Stair maths: risers, treads, stringer length and stairwell opening

How does the stair calculator work?

It runs the formulas of MeisterCalc's Stairs calculator, in millimetres inside. Feet and inches are converted at 25.4 mm to the inch on the way in and rounded to the nearest 1/16" on the way out. Pick what you know:

• Rise only (total rise and going): target riser = (600 − going) ÷ 2. Risers = total rise ÷ target riser, rounded to the nearest whole number. Riser height = total rise ÷ risers. Treads = risers − 1. Total run = risers × going.
• Rise + run (total rise and total run): risers = total rise ÷ the desired riser height (190 mm unless you change it under Advanced), rounded, and at least 2. Treads = risers − 1. Going = total run ÷ treads.
• Run only (total run and going): treads = total run ÷ going, rounded. Risers = treads + 1. Going = total run ÷ treads. Riser = (600 − going) ÷ 2, and the total rise is that riser × risers. It's an estimate of the rise that suits the run.
• Riser Limited (under Advanced) rounds the riser count up instead of to the nearest, from the desired riser height, so no riser is taller than it. In Run only it caps the riser at the desired height.
• Every mode: stringer length = √(total rise² + total run²). Incline angle = arctan(total rise ÷ total run). Stairwell opening = (floor thickness + headroom) × going ÷ riser.

The 600 comes from the 2R + G rule: twice the riser plus the going comes to about 600 mm on a comfortable stair. This page also shows 2R + G for the stair you get, and checks the riser, going, 2R + G, pitch and headroom against the country you pick. More on the rule in the 2R + G stair formula.

Worked example: a 2700 mm floor-to-floor rise

1. Target riser with a 240 mm going: (600 − 240) ÷ 2 = 180 mm.
2. Risers: 2700 ÷ 180 = 15, so 15 risers of 2700 ÷ 15 = 180 mm.
3. Treads: 15 − 1 = 14, each with a 240 mm going.
4. Total run (Rise only): 15 × 240 = 3600 mm. The treads themselves take 14 × 240 = 3360 mm.
5. Stringer length: √(2700² + 3600²) = 4500 mm, at arctan(2700 ÷ 3600) = 36.87°.
6. 2R + G: 2 × 180 + 240 = 600 mm.
7. Stairwell opening, with a 200 mm floor and 2000 mm headroom: (200 + 2000) × 240 ÷ 180 = 2933.3 mm.

Against the NCC limits for a house in Australia (riser 115 to 190 mm, going 240 to 355 mm, 2R + G 550 to 700 mm), every figure passes. The going sits right on the 240 mm minimum, so don't let it shrink on site.

Worked example: a 9 ft rise with 10 in treads

Switch the calculator to Feet and inches. It works in millimetres inside, so 9 ft is 108 × 25.4 = 2743.2 mm and 10 in is 254 mm.

1. Target riser: (600 − 254) ÷ 2 = 173 mm.
2. Risers: 2743.2 ÷ 173 = 15.86, which rounds to 16 risers of 2743.2 ÷ 16 = 171.45 mm, which is 6 3/4".
3. Treads: 15, each 10" deep (nosing to nosing).
4. Total run (Rise only): 16 × 10" = 13' 4". The 15 treads take 12' 6".
5. Stringer length: √(2743.2² + 4064²) = 4903.2 mm, which is 16' 1 1/16", at 34.02°.

Against the IRC (riser at most 7 3/4", tread at least 10"), it passes. Tick Riser Limited with a desired riser of 7 3/4" and you get 14 risers of 7 11/16" and 13 treads instead: a steeper stair that is 11' 8" long in Rise only.

What the totals measure

The calculator gives the same totals as the app, and they don't all measure the same line in every mode. That matters when you set out the stair or buy the stringer timber.

• Total run in Rise only is risers × going, as the app gives it. That is one going more than the treads cover: the extra going runs past the top riser onto the upper floor. The floor space the treads take is treads × going (3360 mm in the first example). The result card says which one you are looking at.
• Total run in Rise + run and Run only is treads × going: the level distance from the face of the bottom riser to the face of the top riser.
• Stringer length is √(total rise² + total run²). In Rise only that line runs from the foot of the first riser, through the inside corner of every step, to the upper floor level, at the same angle as the stair. In the other two modes it is the straight line from the foot of the first riser to the top of the last one, which is a little steeper than the line of the nosings.
• Incline angle is arctan(total rise ÷ total run), so it follows the same rule. The pitch that stair rules limit is the slope of the nosing line, arctan(riser ÷ going); the check under the calculator uses that one. In Rise only the two are the same.
• 2R + G is 2 × actual riser + actual going, the comfort check.
• Stairwell opening is the length of floor that must be left open above the stair so you clear the headroom on the way up: (floor thickness + headroom) × going ÷ riser. The method is in how big a stairwell opening needs to be.

Stair stringer length

The stringer length here is a line length, the hypotenuse of the total rise and total run. It's the number to compare with timber lengths, not the length of the board to buy. Add enough for the cut at the foot, the cut where it bears at the top, and any part that runs past the top riser to the trimmer or a hanger. How it sits depends on the fixing, so set it out on the board before cutting.

To mark the steps on a cut stringer, set a framing square to the riser on one arm and the going on the other, and step it along the board once per tread. For 180 mm by 240 mm, each step is a right triangle with a 300 mm long side, because √(180² + 240²) = 300. The calculator and the app don't mark the cuts or allow for the tread and riser board thickness, so take those off by hand: how to lay out a stair stringer goes through the marking, the drop for the tread thickness and a check of the layout, step by step.

