Staircase Calculator

Calculate stair dimensions including rise, run, number of steps, and stringer length. Ensure code compliance with standard residential stair requirements.

Unit System

Imperial (inches)

Metric (cm)

Total Rise / Floor-to-Floor Height (inches)

Available Horizontal Run (inches) — optional

Preferred Riser Height (inches) — default: 7.5"

About Staircase Calculator

Staircase Geometry Basics

A staircase is defined by a few fundamental measurements: the total rise (vertical height from one floor to the next), the total run (horizontal distance the staircase covers), and the individual riser heights and tread depths that make up each step. The number of risers is always one more than the number of treads because the top floor serves as the final landing.

The relationship between rise and run determines the stair angle and overall comfort. Steeper stairs save floor space but are harder to climb, while shallower stairs are easier to use but require more horizontal room. Finding the right balance is the core challenge of stair design, and building codes set strict limits to ensure safety.

Key Stair Dimensions

• Total Rise: Floor-to-floor vertical height
• Total Run: Horizontal distance from first riser to last
• Riser Height: Vertical distance of one step
• Tread Depth: Horizontal depth of one step
• Stringer: Diagonal support board beneath the steps
• Stair Angle: Incline measured from the horizontal plane

Building Code Requirements (IRC Standards)

The International Residential Code (IRC) establishes minimum requirements for residential stairways to ensure occupant safety. These standards have evolved over decades based on ergonomic research and accident data, and most local jurisdictions adopt them as the baseline for residential construction.

Uniformity is a critical code requirement. The greatest riser height within a flight of stairs cannot exceed the smallest by more than 3/8 inch. The same applies to tread depth. Non-uniform steps are one of the leading causes of stair-related falls in residential buildings.

Dimension	IRC Requirement
Maximum Riser Height	7.75 inches (196 mm)
Minimum Riser Height	4 inches (102 mm)
Minimum Tread Depth	10 inches (254 mm)
Minimum Width	36 inches (914 mm)
Minimum Headroom	6 feet 8 inches (2032 mm)

Rise and Run Relationship

The relationship between riser height and tread depth is the most important factor in stair comfort and safety. A widely used rule of thumb is that the sum of two risers plus one tread should equal 24 to 25 inches (the "rule of 25"). Another common guideline states that the riser height multiplied by the tread depth should fall between 70 and 75 square inches.

To calculate the number of risers, divide the total rise by the preferred riser height and round to the nearest whole number. Then recalculate the actual riser height by dividing the total rise by that number. The number of treads is always one fewer than the number of risers. Multiplying the number of treads by the tread depth gives the total run.

Comfort Guidelines

Preferred Ranges

• Riser height: 7–7.5 inches
• Tread depth: 10–11 inches
• Stair angle: 30°–37°

Common Formulas

• 2R + T = 24–25 inches
• R × T = 70–75 sq in
• R + T = 17–18 inches

Stringer Calculations

Stringers are the diagonal structural members that support the treads and risers. The stringer length is calculated using the Pythagorean theorem: the square root of the total rise squared plus the total run squared. This gives the minimum board length needed before any cuts are made at the top and bottom for attachment.

Most residential stairs use three stringers: two on the outside edges and one in the center for additional support. The stringer board should be wide enough so that after cutting the step notches, at least 3.5 inches of solid wood remains along the bottom edge for structural integrity. A 2×12 board is the standard choice for cut stringers in residential construction.

Stringer Sizing Guide

• Standard stringer board: 2×12 lumber (1.5″ × 11.25″ actual)
• Minimum remaining wood after notching: 3.5 inches
• Typical stringer spacing: 16 inches on center
• Add 12–18 inches to calculated length for top and bottom attachment cuts

Safety Considerations

Stairs are one of the most dangerous areas in a home, accounting for a significant percentage of residential fall injuries each year. Proper design, code compliance, and careful construction are essential to minimizing risk. Uniform step dimensions, adequate lighting, and properly installed handrails are the three most important safety factors.

Beyond basic code compliance, consider the needs of all users including children and elderly occupants. Non-slip tread surfaces, contrasting nosing strips for visibility, and handrails that extend beyond the top and bottom steps all contribute to safer stairs. Always verify local code amendments, as many jurisdictions have requirements that exceed the base IRC standards.

Safety Checklist

Design Safety

• Uniform riser and tread dimensions
• Code-compliant stair angle
• Adequate headroom clearance
• Proper landing at top and bottom

Construction Safety

• Handrails on at least one side
• Non-slip tread surfaces
• Adequate lighting at top and bottom
• Secure stringer attachment to framing

Frequently Asked Questions

What is the standard riser height for residential stairs?

The International Residential Code (IRC) specifies a maximum riser height of 7.75 inches (196 mm) and a minimum of 4 inches (102 mm). Most builders aim for a riser height between 7 and 7.5 inches for comfortable climbing. The exact height depends on the total floor-to-floor rise divided evenly among all risers, which must be uniform within a tolerance of 3/8 inch.

How do I ensure my staircase meets building code requirements?

To meet IRC building code, ensure each riser is between 4 and 7.75 inches tall, each tread is at least 10 inches deep, the stairway is at least 36 inches wide, and headroom is a minimum of 6 feet 8 inches. All risers and treads must be uniform in size with no more than 3/8 inch variation. Handrails are required on at least one side, mounted 34 to 38 inches above the stair nosing.

How do I calculate the stringer length for my staircase?

Stringer length is calculated using the Pythagorean theorem: stringer length equals the square root of (total rise squared plus total run squared). For example, if your total rise is 108 inches and total run is 120 inches, the stringer length is √(108² + 120²) ≈ 161.5 inches or about 13.5 feet. Always add a few extra inches to account for cuts at the top and bottom of the stringer.

What is the ideal stair angle and how does it affect comfort?

The ideal residential stair angle is between 30 and 37 degrees. Stairs steeper than 42 degrees feel uncomfortable and may violate building codes, while stairs shallower than 20 degrees waste floor space and feel more like a ramp. The angle is determined by the ratio of riser height to tread depth. A 7-inch riser with a 11-inch tread produces a comfortable angle of about 32.5 degrees.

Additional Resources

Stairs - Wikipedia Stringer (stairs) - Wikipedia Building code - Wikipedia

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