How to Calculate Stairs

Working out stairs can sometimes be a bit of a headache. In this article we are going to look at how to calculate stairs, the 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.

 

Building regulation requirements for stairs rise and going

 

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

How to Calculate Stairs – Example 1

 

Determining the risers

How to calculate stairs - Determining the risers

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.

3 risers how to calculate stairs

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.

Determining the going

How to Calculate Stairs – Example 2

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

Floor to floor how to calculate stairs

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

How to calculate stairs part 2

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.

[Be aware that according to the regulations a stair of 14 risers would require a landing – see further down this article for details]

How to calculate stairs part 3

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 (note that when working out the angle the top step 14 is included in the total run)

Tan = Opposite / Adjacent

How to work out stair angle

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.

You can also work out the angle by using the calculation run / rise. So for this example:

Run = 275

Rise = 200

200/275 = 0.72

Inverse Tangent of 0.72 = 36 degrees

Stair FAQs – what do the Building Regulations say?

 

What is the maximum / minimum width of a stair?

 

For buildings other than dwellings:

A minimum stair width of 1200mm is acceptable where the stair is between enclosing walls, strings or up stands.

A minimum width between handrails of 1000mm.

If the width of the stair is more than 2m wide, the flight must be divided with a handrail to a minimum of 1m wide.

For dwellings:

900mm is an acceptable width for stairs.

 

How many steps require a landing?

For general access stairs a maximum allowance of 12 steps before a landing is required. With utility stairs, a maximum of 16 steps is allowed before a landing. In no circumstances should there be a single step, so it is better to balance out the landing position so that there are at least two or more steps either side of the landing.

 

What is the minimum height between the stair and ceiling?

It is stipulated in the building regulations that headroom on landings and on the flight of stairs must be at least 2m.

Minimum headroom for a loft conversion can be reduced to 1.8m at its lowest point, but 1.9m at the centre point of the stair.

Building regs for stairs Reduced headroom for lofts

 

Can a stair have open risers?

Yes. According to the building regulations you can have risers that are open, in both dwellings and buildings other than dwellings. There are certain restrictions worth noting:

Dwellings

Treads must overlap by a minimum of 16mm.

The steps must be constructed so that a 100mm diameter spare cannot pass through the open riser.

Buildings other than dwellings

As above, although a closed riser is preferable.

 

How long can a flight of stairs be?

A flight of stairs with more than 36 risers in consecutive flights a minimum of one change of direction must be included between flights – this applies to both dwellings and buildings other than dwellings.

Building regulations for stairs change of direction

For flights between landings the maximum number of riser should be:

Utility stairs – 16 risers

General access stairs – 12 risers

 

Does a handrail have to be provided?

Yes, in all buildings a handrail must be provided and positioned between 900mm and 1100mm from the pitch line or floor.

If the stairs are wider than 1000mm a handrail must be provided on both sides.

 

Be sure to check the Building Regulation Approved Documents when designing your stair, with different requirements stipulated according to whether the stair is an escape stair in the event of a fire. You can see all of the Building Regulation Approved Documents here. 

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!

Download our Guide

 
You can download the full 20 page Stair Design Guide Series in PDF format. Just click the link below.

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52 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.

    Reply
    • Hi Phil, thanks for pointing that out – I’ll check it and amend if needs be. Thanks again.

      Reply
    • The guy explains about 14 risers ……. not to include top going of no 14.

      Reply
  2. Dear Sir/Madam

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

    Many thanks for your effort.

    Reply
    • Thank you.

      Reply
  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

    Reply
    • 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

      Reply
    • 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

      Reply
  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 .

    Reply
  5. 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.

    Reply
    • Hi Sarah – I’ve emailed you.

      Reply
    • Hi Sarah,

      I have a similar problem. Could I ask how you solved this ?

      Reply
  6. 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.

    Reply
    • Thank you for the feedback – glad I could help!

      Reply
      • Hi Emma it is look like similar but i couldn’t get it the right calculated my house is Design a straight flight stair to fit a floor to floor the height 2.6m and a total possible going of 4m.
        if you don’t mind could you email me how work out please.

        thanks

        Teddy

        Reply
  7. 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. 🙂

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

      Reply
  8. 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.

