Curved Stair Calculator: How to Measure & Build

A curved stair calculator works out the dimensions of a spiral or curved staircase—typically the number of steps, riser height, tread depth, and the total angle or radius—from the floor-to-floor height, the available floor opening, and the stair’s curvature. You enter those basic measurements, and the calculator returns the step geometry you need to build or order the stair. This article explains the formulas, how to use them, and what to watch out for.

Formula

The core geometry of a curved stair is the same as a straight stair, except the horizontal run is measured along the arc of the centerline. The two main formulas are:

• Riser height = floor-to-floor height ÷ number of risers
• Tread depth (at centerline) = (2 × Ï€ × radius × (turn angle / 360)) ÷ number of treads

Variables:

• h – floor-to-floor height (mm or in)
• r – radius measured to the centerline of the stair (the line where you walk)
• angle – total turn in degrees (e.g., 180° for a half-turn, 360° for a full circle)
• n – number of risers (equals number of treads for a simple stair)
• tread – horizontal depth of each step measured along the centerline arc

The centerline is usually taken at 300 mm (about 12 in) from the inside handrail, because that’s where people naturally walk. The tread depth at the inner edge will be smaller, and at the outer edge larger.

Worked Example

Using the default values from the calculator: floor height = 2700 mm, radius = 1200 mm, turn angle = 360°, desired tread = 220 mm.

1. Number of risers: 2700 ÷ 190 = 14.21, so round up to 15 risers.
2. Riser height: 2700 ÷ 15 = 180 mm.
3. Centerline arc length: 2 × π × 1200 × (360/360) = 2 × 3.14159 × 1200 = 7539.8 mm.
4. Tread depth: 7539.8 ÷ 15 = 502.7 mm.

That gives a tread depth of about 503 mm, which is much larger than the 220 mm you might have wanted. In practice, you would either increase the radius, reduce the turn angle, or accept a deeper tread. The calculator shows that a full-circle stair with a 1.2 m radius simply needs a large tread to keep the riser height reasonable.

When to Use a Curved Stair Calculator

Use this calculator during the design phase, before you buy materials or order a prefabricated stair. It helps you:

• Check whether a given floor opening can accommodate the stair’s diameter.
• Determine the number of steps needed for a comfortable rise.
• Compare different radii and turn angles to hit a target tread depth.
• Estimate the total length of stringer or handrail needed.

It is also useful for remodeling, where you have a fixed opening and need to know if a curved stair will fit.

How to Choose Your Inputs

Measure carefully, because small errors become large over a full turn.

• Floor-to-floor height: measure from finished floor to finished floor, not from subfloor.
• Radius: measure from the center of the circle to the centerline of the stair. If you have a curved wall, the radius is the distance from the wall’s center to the stair’s centerline.
• Turn angle: 90° for a quarter-turn, 180° for a half-turn, 360° for a full circle. If your stair is a segment, use the included angle.
• Desired tread depth: building codes often specify a minimum, but a comfortable residential tread is around 250 mm (10 in) at the centerline. Check your local code.

If you are designing a spiral stair (a subset of curved), the same formulas apply, but the radius is typically smaller (1.0–1.5 m) and the tread depth at the inner edge becomes very narrow.

Common Mistakes and Misconceptions

One frequent mistake is using the outer radius instead of the centerline radius. That makes the tread depth appear larger than it actually is at the walking line. Another is forgetting that the number of risers must be an integer; you cannot have 14.5 steps. Round up to the next whole number, then recalculate the riser height.

A common misconception is that a curved stair saves space compared to a straight stair. In reality, a 360° spiral with a 1.2 m radius occupies a 2.4 m diameter circle, which is about 4.5 m² of floor area—often more than a straight stair. Curved stairs are chosen for aesthetics or layout, not for space savings.

Another issue: the tread depth at the inner edge. For a spiral stair, the inner edge can be only 100 mm (4 in) deep, which is dangerous. Many codes require a minimum tread depth at a certain distance from the inner edge. Always check your local building code.

Limitations of the Formula

This calculator gives the basic geometry, but a real curved stair involves more:

• Headroom: you need at least 2 m (6 ft 8 in) of clearance above the stair. The formula doesn’t account for the floor opening shape.
• Landings: if your turn angle is not a multiple of 90°, you might need a landing, which changes the tread count.
• Stringer curvature: the structural support must be bent or fabricated, which requires a shop drawing.
• Handrail: the handrail length is longer than the centerline length because it sits at a larger radius. For a 360° stair with a 1.2 m centerline radius and a handrail at 1.3 m, the rail length is about 8.17 m.

The calculator is a starting point, not a substitute for professional fabrication.

Safety and Building Codes

Safety is the most important part of stair design. A few key points:

• Riser height should be between 150 mm and 200 mm (6–8 in) for comfort. The calculator uses 190 mm as a default, which is on the higher side.
• Tread depth at the centerline should be at least 200 mm (8 in) for residential stairs, but check local codes.
• All steps in a flight must have the same riser height and tread depth; variation causes trips.
• Handrails are required on at least one side, and the inside of a curved stair often needs a handrail on both sides.
• For spiral stairs, the minimum clear width is typically 600 mm (24 in), but 700 mm is more comfortable.

Always consult your local building department before construction.

Frequently Asked Questions

How do I measure the radius of an existing curved stair?

Find the center of the circle by measuring the chord and the sagitta (the distance from the midpoint of the chord to the arc). Then use the formula: radius = (chord² / (8 × sagitta)) + (sagitta / 2). Or, if you have the blueprints, read the radius from the drawing.

What is the difference between a curved stair and a spiral stair?

A curved stair has a constant radius and usually a larger turn radius (2–3 m), while a spiral stair has a smaller radius (1–1.5 m) and often a central column. Spiral stairs have wedge-shaped treads that are narrow at the inner edge; curved stairs can have more uniform treads if the radius is large enough.

Can I use a straight stair calculator for a curved stair?

Only if you convert the curved run to a straight line. Measure the centerline arc length and use that as the “run� in a straight stair calculator. But you still need to account for the varying tread depth across the width.

What is the minimum radius for a comfortable curved stair?

For a residential curved stair, a centerline radius of at least 1.2 m (4 ft) is recommended. Below that, the inner edge becomes too narrow to be safe. Spiral stairs can have a radius of 1.0 m, but they are less comfortable.

How many steps do I need for a 3 m high ceiling?

With a 190 mm riser, you need 3000 ÷ 190 = 15.8, so 16 risers. That gives a riser height of 187.5 mm. The number of treads is the same as risers for a simple stair.

Does the calculator work for a 180° curved stair?

Yes. Set the turn angle to 180°. The centerline length becomes half of a full circle, and the tread depth is calculated accordingly.

Related

• Board and Batten Measurement Calculator
• Board & Batten Calculator: Measure & Estimate
• Board and Batten Calculator: Inches & Spacing

in h | Floor-to-floor height | mm | 2700 | 0
in r | Centerline radius | mm | 1200 | 0
in angle | Total turn angle | degrees | 360 | 0
in t_read | Desired tread depth at centerline | mm | 220 | 0
out n | Number of risers | - | ceil(h / 190) | 0
out rise | Riser height | mm | h / n | 1
out tread | Tread depth at centerline | mm | (2 * pi * r * (angle / 360)) / n | 1
out total_len | Centerline length | mm | 2 * pi * r * (angle / 360) | 0