Stair rules by country

There is no single stair rule. Each country sets its own limits, states and councils adopt and amend them, and the type of stair changes the numbers. These are the figures the calculator checks against, quoted from each document. Checked on 1 November 2026.

Read the notes that go with each: the NCC table is for stairs other than spiral and has a separate table for stairs to rooms used only now and then; D1/AS1 measures tread depth as its Figure 12 shows; Approved Document K applies in England, and Wales and Scotland publish their own guidance; US states and cities adopt the IRC with their own amendments, and some change the riser and tread figures. Your council, certifier or building department decides what applies to your stair. For the background, see how many steps a floor height needs and stairs in a tight space.

Using the stair calculator in Australia (NCC 2025)

In millimetres, the check under the calculator starts on Australia (NCC 2025). Every stair you work out is tested against the Housing Provisions limits for a stair other than a spiral: riser 115 to 190 mm, going 240 to 355 mm, 2R + G 550 to 700 mm, 2 to 18 risers in a flight, and the headroom you enter against 2.0 m. Each limit gets its own line with ✓ or ✗ and the figure it was tested against, so you can see which number to change.

The usual Australian problem is a stair that has to fit a fixed length of floor. Say the floor-to-floor rise is 2700 mm and the plan leaves 3000 mm of run, from the face of the bottom riser to the face of the top riser. Pick Rise + run, enter 2700 and 3000, and leave the desired riser at 190 mm:

1. Risers: 2700 ÷ 190 = 14.21, which rounds to 14 risers of 2700 ÷ 14 = 192.9 mm. Treads: 13. Going: 3000 ÷ 13 = 230.8 mm.
2. The check shows ✗ on the riser (192.9 mm is over 190) and ✗ on the going (230.8 mm is under 240). 2R + G is 2 × 192.86 + 230.77 = 616.5 mm, a ✓, which is why a comfort rule alone doesn't catch it.
3. Tick Riser Limited under Advanced. The riser count now rounds up: 2700 ÷ 190 = 14.21, up to 15 risers of 180 mm. That passes, but 14 treads in 3000 mm leaves a going of 3000 ÷ 14 = 214.3 mm, still a ✗.
4. So the floor is too short, not the sums. 14 treads at the 240 mm minimum need 14 × 240 = 3360 mm. Enter 3360 as the run: 15 risers of 180 mm, a 240 mm going and 2R + G of 2 × 180 + 240 = 600 mm, all ✓.

If 3360 mm won't fit, the answer is a different stair, not a steeper one: a landing that splits the rise into two flights (work each flight here on its own), or a stair in another spot. The calculator only does straight flights, so a landing's size and any winders are set out by hand against the NCC.

What the Australian check doesn't cover: balustrades and handrails (see the 125 mm gap and 1 m height), openings in treads and open risers, slip resistance of treads and nosings, landings, spiral stairs, and any state variation. Those rules, clause by clause, are in stair rules in Australia. Your certifier decides which NCC edition and which variations apply to the job.

Common mistakes

• Measuring the rise to the bare floor. Total rise is finished floor to finished floor. Tiles or boards added later change the top or bottom step and nothing else.
• One tread too many. A straight flight has one tread fewer than risers, because the upper floor is the last step.
• Treating the total run as the floor space. In Rise only it is risers × going. If the bottom riser has to land at a wall or a path, use treads × going, or switch to Rise + run.
• Rounding the riser to a nice number. Divide the rise by the count and keep the decimal: 2700 ÷ 14 is 192.9 mm, and 14 risers of 193 mm come 2 mm over.
• Using the wrong country's limits. A 200 mm riser passes in England and fails for an Australian house. Pick the right rules in the check.
• Forgetting the headroom. A stair that fits the run can still hit the floor above. Check the stairwell opening before you frame it.

Questions people ask

What this calculator doesn't do

• Straight flights only. No landings, winders, spiral or alternating-tread stairs.
• It doesn't mark stringer cuts, deduct tread or riser board thickness, or size the stringer timber.
• It doesn't decide what complies. The check quotes four documents; your local code and your council, certifier or building department decide.
• Inputs and results are rounded for display: millimetres to one decimal place, inches to the nearest 1/16", angles to two places.
• In Rise only, a going of 600 mm (23 5/8") or more has no target riser, so there is no result.

Stairs in MeisterCalc

The same maths is in MeisterCalc's Stairs calculator (Home ▸ Stairs), with the Rise Only, Rise + Run and Run Only modes, the Advanced section with Riser Limited, and a live side view of the flight with the stairwell opening marked. It shows amber warnings at fixed limits: a riser over 190 mm or under 115 mm (the Australian house limits), a going under 150 mm or over 450 mm, or an incline over 45°. The going limits are wider than any country's above, so check your country's figures in the table. For feet, inches and sixteenths, go to Settings ▸ Units ▸ Default units ▸ Imperial (ft/in). Stairs is one of three MeisterCalc calculators that are free to use, with Concrete and Check Square, and it works offline on site, on Android 7.0 or later. The other 13 calculators unlock with a weekly subscription that starts with a 3-day free trial, or with a one-time lifetime unlock; Google Play shows the prices in your currency.

Related guides

• Stairs in the MeisterCalc app: every input and result
• How many steps do I need for a 2.7 m or 3 m floor height?
• What is the 2R + G stair formula, and how do I use it?
• How big does a stairwell opening need to be?
• How do I fit a staircase into a fixed length?
• What is the going of a stair?
• How to lay out a stair stringer with a framing square
• More guides on the blog
• Calculators for stair builders: worked flights, openings and balusters