    Reply
  9. 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

    Reply
  10. Wow!! This really came in handy, God bless!!

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

    Reply
  12. 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

    Reply
  13. 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.

    Reply
  14. Hi, not sure if you can help.

    I have a stair designed using your calcs, thanks for the help 🙂
    The bottom rise has been installed 10mm shorted that the rest, will this pass building regulations or does it need lifting?

    Pete

    Reply
    • Hi Peter – I would recommend contacting your local building control to discuss, I can’t honestly say if it will be an issue or not. Best of luck, Emma

      Reply
  15. Hi sir thanks very much,this really help me….cheers

    Reply
  16. Hi pls I have try your method several times on my yet to be constructed staircase but from landing to landing the last riser am not getting it right so pls help ie total height is 160 cm by 160 cm total length pls urgent thanks in advance

    Reply
  17. Thanks so much, your simple explanation was quite helpful.

    Good job.

    Reply
    • Is 212mm a comfortable rise height. I know the max according to regs is 220mm but how will 212mm feel in reality.

      I have been checking rises in friends houses but the max I found was 200mm.

      Reply
      • Hi Sean, I think this will be fine, as long as you design a going that is deep enough to give a comfortable step. Obviously you need to make sure it sits within the regulations but there shouldn’t be an issue with a 212mm riser.

        Reply
  18. Please post the stair publication on Canadian Woodworking & Home Improvement Forum for their benefit. You’ll need to register (free).
    If questions, Steve S., woodbilder@yahoo.com

    Reply
  19. pls correct my prior note re Canadian WW & Home to woodbilder@mac.com
    thank you
    Steve S

    Reply
  20. HI I NEED HELP WITH RESPECT TO SOIL MECHANIC STUDY MATERIAL TO IN HENCE MY KNOWLEDGE

    Reply
  21. hi , for an entrance stairs 8 steps , we are looking at riser of 205mm and a thread depth of 355mm , will this work ?
    the 2r +t is 765mm . will this be too clunky? we will be going up and down it all day every day so keen to get it right .

    Reply
  22. Such a simple and easy to use site – thank you very much!

    Reply
  23. tanks a lot on the expiation on stairs

    Reply
  24. Hello,

    I have 3 questions?

    1. Where is the headroom measured from on a winder staircase? The Pitch Line?
    2. Is the the 16mm overlap of treads only applicable to open treads in dwellings?
    3. How much timber should be left on a cut string? is there a cut string calculator?

    Reply
  25. A very useful website!! thanks a lot for sharing your knowledge!!

    Salim,

    Reply
    • Thank you Salim 🙂

      Reply
  26. Very Helpful , keep publishing more details about construction

    Reply
  27. First In Architecture my first choice

    Reply
  28. This was extremely helpful
    I was able to understand all about stairs

    Reply
  29. this is great website. please what is the best stair fro a space of 3150mm by 2950mm with head room of about 9feet

    Reply
  30. Hi,
    Please, I need dog legged designed staircase of 3000mm run by 2720mm total rise.
    Thanks in anticipation

    Kingsley

    Reply
  31. my run can only 50in my rise is 90in no body talks about a short space

    Reply
  32. Hi Emma, How can you calculate the run with two sets of stairs with a landing in between (as we need 25 stairs with a min 240mm going; and a min of 18 consecutive stairs in Australian standards/BCA). Can you do an example of that – stairs with a landing?
    Thank you!

    Reply
  33. hi there, im having issues understanding the math on inversion. if the results were .72, how was 36 degrees found in this? this is an amazing resource! thank you!

    Reply
  34. Hi,
    Can a new straight flight of stairs serving an existing small office building have more than 12 steps?
    The floor to floor height is just under 2.7m so it would have 14 steps with 190mm rise and 250mm going as a Utility stair rather than a General Access stair if allowed. There is limited space in the building and it would be the only staircase.

    Reply
  35. Wow so good to learn

    Reply
    • thank you Ambrose 🙂

      Reply
  36. Hi doing a loft conversion want to put stairs in a cuboard up to the attic
    The problem being the cuboard floor is about 7 inch’s higher than the measurement from the attic floor at top of existing stairs

    Reply

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