How to Calculate Stairs

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.

Regulations

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

Example 1

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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.

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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
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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.

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

large stair 03

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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
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.

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

Run = 200

Rise = 275

200/225 = 0.72

Invest 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.

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.

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!

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