Fortress Evolution Stair Calculator Guide

This calculator works out the number of stairs you need for a given total rise and desired step height, and it also gives you the total stringer length and the horizontal run. You enter the total height from finished floor to finished floor, the number of steps you want (or let it default), and the tread depth; it returns the exact riser height, the total run, and the stringer length. The result is the stair geometry you would use to build a straight-flight staircase, which is the core of any fortress or building project.

Formula

The fundamental stair formula is simple: Riser height = Total rise ÷ Number of steps. In symbols: R = H / N, where H is the total vertical distance from one finished floor to the next (in mm or inches), N is the number of risers (steps), and R is the resulting height of each riser. The total horizontal run is T × N, where T is the tread depth (the horizontal depth of each step). The stringer length (the diagonal board that supports the steps) is found with the Pythagorean theorem: √(run² + rise²).

Worked Example

Using the default values from the calculator: total rise = 2800 mm, number of steps = 14, tread depth = 250 mm.

1. Riser height = 2800 ÷ 14 = 200.0 mm
2. Total run = 250 × 14 = 3500 mm
3. Stringer length = √(3500² + 2800²) = √(12,250,000 + 7,840,000) = √20,090,000 ≈ 4482 mm

So for a 2.8 m floor height, you would need 14 steps, each 200 mm high, with a total run of 3.5 m and a stringer about 4.48 m long.

Why Stair Geometry Matters in Fortress Building

In any fortress, tower, or keep, stairs are not just a way to get from one level to another—they are a defensive and structural element. A stair that is too steep is dangerous for defenders carrying equipment or moving quickly; a stair that is too shallow wastes space and materials. The classic medieval spiral stair in a castle turret was built with a specific riser-to-tread ratio that allowed a defender to fight upward while the attacker had to climb awkwardly. While this calculator gives a straight-flight stair, the same riser/tread logic applies to spiral stairs, where the tread depth is measured at the walk line (about 500 mm from the inner edge).

How to Choose the Number of Steps

The number of steps you choose directly determines the riser height. Building codes and ergonomic guidelines typically recommend a riser height between 150 mm and 200 mm (about 6 to 8 inches) for comfortable, safe climbing. To find the right number of steps for your total rise:

• Divide the total rise by a comfortable riser height (e.g., 180 mm) to get a rough count.
• Round to a whole number, then recalculate the exact riser height.
• Check that the result falls within the comfortable range. If not, adjust the step count up or down.
• Remember that the number of steps equals the number of risers, not the number of treads you see from the top (the top tread is the upper floor itself).

For example, a 2800 mm rise divided by 180 mm gives 15.6, so you would choose 15 or 16 steps. With 15 steps, the riser is 186.7 mm; with 16, it is 175 mm. Both are within the comfortable range.

Common Mistakes and Misconceptions

The most frequent error is confusing the number of steps with the number of treads. If you have a 14-step flight, you actually build 13 treads plus the upper floor as the final step. Another common mistake is mixing units—using millimetres for the rise but inches for the tread, or forgetting to convert feet to inches. Always work in one unit system. A third issue is ignoring the nosing (the protruding edge of a tread) and the stair thickness when calculating the stringer length; the formula gives the theoretical diagonal, but you need to add material for the treads and any support brackets. Finally, do not forget that the total rise must be measured from finished floor to finished floor—if you measure from subfloor to subfloor, you will be off by the thickness of the flooring materials.

Limits of This Calculator

This calculator assumes a straight, uniform flight of stairs with identical risers and treads. It does not account for landings, winders, or spiral geometry. It also does not include headroom clearance, which is the vertical distance from the stair nosing to the ceiling above. Building codes typically require a minimum headroom of 2.0 m (6 ft 8 in), and this must be checked separately. The stringer length calculated is the true diagonal length of the stringer board, but you will need to add extra length at the top and bottom for connections to the floor and upper landing. For a fortress with thick stone walls, the stringer might be embedded in the wall, so the actual cut length may differ.

Safety and Accuracy in Stair Construction

Safety is paramount when building stairs, especially in a fortress where people may be carrying heavy loads or moving in low light. Always follow local building codes, which typically specify maximum riser height (usually 200 mm) and minimum tread depth (usually 250 mm). Use a consistent riser height throughout the flight; even a few millimetres of variation can cause trips. When cutting stringers, mark all measurements carefully and test-fit before final installation. Use a level and a framing square to ensure accuracy. For outdoor or defensive stairs, consider adding a non-slip surface to the treads and a handrail on at least one side. If the stair is in a high-traffic area or will bear heavy loads (like a siege engine being moved), consult a structural engineer for timber sizing and connection details.

Frequently Asked Questions

What is the ideal riser height for a comfortable stair?

Most building codes and ergonomic guides recommend a riser height between 150 mm and 200 mm (6 to 8 inches). A riser of 180 mm is often cited as a good middle ground for general use. If you are building a steep defensive stair in a tower, you might go up to 220 mm, but that is not comfortable for everyday use.

How do I calculate the number of steps if I know the total rise?

Divide the total rise by your desired riser height. For example, if your total rise is 3000 mm and you want 180 mm risers, divide 3000 by 180 to get 16.67. Round up to 17 steps, then recalculate the exact riser height: 3000 ÷ 17 = 176.5 mm. That is within the comfortable range.

Does the calculator work for spiral stairs?

No, this calculator is for straight flights. Spiral stairs have a different geometry: the tread depth varies from the inner edge to the outer edge, and the riser height is measured along the centre line of the walk. For spiral stairs, you would need a separate calculation or a specialised tool.

What is the minimum tread depth for safety?

Most building codes require a minimum tread depth of 250 mm (about 10 inches) for residential stairs. For public or defensive buildings, 280 mm is often recommended. The tread depth is measured from the nosing of one step to the nosing of the next, not including any overhang.

How much extra length should I add to the stringer for connections?

The calculator gives the theoretical diagonal length. In practice, you should add at least 100 mm (4 inches) at each end for bearing on the floor and upper landing. For a fortress with thick walls, you may need more, depending on how the stringer is anchored. Always cut the stringer slightly long and trim to fit, rather than cutting it short.

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in rise | Total rise (floor to floor) | mm | 2800 | 0
in n | Number of steps | - | 14 | 1
in tread | Tread depth | mm | 250 | 0
out riser | Riser height | mm | rise / n | 1
out run | Total run | mm | tread * n | 0
out stringer | Stringer length | mm | sqrt(run^2 + rise^2) | 0