At what size does an upstairs make sense?

[Crofter]

It's well known that to minimise cost/m², building over two stories can work well. You sacrifice some space to fit in the stairs, but your expensive roof and foundations are now serving twice the floor area. 

 

Is there a rough rule of thumb for how large a house has to be before these savings kick in?

[nod]

I’ve found that the larger the house the lower the cost per m2 Endless surveys services are all the same 

So my answer would be The bigger the house the larger the saving on a middle floor 

But your right Big savings adding a middle floor I’m not sure what percentage of the build cost doing this would be I’d guess no  more than 20%

[ProDave]

Reading between the lines, I suspect @Crofter is asking at what size does room in roof make sense?

 

Ours is 150 square metres total and that is what we in Scotland know as 1 3/4 storey.  With the "normal" roof pitch here being 45 degrees (which I would thoroughly recommend for a variety of reasons) it is easy to turn a dead loft space into very economical extra accommodations.  Our walls extend just over a metre above the first floor level before they turn into "roof" and by building the roof as a warm roof hung from ridge beams, you get almost all of the upper floor as usable space with no obstructions or wasted space.

 

So in simple terms  going from a bungalow with a silly flimsy W joisted roof that is wasted space to a proper room in roof design is a very economic way of almost doubling your floor area.

 

Then it comes down to good design to minimise wasted space, i.e efficient stairwells and minimum corridors to get to rooms.

 

The English vernicular of very low pitched roofs make this a whole lot harder.

[Crofter]

Yes, room in roof is an obvious stepping stone- it seems almost daft not to do it.

 

I'm pondering another small build, slightly bigger than the first, and likely going down a conventional build route rather than portable. But I'm not sure if I'll end up going for any sort of an upstairs. Not ruling anything out at this stage.

[saveasteading]

1 hour ago, ProDave said:

almost doubling your floor area.

Almost, depends on how you consider the area, after deducting the stair area on both levels.

[Iceverge]

Short answer 120m². 

 

 

[SteamyTea]

This is a classic mathematics problem.

 

One of the most practical uses of differentiation is finding the maximum or minimum value of a real-world function. In the following example, you calculate the maximum volume of a box that has no top and that is to be manufactured from a 30-inch-by-30-inch piece of cardboard by cutting and folding it as shown in the figure.

 

What dimensions produce a box that has the maximum volume? Mathematics often seems abstract and impractical, but here’s an honest-to-goodness practical problem. If a manufacturer can sell bigger boxes for more money, and he or she is making a million boxes, you better believe he or she will want the exact answer to this question:

1. Express the thing you want maximized, the volume, as a function of the unknown, the height of the box (which is the same as the length of the cut).

   

2. Determine the domain of your function.

   The height can’t be negative or greater than 15 inches (the cardboard is only 30 inches wide, so half of that is the maximum height). Thus, sensible values for h are 0 ≤ h ≤ 15.

3. Find the critical numbers of V(h) in the open interval (0, 15) by setting its derivative equal to zero and solving. And don’t forget to check for numbers where the derivative is undefined.

   

   Because 15 isn't in the open interval (0, 15), it doesn’t qualify as a critical number. And because this derivative is defined for all input values, there are no additional critical numbers. So, 5 is the only critical number.

4. Evaluate the function at the critical number, 5, and at the endpoints of the interval, 0 and 15, to locate the function’s max.

   

The extremum (dig that fancy word for maximum or minimum) you’re looking for doesn’t often occur at an endpoint, but it can — so don’t fail to evaluate the function at the interval’s two endpoints.

You’ve got your answer: a height of 5 inches produces the box with maximum volume (2000 cubic inches). Because the length and width equal 30 – 2h, a height of 5 inches gives a length and width of 30 – 2 · 5, or 20 inches. Thus, the dimensions of the desired box are 5 inches by 20 inches by 20 inches.

[Oz07]

48 minutes ago, SteamyTea said:

This is a classic mathematics problem.

 

One of the most practical uses of differentiation is finding the maximum or minimum value of a real-world function. In the following example, you calculate the maximum volume of a box that has no top and that is to be manufactured from a 30-inch-by-30-inch piece of cardboard by cutting and folding it as shown in the figure.

 

What dimensions produce a box that has the maximum volume? Mathematics often seems abstract and impractical, but here’s an honest-to-goodness practical problem. If a manufacturer can sell bigger boxes for more money, and he or she is making a million boxes, you better believe he or she will want the exact answer to this question:

1. Express the thing you want maximized, the volume, as a function of the unknown, the height of the box (which is the same as the length of the cut).

