Stair Calculator

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!

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

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 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?

1. First, you have to choose whether the stairs will be installed on a standard or a flush mount.
2. 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.
3. 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.
4. 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 total rise - rise in the case of a standard mount.
5. 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 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 pickle. The reality, though, is super simple:

Every time you lift your leg, it’s a stair.

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!

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 double-check 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 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).