Spindle Clear Gaps and Stair Layout

Formula and method

A 2 m opening, 5 cm spindles and a 10 cm maximum gap need13 spindles; equal gaps are135/14 cm.

N=ceil((L+w)/(g+w))−1; equal gap=(L−Nw)/(N+1); centered end gap=(L−Nw−(N−1)g)/2; sloped distance=horizontal distance/cos(pitch).

Worked example

Enter these known values and leave the other values blank.

Assumptions and limitations

• Measure the clear horizontal opening L between the inside faces of end posts, actual horizontal spindle width w, and desired maximum clear horizontal gap g. The count is a nonnegative whole number computed by ceiling, not an editable planning allowance.
• Equal spacing divides the remaining clear length among N+1 gaps. Centered spacing keeps internal gaps at the selected maximum and splits the remaining length equally at the ends; a negative result is infeasible and the retained warning suppresses that layout.
• For stairs, pitch is between zero and90 degrees with positive rise and run. Slanted gaps are measured along the inclined rail and equal the horizontal gap divided by cosine of pitch. Spindles remain vertical; this is not a model for tilted spindles.
• The captured scope requires opening greater than the selected maximum gap, and opening at least as wide as one spindle. A zero-spindle opening is rejected. A one-spindle centered layout has no internal gap; the end gap is the applicable position measurement.
• The defaults retain metric10 cm and imperial4 in maximum gaps. These are editable example defaults, not building-code limits. The arithmetic does not assess loading, fasteners, structural capacity or compliance.
• Counts below 10^50 use exact rational ceiling before rounding. Valid numeric syntax outside the exact rational grammar, such as implicit multiplication, square roots and fractional powers, uses the existing numeric parser; the count then uses its retained decimal value. The three layout length inputs preserve decimal literals up to 4096 significant digits and exponent magnitude 4096, and finite decimal arithmetic expressions up to 256 tokens and 16384 working digits. Resource errors are explicit; there is no physical minimum length.
• Extremely small or large finite values use scientific notation when ordinary decimal formatting exceeds its display range. This changes display only and does not impose a minimum physical length.

Common questions

References

• OpenStax: slope and rise/run
• NIST: exact international length units
• OpenStax: right-triangle trigonometry
• OpenStax: exponents and scientific notation
• Calculation definition and unit reference

Project centered horizontal end gaps by endSpace_centered/cos(pitch). Compute the count ceiling and length-conserving gaps from exact bounded rational representations of the three retained decimal lengths, before division or subtraction can round across integer transitions. Source-only input and unit conversion preserve finite decimal expressions and captured length factors. Counts must remain below 10^50; parser and rational resource bounds are explicit, with no physical minimum or global precision change. Require finite positive layout lengths and a spindle count below 10^50 using the source-pinned exact rational layout policy. Withhold layout outputs and warnings until all three lengths are present. Enforce strict signs with sign(...) and use the established source-pinned scientific fallback for finite display overflow, without a physical minimum.

Related calculators

Explore construction materials calculators 🧱 or browse all construction calculators.

• Aggregate Volume Mass and Cost
• Baluster Aggregate Count from Clear Span and Gap Target
• Brick Wall Materials and Mortar Budget
• Bulk Material Tonnage & Allowance Calculator
• Circular Arc Chord & Sagitta Calculator
• Deck Board Area Allowance & Fastener Budget