Comparing your riser and tread against three formulas
This tool doesn't design a whole stair — it scores one riser/tread pair against the three comfort rules pros actually reference, so you can settle disagreements between them before you commit.
Enter your riser height
Use the actual, uniform riser your stair will have — not a rough target. If you haven't landed on one yet, use the Stair Rise and Run Calculator first to get an exact number from your total rise.
Add your tread depth, if you have one
Leave it blank to just see what each formula considers ideal for your riser. Enter it to get a pass/fail score against all three at once.
Set nosing if your tread has one
Most treads overhang the riser below by roughly 3/4"–1 1/4". That overhang isn't walking surface — subtracting it gives the effective unit run the formulas and some code checks actually use.
Read the verdict, then check code separately
A high comfort score doesn't guarantee code compliance and vice versa — the compliance chips check your numbers against IRC or IBC limits independently of the three comfort formulas.
The three comfort formulas, and where they come from
Each one relates riser and tread to a target sum that lines up with a comfortable walking stride on stairs. None is code — they're the difference between a stair that's legal and a stair that feels right.
7-11 Rule
The simplest rule of thumb: a fixed 7" riser paired with an 11" tread. Scored here as a target sum near 18" so it can be checked against any riser, not just exactly 7".
2R + T Rule
The standard U.S. residential comfort formula. Twice the riser plus the tread should land in a narrow 24–25" band — this is the rule most stair layouts are checked against first.
Blondel's Formula
The 17th-century French architectural formula the 2R+T rule descends from, expressed in its original metric form. The target band shifts with the Target Stride Band setting below.
Effective Unit Run
All three formulas above were derived using unit run, not the full board depth. A tread with generous nosing can pass the formulas on paper while its actual walking surface falls short.
Walking through a 7.5" riser with a 10.5" tread
Same inputs this calculator loads with by default, including a 1" nosing overhang — chosen because it's a realistic pair that doesn't agree cleanly across all three checks.
7-11 rule check
R + T = 7.5 + 10.5 = 18.0", landing exactly on the rule's ≈18" target. Pass.
2R+T rule check
2(7.5) + 10.5 = 25.5", which is 0.5" past the 24–25" band. Fail — this pair is slightly deep-treaded for a 7.5" riser under this specific rule, even though it passed the 7-11 check a moment ago.
Blondel's formula check
25.5" converts to 25.5 × 2.54 = 64.77 cm, which sits inside the 63–65 cm standard band. Pass. The same sum that failed 2R+T passes Blondel, because Blondel's band is very slightly wider in this range — a good example of why the three rules don't always agree.
Effective unit run and the code check it triggers
Subtract the 1" nosing: 10.5 − 1 = 9.5" effective run. The tread depth itself (10.5") clears the 10" IRC minimum, but the effective run does not — a compliant-looking tread can still represent a walking surface that's technically undersized once the nosing is accounted for.
Net result: 2 of 3 comfort formulas pass, the tread depth itself is code-legal, and the effective run flags a check worth a second look. None of these four checks contradicts the others — they're just answering different questions about the same step.
All three rules, side by side
The same reference table used across our stair calculators, so a rule's target here matches what you'll see anywhere else on the site.
| Rule | Formula | Target | What it optimizes for |
|---|---|---|---|
| 7-11 Rule | R = 7", T = 11" | R+T ≈ 18" | Simple carpenter's rule of thumb, slightly conservative on tread depth. |
| 2R + T Rule | 2R + T = 24–25" | ≈ 24.5" | The industry-standard comfort formula; the most commonly cited of the three. |
| Blondel's Formula | 2R + T = 63–65 cm | ≈ 24–25.6" | The 19th-century architectural origin of the 2R+T rule, in metric. |
Want the full plan — step count, total run and stringer length, not just the riser/tread comfort check? Use the Stair Rise and Run Calculator.
IRC and IBC limits these comfort numbers get checked against
Comfort formulas describe a preference. These are hard limits — a stair can fail here regardless of how it scores on the three rules above.
| Element | Residential (IRC) | Commercial (IBC) |
|---|---|---|
| Max riser height | 7.75" | 7" |
| Min tread depth | 10" | 11" |
| Riser variance across a flight | 3/8" | 3/8" |
| Typical nosing projection | 3/4"–1 1/4" [VERIFY: confirm exact IRC nosing projection range and section number for the adopted code year] | Varies by jurisdiction [VERIFY] |
Reference only — always confirm against your local jurisdiction's adopted code before building.
Nosing, unit run, and where the stride assumption comes from
A riser/tread pair can pass every comfort formula on paper and still walk differently in practice, for reasons that have nothing to do with which formula you picked.
Why unit run isn't tread depth
The comfort formulas above were derived from unit run — the horizontal distance from one riser face to the next — not the full dimension of the tread board. A deep nosing can make a tread measure comfortably on a tape while the actual foot-landing surface is noticeably shorter.
Where the stride target comes from
Blondel's original insight was that a comfortable stair should roughly match a person's normal stride on flat ground [VERIFY: confirm the historical stride figure most commonly cited for Blondel's original derivation]. That's why the target is a stride length, not an arbitrary number — and why it shifts for different kinds of stairs below.
Why the stride band is adjustable here
An interior stair used briskly by adults can comfortably run a tighter stride than a formal entry stair or an exterior stair meant to be walked slowly. This calculator's Compact and Generous bands [VERIFY: confirm the specific cm ranges used for Compact and Generous stride categorizations against a published source] let you shift Blondel's target without changing the underlying formula.
Comfort formulas aren't accessibility formulas
A shallower, more generous stair often reads as more accessible, but ADA 505 governs handrail, tread and riser dimensions independently and with its own limits. Use the ADA Stair Compliance Calculator for that check specifically.
Common mistakes when applying comfort formulas
Most disputes over "is this stair comfortable" trace back to one of these five mix-ups, not to a wrong formula.
Using tread depth instead of unit run
Plugging the full tread board dimension into 2R+T or Blondel without subtracting nosing overstates how comfortable the actual walking surface is.
Treating one rule as the tiebreaker
The 7-11 rule, 2R+T and Blondel can each give a different verdict for the same pair, as in the worked example above — none of them is automatically correct over the others.
Mixing residential and commercial limits
Applying IRC's 7.75" riser max to a commercial project, or IBC's 7" max to a house, produces a check against the wrong code entirely — the comfort formulas don't change, but the hard limits they sit next to do.
Chasing an exact number instead of a range
Every formula here defines a comfortable band, not a single correct riser/tread pair. Treating 24.5" as a hard target rather than the center of a 24–25" range leads to unnecessary redesigns.
Assuming comfort means compliant
A riser/tread pair that passes all three comfort formulas can still violate a hard IRC or IBC minimum or maximum — always run the code check in addition to the comfort check, not instead of it.
When to use a stair comfort formula calculator
This tool earns its place any time a riser/tread pair needs a second opinion before it's finalized.
Design-Stage Sanity Check
Confirming a drawn riser/tread pair against all three standard formulas before it goes to the plan set.
Evaluating an Existing Stair
Checking an older or non-standard staircase against modern comfort formulas before a remodel.
Settling a Design Disagreement
Resolving a dispute between a carpenter's 7-11 instinct and an architect's 2R+T spec with a shared, neutral comparison.
Exterior & Deck Stairs
Checking a shallower, slower-paced comfort target for outdoor steps using the Generous stride band.
Aging-in-Place Planning
Comparing a gentler riser/tread combination against the same formulas before committing to a redesign.
Reviewing Someone Else's Spec
Quickly checking a contractor's or architect's proposed dimensions without re-deriving three formulas by hand.