Blondel's Formula for Stair Design

What Is Blondel's Formula?

Blondel's formula, also known as the comfort formula, is a rule of thumb used by architects and builders to design stairs that feel natural and safe to climb. The formula states that the sum of twice the riser height plus the tread depth should fall between 24 and 25 inches (61–63.5 cm). It is expressed as:

2 × Rise + Run = 24 to 25 inches

Where:

• Rise = vertical height of each step (typically 6.5–8.25 inches)
• Run = horizontal depth of each step (typically 9–11 inches)

The formula is named after French architect François Blondel (1618–1686), who studied human gait and determined that a step's proportions should mimic a comfortable walking stride on level ground. Blondel observed that ascending stairs requires roughly twice the vertical effort of a horizontal step, so the 2× multiplier on the rise accounts for the energy needed to lift the body.

Why Does Blondel's Formula Work?

Blondel's formula is based on the biomechanics of walking. When you climb stairs, you expend energy both to lift your body (vertical component) and to move forward (horizontal component). The formula creates a balance between these two forces. The result (24–25 inches) approximates the average human stride length on flat ground, making the stair feel natural.

For safety, a companion formula—often called the safety formula—requires that Rise + Run = 17 to 18 inches. This ensures the stair slope is not too steep or too shallow. The safety formula acts as a check: if the comfort formula produces dimensions that violate the safety range, the design may be awkward or risky. The Stair Calculator automatically applies both formulas to find valid step dimensions.

Practical Implications of Blondel's Formula

Residential vs. Commercial Stairs

For residential stairs, building codes (e.g., IRC) typically recommend a riser of 7–7.75 inches and a tread of 10–11 inches. Using Blondel's formula: 2×7.25 + 10 = 24.5 inches, which lands perfectly in the comfort zone. For commercial stairs (IBC), slightly larger treads (11 inches) and lower risers (7 inches) give 2×7 + 11 = 25 inches. The formula helps balance comfort across different applications.

Stair Types and Blondel's Adaptability

Blondel's formula works for straight stairs, but for winder stairs the tread depth varies along the step. In such cases, the formula is typically applied at the walk line (12–18 inches from the narrow end) to ensure comfortable stepping. Landings in L- or U-shaped stairs also affect the total run but not the per-step formula.

Using the Formula with the Stair Calculator

If you're manually checking your stair design, first measure the total rise (floor-to-floor height). Then divide by a trial riser height (e.g., 7 inches) to get the number of steps. Multiply the number of treads (steps minus one) by a trial tread depth, and check the comfort and safety formulas. The step-by-step manual calculation guide explains this process in detail. For fastest results, let the calculator do the iteration.

Edge Cases and Limitations

While Blondel's formula is widely used, it has limitations:

• Very tight spaces: When total run is limited, the formula may force a riser above 8.25 inches, which violates building codes. In such cases, you might need a different design strategy like a steeper stair with a shorter step count.
• Unique user needs: People with mobility issues may prefer lower risers (6–6.5 inches) and deeper treads (12+ inches). The comfort range is a guideline, not a rule for every individual.
• Non-standard stair types: Spiral stairs or ship ladders don't follow Blondel's formula because the stepping pattern is different.

The FAQ page addresses common questions about when to adjust beyond the formula.

Blondel's Formula in Modern Code Compliance

Today, building codes like the IRC and IBC incorporate Blondel's principles implicitly. For example, the IRC requires risers between 4 and 7.75 inches and treads at least 10 inches, but these ranges naturally align with the comfort formula. Checking your design against 2R + T = 24–25 ensures the stairs feel comfortable beyond bare code minimums. The Stair Calculator on this site outputs both a comfort rating and code compliance so you can see at a glance if your stairs will be pleasant to use.