begin{gather*}\rm actual\\[-5px]\rm riser\ rise \end{gather*} &=\rm \frac{total\ rise}{\begin{gather*}\rm number\\[-5px]\rm of\ steps \end{gather*}}\\\\&=\rm \frac{120\ inches}{15\ steps}\\\\&=\rm 8\ inches\end{align*}$$actualriserrise​​=numberofsteps​totalrise​=15steps120inches​=8inches​

By subtracting 1 from the number of steps, we can find the number of treads we need for our spiral staircase, as we can see below:

$$\footnotesize\begin{align*}\begin{gather*}\rm number\ of\\[-5px]\rm treads \end{gather*} &=\begin{gather*}\rm number\\[-5px]\rm of\ steps \end{gather*} - 1\\&=\rm 15\ steps - 1\\&=\rm 14\ treads\\\end{align*}$$numberoftreads​​=numberofsteps​−1=15steps−1=14treads​

$$\footnotesize\begin{gather*}\rm tread\\[-5px]\rm angle \end{gather*} = \rm \frac{angle\ of\ rotation}{number\ of\ steps}$$treadangle​=numberofstepsangleofrotation​

Let's say that for this spiral staircase, we want a full 360°-angle of rotation. That means the first step of our DIY spiral staircase is aligned with the last step of our spiral staircase, which is also placed level on the second-floor landing. Calculating the tread angle, we have the following:

$$\footnotesize\begin{align*}\begin{gather*}\rm tread\\[-5px]\rm angle \end{gather*} &= \rm \frac{angle\ of\ rotation}{number\ of\ steps}\\\\&= \rm \frac{360°}{14\ treads}\\\\&= \rm 25.714°\end{align*}$$treadangle​​=numberofstepsangleofrotation​=14treads360°​=25.714°​

The next measurement we need is the dimensions of our tread. For that, we can start with this formula for the tread length.

$$\footnotesize\begin{gather*}\rm tread\\[-5px]\rm length \end{gather*} = \rm \frac{\begin{gather*}\rm outside\\[-5px]\rm diameter \end{gather*} - \begin{gather*}\rm inside\\[-5px]\rm diameter \end{gather*}}{2}$$treadlength​=2outsidediameter​−insidediameter​​

Looking closer, here is the isometric view of a single tread and its other dimensions we can find useful when fabricating our treads:

To calculate these dimensions, here are the formulas we'll need:

$$\footnotesize\begin{gather*}\rm inner\\[-5px]\rm arc \end{gather*} =\begin{gather*}\rm tread\\[-5px]\rm angle \end{gather*} \times \frac{\pi}{180 \degree} \rm \times \rm \frac{inside\ diameter}{2}$$innerarc​=treadangle​×180°π​×2insidediameter​

We use a similar formula for the outer arc, but we use the outside diameter, as we can see in the following formula:

$$\footnotesize\begin{gather*}\rm outer\\[-5px]\rm arc \end{gather*} =\begin{gather*}\rm tread\\[-5px]\rm angle \end{gather*} \times \frac{\pi}{180 \degree} \rm \times \rm \frac{outside\ diameter}{2}$$outerarc​=treadangle​×180°π​×2outsidediameter​

Other dimensions we will find useful are the handrail length and inner and outer stair angles of our spiral staircase. We may also calculate the inner stringer length, which is more useful for concrete spiral staircases. For these measurements, we have the following formulas:

$$\scriptsize\begin{gather*}\rm handrail\\[-5px]\rm length \end{gather*} = \sqrt{\begin{gather*}\rm outer\\[-5px]\rm arc \end{gather*}^2 + \begin{gather*}\rm actual\\[-5px]\rm riser\\[-5px]\rm rise\end{gather*}^2} \times \begin{gather*}\rm number\\[-5px]\rm of\ steps \end{gather*}$$handraillength​=outerarc​2+actualriserrise​2​×numberofsteps​

$$\scriptsize\begin{gather*}\rm inner\\[-5px]\rm stringer\\[-5px]\rm length \end{gather*} = \sqrt{\begin{gather*}\rm inner\\[-5px]\rm arc \end{gather*}^2 + \begin{gather*}\rm actual\\[-5px]\rm riser\\[-5px]\rm rise\end{gather*}^2} \times \begin{gather*}\rm number\\[-5px]\rm of\ steps \end{gather*}$$innerstringerlength​=innerarc​2+actualriserrise​2​×numberofsteps​

$$\scriptsize\begin{gather*}\rm outer\ stair\\[-5px]\rm angle \end{gather*} = \tan^{-1} \left(\frac{\rm actual\ riser\ rise}{\rm outer\ arc}\right)$$outerstairangle​=tan−1(outerarcactualriserrise​)

$$\scriptsize\begin{gather*}\rm inner\ stair\\[-5px]\rm angle \end{gather*} = \tan^{-1} \left(\frac{\rm actual\ riser\ rise}{\rm inner\ arc}\right)$$innerstairangle​=tan−1(innerarcactualriserrise​)

To illustrate the last two parameters, we see a diagram below showing the inner stair angle we denote as $\alpha$α and the outer stair angle we indicate as $\beta$β.

💡 You can also check our spiral length calculator to learn more about determining length measurements in a spiral arrangement.

Finally, we'll need to determine the headroom clearance of our spiral staircase. For that, we first need to find the number of treads that will complete a "full circle," especially if its angle of rotation is 360° or more. For that, we'll need this equation below:

$$\footnotesize\begin{gather*}\rm number\\[-5px]\rm of\ treads \end{gather*}_{360^\circ} = \rm \frac{360^\circ}{tread\ angle}$$numberoftreads​360∘​=treadangle360∘​

For answers that have decimal places, we'll need to round them down to the next whole number and use that value on our following headroom clearance equation, shown below:

$$\footnotesize\begin{gather*}\rm headroom\\[-5px]\rm clearance \end{gather*} = \begin{gather*}\rm actual\\[-5px]\rm riser\ rise\end{gather*} \times \begin{gather*}\rm number\\[-5px]\rm of\ treads \end{gather*}_{360^\circ}$$headroomclearance​=actualriserrise​×numberoftreads​360∘​

How to use this spiral staircase calculator

FAQ

How do I calculate a spiral staircase's number of steps

What is the tread angle of a 19-step 360-degree spiral staircase?

The tread angle of a spiral staircase with 19 steps and a spiral angle of 360° is 20°. We get that value by subtracting 1 from the number of steps (to get the number of treads). For that, we get 19 − 1 = 18. Then divide the spiral angle by the number of treads to find the tread angle to be: 360° / 18 = 20°.

How do I calculate spiral staircase handrail length?

What is the maximum tread height for spiral staircases?

The maximum tread height for spiral staircases is 9.5 inches. Using a higher tread height or riser rise could make a spiral staircase challenging to climb and pose a danger to the people using the stairs.