Why Building Codes Worldwide Base Stair Dimensions on François Blondel's 1675 Formula

Every time a person ascends a staircase in a modern commercial building or a newly renovated home, their gait is governed by a mathematical constraint drafted in Paris before the invention of the steam engine. The dimensions of the steps beneath their feet are not arbitrary.

They are the direct application of a 350-year-old observation about how the human body spends energy against gravity. When French architect François Blondel published his step formula in 1675, he established a biological exchange rate that would outlast every architectural movement from the Baroque to Brutalism.

Blondel watched people walk and noticed that the natural, comfortable stride of an adult on flat ground was roughly 63 to 65 centimeters. But when faced with an incline, the mechanics of human locomotion changed entirely, forcing the body to trade horizontal distance for vertical lift.

He determined that the physical effort required to lift the foot vertically by one unit was exactly equal to the effort required to move it horizontally by two units. To maintain a consistent energy expenditure, he formalized the relationship into a simple, enduring equation.

The Biomechanics of the Ascent

Going up a flight of stairs is a concentric muscular action, relying heavily on the quadriceps to extend the knee and the gluteus maximus to extend the hip. Because the body must overcome gravity, vertical travel is metabolically expensive and requires immense mechanical power.

Clinical sports biomechanics literature confirms that stair climbing requires joint moments considerably higher than those needed for level walking. The geometry of the steps forces the body to lean slightly forward, shifting the load from the skeletal joints to the active musculature of the calves.

Written as 2R + T = 63 centimeters, Blondel’s step formula perfectly maps to this muscular effort. If a step rises 18 centimeters, it consumes 36 centimeters of horizontal effort, leaving 27 centimeters for the tread to reach the 63-centimeter total.

Modern ergonomic research has validated this 17th-century math. Studies measuring metabolic cost show that staircases designed to the step formula require the least energy to climb and descend, and users consistently report the highest subjective comfort ratings on these specific proportions.

Interestingly, descending stairs is often more physically destructive than climbing them. Going down is an eccentric action—essentially a controlled fall—that isolates the knee joint and forces the quadriceps to lengthen while contracting, drastically increasing patellofemoral shear stress.

The Evolution of Egress

Before these dimensions were standardized by law, stairs were often built to fit whatever space was left over in a floor plan. In the 17th-century Dutch Republic, narrow plots of land forced builders to construct incredibly steep, cramped staircases that functioned more like ladders.[2]

Those historical "Dutch stairs" often featured a tread that was the same size as the riser, leaving only about 15 centimeters of space for the foot. While they saved valuable square footage in Amsterdam canal houses, they were notoriously dangerous and physically exhausting to navigate.[2]

It took mass-casualty disasters to turn Blondel's ergonomic guideline into a strict legal requirement. Tragedies like the 1942 Cocoanut Grove fire in Boston proved that inconsistent step dimensions and missing handrails could cause fatal surges and trampling during emergency evacuations.

Today, the 2024 International Building Code strictly regulates not just the rise and run, but the absolute uniformity of the flight. The difference between the largest and smallest tread depth or riser height in a single stairway cannot exceed three-eighths of an inch.

The human brain operates on a rhythm when climbing, assuming each subsequent step will exactly match the first. When a riser is even slightly off, the foot catches the nosing, turning a minor carpentry error into a severe liability risk.

Hardcoded into Global Law

Fast forward to 2026, and Blondel's exact ratio is hardcoded into the statutory law of nearly every developed nation. The 2024 IBC, which governs commercial construction across the United States, mandates a maximum riser height of 7 inches and a minimum tread depth of 11 inches.

Plug those statutory limits into the French architect's equation, and the math aligns perfectly. Twice the 7-inch rise plus the 11-inch tread equals exactly 25 inches, or 63.5 centimeters—landing squarely inside Blondel’s original 63 to 65-centimeter comfort band.

The United Kingdom's Approved Document K, which regulates domestic staircases in England, is even more explicit in its homage. It legally requires that twice the rise plus the going must fall between 550 and 700 millimeters for private stairs.[1]

England's regulations allow a steeper maximum pitch of 42 degrees for domestic stairs, permitting a rise of up to 220 millimeters. However, the proportion formula ensures that if the rise is pushed to its maximum, the going must expand to maintain the biomechanical balance.[1]

Norway's TEK17 building standard takes a similar approach, using a pre-accepted formula of twice the rise plus the going equaling 620 millimeters, plus or minus 20 millimeters. Across continents and regulatory bodies, the fundamental geometric ratio governing stair design has not drifted.

The Paradox of Modern Height

Yet, the rigid application of a 17th-century formula to a 21st-century population presents a biological paradox. The average human height has increased significantly since 1675, and with it, the average leg length and natural stride on flat ground.

A formula optimized for a Parisian pedestrian in the 1600s should theoretically feel cramped to a modern user. However, the constraint on stair climbing is not leg length, but the immutable leverage of the human hip and knee joints.

When ascending stairs, the next step physically rises to meet the foot, drastically shortening the vertical distance the body falls between strides. This geometry cuts the peak vertical ground reaction forces down immensely, sparing the bones from jarring impact.

Because the energetic cost of fighting gravity remains constant regardless of height, the 63-centimeter rule survives. Blondel did not invent the perfect stair; he simply measured the bipedal machine that had to climb it, locking architecture into a permanent biological standard.