Stair Calculator

Stair Calculator: Rise, Run, Treads and Stringer Layout

Do not start with the numbers; instead, use the region selector. This stair calculator checks the result against the building codes in your country and marks the design in red if it doesn’t meet the standards. This is because a staircase that’s off by a quarter inch needs to be torn down and rebuilt. The total rise is the height from the finished floor to the next level below. 

This number tells the stair calculator how many steps you need, how tall each one should be, how far the stairs stick out, and what length of stringer board you need to buy. The order is the same on the next page. First write the code limits. Then write the math inside those limits. Finally, write the code for how to lay out and cut a stringer.

Safety note: stairs are a structure people fall down. Everything here is general guidance, and codes change. Check your plan with your local building authority before you cut anything.

Start Here: Stair Code Limits by Region

Plan inside these numbers from the start. It spends a weekend and a pile of lumber to plan out a beautiful staircase only to find out that it doesn’t follow building codes.

United States (IRC)

For one and two family homes, the International Residential Code sets two hard numbers.

Two mistakes people make. First, the 3/8-inch uniformity rule applies to both the riser height and the tread depth. This is one of the main reasons stairs fail inspection. Second, the depth of the tread is determined from nose to nose, not from front to back.

Take note that the IRC talks about homes. Instead, apartments, offices, and public buildings are governed by the IBC, which has tighter rules about roof heights (7 inches at most) and treads (11 inches at the very least).

United Kingdom (Building Regulations Part K)

The stair calculator uk uses different words and different numbers. What Americans call tread depth, the UK calls going.

In a flight, every rise and fall must be the same. Because a high staircase may meet the rise and going limits on its own and still go over the angle, the 42-degree pitch cap is what stops loft conversions.

Australia (NCC and AS 1657)

The National Construction Code of stair calculator australia is more like a list of ranges than a single maximum. It also requires the 2R + G relationship instead of just suggesting it.

The ±5 mm tolerance in Australia is smaller than the 3/8 inch (about 9.5 mm) tolerance in the US. This means that the same builder needs to be more precise when making an Australian flight.

Please read this part. They were made to help you make plans. The tables above are general summaries. They’re not the code text, either. Codes are changed, and then states, towns, and local governments make their own changes on top of that. At this point, Australia is in the middle of switching from NCC 2022 to NCC 2025. Before you start building, check with your local building department or an experienced builder to see what the rules are right now. At the end of this page, there are links to main sources.

Stair Rise and Run Calculator: The Core Formula

Now the math worked inside those limits. Three steps.

Step 1: Number of risers = Total rise ÷ Target riser height, rounded to a whole number.

Step 2: Actual riser height = Total rise ÷ Number of risers. The whole point is this exact division. You can’t just pick a nice round riser height and hope the last step works because each riser has to be the same. Instead, you divide the real total rise by a whole number of steps.

Step 3: Total run = (Number of risers − 1) × Tread depth. There is always one fewer tread than riser, because the top surface you step onto is the floor or deck, not a tread.

As an example, let’s say the height goes up by 108 inches (9 feet).

Step 1: 108 / 7.5 equals 14.4, so round up to 14 risers.

Step 2: Divide 108 by 14 to get 7.71 inches for each step.

Step 3: Do 13 times 10 runs, which is 130 in.

Just barely, that 7.71-inch spike fits under the 7 3/4-inch IRC limit. It’s only 0.04 inches, which is very small on a real job site.

Round the other way and look what happens:

It takes up 10 inches more floor space to add 15 risers, but the stairs are easier to climb and don’t get close to the code ceiling. Take the space if you have stair calculator.

Measure the total rise last, not first.  Get the length from one finished floor to the next. If you add 1.5 inches of concrete to your basement or decking boards over the frame, those widths will change the total rise. If you measure the total rise before they are added, you will have an odd step at the bottom.

Stair Tread Calculator: Depth, Nosing and the 2R+T Rule

Tread depth is the distance from the front to the back of the shoe that you actually put your foot on.

The lip that hangs over the step below is called the nosing. In the US, the IRC lets the nosing project up to 1 1/4 inches, and it’s needed when the tread depth is less than 11 inches. Nosing gives your heel more room to fall without making you run faster.

