How to Calculate Stair Rise and Run: A Step-by-Step Guide
By The Calcumatix Team Reviewed by Calcumatix Editorial Review 4 min read
Quick Answer
Divide the total rise (floor to finished floor, in inches) by your target riser height (near 7 inches) and round to the nearest whole number to find the riser count. Divide the total rise by the riser count to find the actual riser height. Set tread depth using the Blondel formula: 2 × riser height + tread depth = 24 to 25 inches. Multiply tread depth by (riser count − 1) for total run. Use the Pythagorean theorem for stringer length.
Stair rise and run are the vertical height of each step (riser) and the horizontal depth of each tread. Getting the numbers right before cutting stringers saves material, prevents structural failure, and keeps the stairs within the limits of your building permit. The International Residential Code (IRC) sets maximum riser height at 7 3/4 inches and minimum tread depth at 10 inches, but local codes may be stricter. This guide covers the calculation steps only. Always verify the final dimensions against your local authority’s requirements before construction.
How Do You Calculate Stair Rise and Run Step by Step?
To calculate stair rise and run:
- Measure total rise (finished floor to finished floor in inches).
- Divide total rise by target riser height (~7 in) and round to nearest whole number for riser count.
- Calculate actual riser height, set tread depth with the Blondel formula, and find total run and stringer length.
Rise And Run Worked Through One Step At A Time
Step 1, Measure total rise. Total rise is the vertical distance from the finished lower floor surface to the finished upper floor surface, measured in inches. Measure to the finished surface, not the subfloor: hardwood flooring or tile thickness must be included.
Step 2, Choose a target riser height. A riser height near 7 inches produces a comfortable stair for most adults. The IRC allows up to 7 3/4 inches (7.75 in) and most codes require a minimum of 4 inches.
Step 3, Calculate and round the riser count. Riser count = total rise ÷ target riser height (round to nearest whole number)
Rounding is mandatory because you cannot have a fractional step. Always round to the nearest whole number, not always up, rounding up consistently produces risers that are too short.
Step 4, Calculate actual riser height. Actual riser height = total rise ÷ riser count (exact, not rounded)
All risers must be cut to this exact height. The IRC requires that no riser varies from any other by more than 3/8 inch. Even a small inconsistency creates a tripping hazard at the top or bottom step.
Step 5, Choose tread depth using the Blondel formula. The Blondel comfort formula: 2 × riser height + tread depth = 24 to 25 inches. Solve for tread depth: tread depth = 24 to 25 − (2 × riser height). The result should be at least 10 inches (IRC minimum).
Step 6, Calculate total run. Total run = tread depth × (riser count − 1) The tread count is one less than the riser count because the upper floor landing acts as the last “step.”
Step 7, Calculate stringer length. Stringer length = √(total rise² + total run²)
Stair Rise and Run Worked Example
Inputs: Total rise = 109 inches (finished floor to finished floor). Target riser height near 7 inches.
Step 1: Find riser count 109 ÷ 7 = 15.57, rounded to 16 risers
Step 2: Find actual riser height 109 ÷ 16 = 6.8125 inches (exact, cut all risers to this height)
Step 3: Check IRC limit 6.8125 inches is below the 7.75-inch maximum. IRC compliant.
Step 4: Find tread depth via Blondel formula 2 × 6.8125 = 13.625 Tread depth = 24.5 − 13.625 = 10.875 inches (using midpoint 24.5 of the 24 to 25 range) 10.875 inches exceeds the 10-inch IRC minimum.
Step 5: Calculate tread count and total run Tread count = 16 − 1 = 15 treads Total run = 10.875 × 15 = 163.125 inches = 13.59 ft (rounded to two decimal places)
Step 6: Calculate stringer length Stringer length = √(109² + 163.125²) = √(11,881 + 26,609.77) = √38,490.77 = 196.2 inches = 16.35 ft (rounded to two decimal places)
Result: 16 risers at 6.8125 inches, 15 treads at 10.875 inches, total run 163.1 inches (13.6 ft), stringer length 196.2 inches (16.4 ft). Order 18-ft stringer stock.
Use the stairs calculator to quickly find risers, run, and stringer line length.
What Does the IRC Say About Stair Rise and Run?
The International Residential Code (IRC) sets the following limits for residential stairs. Local amendments may be stricter; verify with your local building department before construction.
| Measurement | IRC Limit |
|---|---|
| Maximum riser height | 7 3/4 inches |
| Minimum tread depth | 10 inches |
| Maximum riser variation | 3/8 inch (between any two risers in the flight) |
| Minimum headroom | 6 ft 8 inches (measured vertically above nosing) |
| Nosing required if tread < 11 in | 3/4 to 1 1/4 inches |
The uniformity rule (3/8-inch maximum variation) is the most frequently failed inspection item. It means every riser in the flight must be cut to the same height, including the top and bottom steps, where subfloor transitions or floor covering thickness changes can introduce unintended variation.
What Is the Blondel Comfort Formula?
The Blondel formula is an ergonomic guideline developed by the French architect François Blondel in 1675. It states that twice the riser height plus the tread depth should equal 24 to 25 inches, matching the average human stride length. A 7-inch riser paired with an 11-inch tread gives 2(7) + 11 = 25 inches, which is in the target range and produces a stair that most people find comfortable to climb. Steeper stairs (higher risers, shallower treads) fall outside the formula and feel more like ladders. Shallower stairs (lower risers, deeper treads) fall on the other end and feel more like ramps.
Sources
- IRC: Chapter 3, Stairways, riser height, tread depth, uniformity, nosing, and headroom requirements.
- NAHB: Stair Design Guidelines, Blondel formula reference and comfort-based stair proportioning.
Find concrete volume for poured steps with the concrete for stairs calculator or see all tools in the construction calculators hub.
Frequently asked questions
Why Is the Tread Count One Less Than the Riser Count?
The upper landing acts as the final step surface. A stair with 16 risers lifts you through 16 vertical increments, but only 15 of those increments have a tread below them. The 16th riser delivers you to the upper floor, which serves as the top tread. Cutting 16 treads would mean one extra tread overhangs the upper landing or the bottom step sits below the lower floor level.
What Happens If I Round the Riser Count Up Always?
If you always round up, the actual riser height (total rise ÷ riser count) will be shorter than your target, sometimes producing risers below 6 inches. Low risers combined with deep treads are code-compliant but feel awkward and waste floor space for the stair run. Round to the nearest whole number and then verify the actual riser height is within the 4-to-7.75-inch range.
Can I Use This Calculation for Concrete Stairs?
Yes, the same rise, run, and stringer length calculations apply to concrete stairs. The difference is that concrete stairs are typically formed rather than cut from stringers, and the geometry must account for the poured-concrete finish thickness. The Concrete for Stairs Calculator handles concrete stairs specifically, including riser face thickness and the volume of concrete needed for the pour.
How Do I Handle a Non-Standard Total Rise?
The calculation works for any total rise. If the total rise does not divide evenly into a round number of risers, adjust the target riser height up or down by small increments and recalculate until the riser count rounds to a practical number (typically 12 to 20 for interior stairs) and the actual riser height falls within the allowed range.