Stride length rule (Blondel formula)

The stride length rule is a design formula that links the riser height h to the tread depth b through the sum 2h + b. Both are in millimetres. A flight whose sum matches the average human step length feels natural to climb. The Slovak university textbook Konštrukcie pozemných stavieb: Schody writes it as 2hs + bs = a. It cites STN 73 4130 as the source of the recommendation. It carries the name Blondel formula after the French architect François Blondel (1618 to 1686). The textbook names him as a pioneer of stair design.

What does the 2h + b rule measure?

The rule measures how the two dimensions of a step combine, not the angle of the stair. Two risers and one tread together form the total. The textbook builds the rule on two assumptions. The average human step is 630 mm (men 750, women 600, pupils 540 mm). A vertical step on a ladder is half as long as a horizontal one. The total stands for a step length. A designer who keeps it near the target gets a regular, comfortable pace. The rule sits beside the stair pitch and does not replace it. A stair can satisfy one measure while missing the other.

What value does the formula use, 630 mm or 650 mm?

The textbook gives a = 630 mm according to STN 73 4130. It allows the value to be lowered to 600 mm when the highest permitted slope for the type of building is not exceeded. The textbook says Blondel himself wrote the relation as 2h + b = 650 mm. The standard is a paid text and was not read for this entry. This entry gives the 630 and 600 mm values as the textbook quotes them.

What are the ideal riser and tread?

For the lowest energy use of a person climbing, the textbook names a step of 152.5 mm riser and 325 mm tread. That is a slope of 25 degrees. It adds that step dimensions should always satisfy the formula. It also says sizing a stair only from the formula is wrong, because the energy needed to climb the height counts too. Any riser and tread pair whose sum equals the target works, so the designer picks the pair that suits the space. A taller riser needs a shallower tread, and a deeper tread allows a lower riser. The pitch column is the arctangent of riser over tread, rounded to one decimal place.

What is the maximum slope of a stair in a family house?

The Slovak general technical requirements decree 532/2002 Z. z. sets the limits a design has to meet. Section 27(4) caps the pitch of a main stair flight at 35 degrees. In an apartment building without a lift the cap is 33 degrees. A stair inside a dwelling under 3,000 mm construction height, or down to a basement, may go to 41 degrees. Section 27(3) requires every riser in one flight to have the same height. It limits a main flight to 16 steps and an auxiliary stair to 18. The decree states no step height and no 2h + b requirement. Section 27(2) leaves the step width to the Slovak technical standard, STN 73 4130. So the rule is a recommendation of the textbook and the standard. The decree does not write it as a test. The decree stays in force until the implementing regulations of the new building act 25/2025 Z. z. take effect, at the latest until 31 March 2027 (section 84(23)(b) of the act).

How does the stride rule differ from staircase pitch?

The two measures describe the same stair from different sides. The staircase pitch is a single angle that the riser and tread produce together. The stride rule is a sum of the two dimensions, with no angle in it. Two stairs can share one angle yet give different sums, because scaling both dimensions keeps the angle and changes the total. The table sets the two measures side by side.

How should the rule be used on a residential project?

Start from the storey height, which the design fixes, and decide how many risers the flight needs, at most 16 in a main flight. Divide the storey height by that count to get a riser height, then choose a tread that brings 2h + b to the target. Check the pitch against the decree maximum and check that every riser in the flight matches. Check that headroom and landing sizes work in the plan, as described under stair headroom. Where the numbers do not close, change the layout or add a landing. This usually works better than squeezing the stair into a tight shape. A stair that misses the target is not automatically unsafe, but it usually means a steep or cramped flight. Put the rule on the design drawings and check it again on site. A built flight can drift from the plan by the thickness of the finishes. The architect checks the figures against the standard in force on the project date.