The 2R+T rule is the oldest comfort rule in woodworking, and it still works.

The Tread + (2 Riser) should land between 24 and 25 inches.

The idea is that your step length stays about the same whether the step is high or low. This means that for high risers to feel normal, they need stair calculator. The stair feels either narrow or like a ramp when you’re outside that band.

When used with the worked example (14 risers):

(2 ÷ 7.71) + 10 = 25.42 in. Just above the band. We already knew from the code margin that the stairs are a little too steep.

How to fix it, and how not to. The tread could be cut down to 9.5 inches, which gives you (2 × 7.71) + 9.5 = 24.92 and puts you in the right range. In the US, don’t do that. It doesn’t meet the IRC 10 minimum tread depth, so you’d give up some ease for a failed inspection.

The fix from the last part is the right one. Jump up 15 times:

(2 x 7.20) + 10 = 24.40 in

The tread inside the comfort band is still at the legal 10 inches, and the riser is now half an inch below the limit. All three problems were solved at the same time by taking one more step.

The same rule applies in both the UK and Australia: 2R + G between 550 mm and 700 mm. The best range is between 600 mm and 650 mm. Up 200 mm and down 250 mm gives you 650 mm, which is a good range.

Stair Stringer Calculator: Laying Out the Cuts

The diagonal board that holds up the steps is called a stringer. You cut it into a sawtooth pattern of three-pointed notches. The size of each hole is the same as your riser height times your tread depth. There are three stringers in most flights: one on each side and one in the middle.

Stringer board length = √(Total rise² – Total run²)

Who is that? Pythagoras. There are three sides to the stairs: the stringer is the long, thin side.

Case study (14 risers, 130 in run):

√(108² + 130²) = √(11,664 + 16,900) = √28,564 = 169 in which is 14 ft 1 in.

Spend more. A 16-foot board is the smart thing to buy because you need extra on both ends for the top hanger cut and the bottom foot.

Dropping the stringer: the step everyone forgets

This is the most common mistake stringers make, and most computer pages don’t even talk about it.

Every notch you make is 7.71 inches high when you cut 14 of them in a row. After that, you put treads on top. Let’s say that each tire is 1 inch thick. The middle flight of steps stays 7.71 inches wide because they got a tread on top and lost one below.

The bottom step didn’t. Since there is nothing under it and it is sitting on concrete, it grows that inch and is now 8.71 inches tall. Every step except the first one is now an inch taller than the others. This is a real trip danger and a code violation because of the 3/8 in uniformity rule.

To fix it, take away one tread thickness from only the bottom step before you cut.

Cut the bottom riser by 7.71 – 1.00, which is 6.71 in.

Every other notch stays at 7.71 inches. All fourteen steps are 7.71 inches long when the wheels are on.

Cutting order that works:

1. Put step gages on a framing square and mark the riser and tread numbers on it.
2. You can mark all 14 notches on the board without changing the gages.
3. Mark where to cut the bottom drop and the top hanger.
4. Cut with a circle saw and use a handsaw to finish the edges. Do not cut the corners too much, as that makes the stringer weaker.
5. Make the other two stringers by following the first one.

Before you drop the stringer, measure your real tread stock. 1 in. wood is usually exactly 1 in., but 5/4 boards are about 1 in. and 2x material is 1.5 in.

Deck Stair Calculator: What’s Different Outdoors

Deck stairs use the same math with four extra things to get right.

1. Measure total rise to the finished ground, not the dirt. To find out where the bottom of the stairs will land, measure from the top of the deck below. When you measure, don’t go down to the ground. Instead, go up to the top of the landing pad. This is the most common mistake people make when building deck stairs. Our concrete tool tells you how big the pad should be.
2. Put something solid at the bottom. Over the course of a season, stringers that land on bare ground will settle. This makes your bottom riser taller. This can be fixed with a pressure-treated kicker board and a concrete pad or a bed of compacted gravel.
3. Use exterior materials throughout. Stringers and treads that have been pressure-treated or made of a composite material; hot-dipped galvanized or stainless steel screws. When used stair calculator for treated wood, regular steel screws quickly rust.
4. Handrails and guards are stricter outdoors than people assume. If you have four or more stairs in the US, you need a handrail on at least one side. If the stairs are high enough off the ground, guards must also be there. The height threshold changes from place to place, so check it there.

