Saturday , 21 October 2017

How to Calculate Stairs

How to Calculate Stairs

Here is a quick and easy way to work out your stair requirements.

First, take a look at the regulations that we can use as a starting point for working out our risers and our going.

Regulations

For the purpose of the following examples we will look at the regulations for Private Stair.

Example 1

Determining the risers
450 stairs

Above we have a change in level that requires a few steps. There is a floor to floor level of 450mm.

If we refer to the regulations we can choose a riser height between 150mm and 220mm.

Take the minimum riser height of 150mm. Divide the overall change in level (overall rise) by 150mm.

450mm / 150mm = 3

This tells us that with a riser of 150mm we will need 3 risers/steps.

450 stairs 02

Perhaps we decided we would rather have 2 steps instead of three. We can divide the change in level by the amount of steps we want:

450mm / 2 = 225mm

Having two steps will give us a rise of 225mm which according to the regulations above would be over the maximum allowance for a riser. So in this case we have to have a riser of 150mm giving 3 steps.

Determining the going / run
As indicated in the regulations above, a normal relationship between the dimensions of the rise and going is:

Twice the Rise plus the Going (2R + G) should be between 550mm and 700mm

To continue with the previous example let’s select a low going of 220mm.

This gives us 2 x 150mm + 220mm = 520mm

As we can see from the guidance above, it is recommended the outcome is between 550mm and 700mm

So let’s now try 275mm

2 x 150mm + 275mm = 575mm

As we can see this is within the normal limits so we can happily go with 150mm risers and 275mm going.

450 stairs 03

Example 2

In this example we will take a Floor to Floor level of 2800mm (Total Rise).
large stair 01

If we refer back to the guidance we can use between 150mm and 220mm as a riser.

Take 200mm as a riser (a nice round number and not too shallow). Now divide the total rise by the suggested riser distance.

2800mm / 200mm = 14

This gives us 14 risers at 200mm

large stair 02

Referring back to the guidance we can have a going between 220 and 300mm

Lets take 275mm as a starting point.

To check if this is ok we can carry out the 2R+G

2 x 200mm + 275mm = 675mm

This is within the range of 550mm and 700mm so we can assume this is acceptable.

The image below shows the finished stair. Note that the total run does not include step 14.

large stair 03

How to work out the angle of the stair

We can also work out the angle of the stair (as according to the guidance it can be a maximum of 42 degrees).

In order to work out our stair angle we can use a bit of basic trigonometry.

Total rise = 2800mm

Total run (when working out the angle) = no of risers x going

Total Run = 14 x 275mm

Total Run = 3850mm

Tan = Opposite / Adjacent
large stair 05

So:

Opposite / Adjacent =

2800 / 3850 = 0.72

Inverse Tangent of 0.72 =36 degrees

Any outcome of Opposite / Adjacent that is under 0.9 will be under 42 degrees.

This was a bit of a long post, but hopefully it will be helpful when you come to working out your stairs. It does tend to be a bit of trial and error, and of course is dependent on the space you have in the building you are designing. If you have any questions, or other ways of carrying out these calculations, please write a comment below. Thanks!

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21 comments

  1. Yes pal, but you have confused me some. Great advice its just the total run part. You say the total run doesn,t include the top riser yet you times by 14 in the example? Other than that,nice an simple. Thanks.

  2. Dear Sir/Madam

    thats the most useful website i have ever seen so far about stair calculations!!!

    Many thanks for your effort.

  3. Hi.
    I have an opening size of 2400 X 1000. After a stair company has come out and measured and made my stairs I’m not meeting building regs with head height. It’s a straight run with a hand rail. Floor to floor is 2600. Don’t know who I should be blaming for this

    • Hi Martin, I’m afraid I can’t comment on individual situations such as this – can I suggest you discuss it with your architect? All the best, Emma

    • Hi bottom line it would be your responsibility, but that said the stairs company would know the height restrictions and as you the lay person and them the professional they should know better. I would check with building regs as to what to do and see if you can get the landing opening made bigger etc by the stairs co at there cost

  4. Thank U sooo much guys it’s really useful and easy way ……if I have any doubt in feature at any members in building how can I ask those doubts .

  5. Thank you.
    There is also the http://www.stair-calculator.com/ website which automatically calculates the dimensions.

  6. I am trying to work out external steps. The area I am putting the steps is already on a slope above existing steps, so finding it difficult to work out an accurate rise as the lowest point where the steps are to start is 2300mm the height from the highest point where the steps are to finish is 1130mm.
    I have tried working on the lowest point with maximum rise of 220 and going as 230 to match existing steps below and it works out that I will need 10 steps which when placing blocks to equivalent is too high.
    I have then worked from highest point on slope to where we need top step to end with rise of 190 and going as 230 and it works out I will need 6 steps which is still too high. Any advice would be greatly appreciated.

  7. I have research on so many site for staircase calculation. So far just
    glancing through you guys your example in just about a minute, i can now boast to my self
    calculating any stairs that comes my way. Thanks so much guys.

  8. Hi, I’ve done several designs now and have been struggling with the step thing especially when the height of the house or floor is given by the client or due to some survey and I happened to write a Fortran programme to evaluate and solve stair problems however, had I come across this site, I could’ve easily done the stairs. May I ask permission to include information from this site into my fortran program steps calculator? All in all, thanks for the information and I appreciate your time and effort in making this information available. 🙂

    • Hi Sylvester, Yes of course you can have my permission to include the information in your fortran program. No problem. Best of luck .

  9. Hi. I would like to say thanks for writing this clear and easy to understand. Your pointing out the fact that the total run does not include the top step has just saved me quite a bit of embarrassment. I am doing a small building project DIY and would have got my foundation size wrong had it not been for that little point. Thanks.

  10. Please help me with this
    Design a staircase for a residential building where space provided is 2.25m by 5m and floor to floor height is 3.3m

  11. Wow!! This really came in handy, God bless!!

  12. Please assist with this design of staircase got an office building with the space of 3000mm x3000mm

  13. hi
    do you know why we multiplicate riser number and tan(x) ? i have seen that this formula 14 x ( 2800/3850). what is that mean? can you please tell me ? thanks

  14. Hi, I have a 1.5metre x 1.5 metre square area where I need to install a stairs to turn and get to the 1st floor. Ceiling height is approx 2.3mts. Old Farmhouse about 100 years old.
    Can it be done. There’s an existing spiral which is not very child friendly.

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