Stair Calculator
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This stair calculator brings together the three things we all love the most:
stairs, math, and people being wrong. We will show you the difference
between stair rises and runs, explain why some steps are a pain to walk on
and show you some neat stair calculation formulas. You'll also learn how to
count stairs correctly, which will give you an advantage should you ever
want to engage in verbal brawls on the identity of a single stair.
Excited? Let's dive right in!
Stair stringers and treads: terminology explained
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Before we plunge into the stair calculation formulas and discuss why
nobody on the Internet knows how to count stairs, we need to establish a
common ground: terminology. Our stair calculator uses many specialist
terms, and it's important that you understand them before we move on:
Run/tread: the run of stairs is the horizontal part you step on.
Rise/riser: the vertical part of the stairs, measured between two
consecutive treads.
Stair stringer: it's the construction that the steps are mounted on.
Angle: the inclination angle of the staircase.
Landing: a platform connecting two flights of stairs.
Nosing: the portion of the stair tread that overhangs the front of a riser.
Flush-mount: in a standard mount, the last tread is one step below the
floor level. In a flush mount, it is at the same height as the floor level.
Headroom: the space between the tread and the point on the ceiling
directly above it.
Handrails: a railing or baluster that runs along the stairs. It serves a
double purpose - you can hold it when walking up- or downstairs, and it
prevents you from falling.
Stair width: it is measured in clear, meaning that it doesn't include
handrails.
Stair calculation formulas
Our stair rise and the run calculator determines the details of your stairs for
various combinations of known and unknown values. For example, we can
assume that you know the rise and run of one step, and you want to
calculate the remaining characteristics. How would you proceed?
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First, you have to choose whether the stairs will be installed on a
standard or a flush mount.
Then you can calculate the total rise of the staircase according to this
formula: number of stairs = total rise / rise Remember that if the first
step has a different height, you should account for it in the calculations.
Once you know the number of stairs, you can easily find the total run:
total run = run * number of stairs Deduct one from the number of stairs
if you decided on a standard mount.
Finally, you can calculate the stair stringer length from Pythagoras'
theorem: stringer length² = total run² + stinger height² What's the
stringer height? It's equal to the total rise in the case of a flush mount,
and to the total rise - rise in the case of a standard mount.
Finally, you can find the angle at which the staircase is inclined: angle =
arcsin(stringer height / stringer length) You can convert it to slope
using our slope calculator.
Remember that our stair rise and the run calculator is applicable only if
you're designing a single flight of stairs - if there's a landing in between, you
need to treat every flight separately.
How to count steps and why you're doing it wrong?
You probably noticed that whether you want to calculate the stair stringer,
the rise, or the run, you will at some point encounter the phrase "number of
stairs". If you are reading the article carefully, you also noticed we didn't
define that number yet. Why is that?
Because it's easy to skim over this definition if you don't know the difficulty
and baggage that comes with it.
You see, most people don't know how to calculate stairs and do it wrong.
They will confuse you, saying that if you look at stairs with a standard
mount, you calculate the number differently than for stairs with a flush
mount. They will give you different formulas for each, just to put you in a
pickle. The reality, though, is super simple:
Every time you lift your leg, it's a stair.
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Look at the two pictures above. They show stairs in a standard and a flush
mount. Regardless of the stringer type, all you need to do is count the
number of times you lift your leg to take a step (instead of just sliding on a
perfectly flat floor).
Why is this so important? Civil engineers will thank you - this is the way they
count stairs. When civil engineers imagine a staircase, they don't see that
pretty colorful picture above. They see this:
This is a technical drawing: a plan of stairs. The arrow shows the direction
of ascent, and each numbered line shows - you guessed it - one stair. It
doesn't matter how big the runs are, and how the stringer is mounted. If it
brings you upwards, it's a stair.
Help! My stairs are uncomfortable to walk on!
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So you built your stairs. And they turned out to be terrible. You hate walking
on them. What happened? What did you do wrong?
If this is the case, you probably forgot about one tiny thing called comfort of
use. The truth is, designing stairs according to the stair calculation formulas
we listed above is a simple task. Creating the optimal and most comfortable
stairs is an entirely different pair of shoes. Luckily, our step calculator can
help you with that, too!
First of all, let's address the issue of step length. Most people (excluding
those that are extremely short or tall) have a similar step length, and we
should design stairs so that walking on them is as natural as possible,
without lengthening or shortening the steps. Typically, you will use the
following rule:
60 cm <= 2 * rise + run <= 65 cm
In Imperial units, it translates to 2 * rise + run ≈ 25 inches. If you breach this
rule, our stair calculator will warn you that the steps you've designed won't
be comfortable to use.
Naturally, this rule is not all, which is why building codes in all countries
define a few additional limits. Our stair rise and run calculator will warn you
about exceeding the limits set in the 2015 International Residential Code
(IRC), but if you're not using this particular document, make sure to doublecheck these values!
Maximum rise of one step: no more than 7.75 inches (196 mm).
Maximum total rise between landings: no more than 147 inches (3734
mm).
Minimum run of one step: no less than 10 inches (254 mm).
Staircase width (important not only because of comfort, but also for
safety): no less than 36 inches (914 mm).
Headroom: no less than 6 feet 8 inches (2032 mm). To verify the
headroom requirement, you need to pick "yes" in the headroom
restriction section.
If you're interested in this topic, check out this fantastic article from Michael
Maines on the 2 rules for Building Comfortable Stairs. He recommends stairs
with a 7" rise and an 11" run as the "ideal stairs," and shows a neat graph
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that sums up comfort requirements.
Building codes vs. children
Apart from the comfort criteria, building codes include also a wide range of
safety criteria. We mentioned some in the paragraph above: the staircase
width (vital in a fire emergency) and the headroom (helps to avoid a bump on
the head). There is one special safety element that the codes tend to
describe in detail: balusters.
Balusters, handrails, railings - they are all there to ensure you don't fall, and
neither does a child. You may laugh, but designing a children-proof baluster
is harder than you think! Here are just a few criteria you should take a look
at:
You need a handrail for every flight of stairs with at least four risers.
The handrail height should be between 34 inches (864 mm) and 38
inches (965 mm).
The space between the wall and the handrail should be no less than 1.5
inches (38 mm) - this ensures your hand doesn't get stuck between the
railing and the wall.
Even though it's not explicitly defined in every building code, you
should make sure that the space below the railing is small enough that
a child can't squeeze through it and fall (for example, a 4" diameter
sphere is not allowed to pass through).
If you plan a baluster for your stairs, make sure that you use vertical
balusters and not mid-rails! Mid-rails (horizontal elements parallel to the
staircase) are an invitation to climb. The vertical baluster spacing must
be small enough that a child can't squeeze through (again, the case of a
4" diameter sphere).
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Is this all? Of course not, but it's a good starting point. Good luck with your
construction project! Make sure to check out our square footage calculator
too .
GO TO Stair Calculator
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