Also, tilt your treads forward just a little—about 1/8 inch more than the depth of the tread—so that water doesn’t pool and freeze.

Working on the deck too? Frame and board count are taken care of by our deck and stair calculator.

Common Stair Building Mistakes

Unequal riser heights. The main reason people fall down stairs is the first thing an inspector checks with a   Pick a riser height and let the last step make up the difference, but divide the real total rise by a whole number of risers.

Forgetting to drop the stringer. Dealt with above. If you find out after cutting, it costs you the whole stringer.

Measuring total rise before the finished floor. Putting down tile, carpet, concrete, or deck boards will all change the number. From one finished surface to the next, measure.

Not enough headroom. No matter how well you build the risers, you could still hit your head on a joist. From the nose lineup, the US minimum is 6 feet 8 inches and the UK minimum is 2000 mm.

Skipping the local code check. Model codes are changed at the local level. The best value for money on this list is the five minutes you spend calling the building department.

FAQs

Q1. How do I calculate the number of stairs I need?

To get a whole number, divide your total rise by the height you want the raise to be. If you want to reach a height of 7.5 inches and the rise is 108 inches, you need to use 14 or 15 risers. Next, take the total rise and split it by 15. This will give you the exact riser height: 108 ÷ 15 = 7.20 in. Divide by 2 again and again, because that’s what makes each step equal.

Q2. What is the maximum riser height allowed?

In the US, the IRC lets houses be up to 7 3/4 inches tall, and the height can change by no more than 3/8 inch across the flight. In the UK, public stairs can rise up to 220 mm. 115 mm to 190 mm is what Australian homes allow. These are just rough estimates. Before you start building, you should check with your local building authority to make sure they are correct.

Q3. Why must every riser be exactly the same height?

People don’t look as they go up and down the stairs. In the first two steps, your body learns the rhythm of the flight and then does it again. This means that the trip happens in the one odd step. Because of this, the US limits fluctuation to 3/8 in. and Australia to about 5 mm. This is also why an uneven flight fails inspection even if each step is within the height limit.

Q4. What is the 2R+T rule for stairs?

It should be between 24 and 25 inches, or 550 mm to 700 mm in the UK and Australia, where it is written as 2R + G. Take twice the pedal height and add the tread depth. It has the same step size as a standard stride. The 14-riser gave us (2 × 7.71) + 10 = 25.42, which is a bit high. The 15-riser gave us 24.40, which is right in the band.

Q5. What does ‘dropping the stringer’ mean?

Before you put anything in place, you have to cut the bottom riser down by exactly one tread thickness. Every middle step gets one tread added to the top and one tread taken off the bottom, so the height stays the same. Without the drop, the bottom step only adds one tread thickness, making it a tread thickness taller than the others. The bottom notch is cut at 6.71 inches on a 7.71-inch riser with 1-inch feet.

Q6. Are UK and Australian stair rules different from US ones?

Yes, in terms of both words and numbers. “Going” is what the UK says, while the US says that the tread depth can go up to 220 mm and the pitch can’t be more than 42 degrees. The US code doesn’t say anything about these things at all. Risers must be between 115 mm and 190 mm in length, and 2R + G must be between 550 mm and 700 mm. Do not guess; instead, check the official source for your own country.

Conclusion

If you follow this plan, the stairs will no longer be hard. First, find the limits of your area. Then, add up all the rises between finished surfaces and divide by the total number of risers. Finally, compare this number to both the code ceiling and the 2R+T comfort band before you touch a saw. There are 15 risers that are 7.20 inches high, a 140-inch run, and a 24-inch tread. 40-inch comfort number on our 108-inch example. 

This means that the stairs pass and feel good to walk on. Then, drop the bottom stringer notch by one tread thickness. This is the part of the process where most do-it-yourself flights go wrong. Use the stair calculator at the top of this page to figure out your own total rise. First, choose your area. Then, print out your results and take them to the building department before you buy any timber.