   

2. Determine the domain of your function.

   The height can’t be negative or greater than 15 inches (the cardboard is only 30 inches wide, so half of that is the maximum height). Thus, sensible values for h are 0 ≤ h ≤ 15.

3. Find the critical numbers of V(h) in the open interval (0, 15) by setting its derivative equal to zero and solving. And don’t forget to check for numbers where the derivative is undefined.

   

   Because 15 isn't in the open interval (0, 15), it doesn’t qualify as a critical number. And because this derivative is defined for all input values, there are no additional critical numbers. So, 5 is the only critical number.

4. Evaluate the function at the critical number, 5, and at the endpoints of the interval, 0 and 15, to locate the function’s max.

   

The extremum (dig that fancy word for maximum or minimum) you’re looking for doesn’t often occur at an endpoint, but it can — so don’t fail to evaluate the function at the interval’s two endpoints.

You’ve got your answer: a height of 5 inches produces the box with maximum volume (2000 cubic inches). Because the length and width equal 30 – 2h, a height of 5 inches gives a length and width of 30 – 2 · 5, or 20 inches. Thus, the dimensions of the desired box are 5 inches by 20 inches by 20 inches.

Did anyone understand any of this 🤯

[SteamyTea]

2 minutes ago, Oz07 said:

Did anyone understand any of this

1^st year engineering mathematics.

 

[Oz07]

Just now, SteamyTea said:

1^st year engineering mathematics.

 

No gce's👍

[Crofter]

3 hours ago, SteamyTea said:

This is a classic mathematics problem.

 

One of the most practical uses of differentiation is finding the maximum or minimum value of a real-world function. In the following example, you calculate the maximum volume of a box that has no top and that is to be manufactured from a 30-inch-by-30-inch piece of cardboard by cutting and folding it as shown in the figure.

 

What dimensions produce a box that has the maximum volume? Mathematics often seems abstract and impractical, but here’s an honest-to-goodness practical problem. If a manufacturer can sell bigger boxes for more money, and he or she is making a million boxes, you better believe he or she will want the exact answer to this question:

1. Express the thing you want maximized, the volume, as a function of the unknown, the height of the box (which is the same as the length of the cut).

   

2. Determine the domain of your function.

   The height can’t be negative or greater than 15 inches (the cardboard is only 30 inches wide, so half of that is the maximum height). Thus, sensible values for h are 0 ≤ h ≤ 15.

3. Find the critical numbers of V(h) in the open interval (0, 15) by setting its derivative equal to zero and solving. And don’t forget to check for numbers where the derivative is undefined.

   

   Because 15 isn't in the open interval (0, 15), it doesn’t qualify as a critical number. And because this derivative is defined for all input values, there are no additional critical numbers. So, 5 is the only critical number.

4. Evaluate the function at the critical number, 5, and at the endpoints of the interval, 0 and 15, to locate the function’s max.

   

The extremum (dig that fancy word for maximum or minimum) you’re looking for doesn’t often occur at an endpoint, but it can — so don’t fail to evaluate the function at the interval’s two endpoints.

You’ve got your answer: a height of 5 inches produces the box with maximum volume (2000 cubic inches). Because the length and width equal 30 – 2h, a height of 5 inches gives a length and width of 30 – 2 · 5, or 20 inches. Thus, the dimensions of the desired box are 5 inches by 20 inches by 20 inches.

For a house, you don't just want maximum volume, you want to divide it up into 2.4m high sections. And you have to work around the pitch of the roof. 

I think the maths would be beyond me, but I have every faith in your abilities... go on, you know you want to!

[JohnMo]

12 hours ago, Crofter said:

Is there a rough rule of thumb for how large a house has to be before these savings kick in?

I think

Any house with two or more floors will always be cheaper and have a lower risk of escalating costs. The biggest unknown on all buildings projects is what you find when you start digging. 200m² single storey has twice the risk of hitting something expensive at foundation level, than a 100m² foundation for a 2 storey house.

 

Other factors - form factor for heat losses, nearer a cube the better.

 

Space usage, stairs take up space, but so do long corridors to get to the large footprint of single storey. So you are trading one for the other. Future proofing - single storey will always have easy access to bedrooms if stairs cannot be used.

 

At the end of the day it's about what is right for the site, ours was single storey, long frontage and not very deep. Rubbish form factor, more expensive to heat. Has a long corridor. But great views from all rooms.

[SteamyTea]

37 minutes ago, Crofter said:

For a house, you don't just want maximum volume, you want to divide it up into 2.4m high sections

That is why you can put limits on differential equations.

You can also use the same calculus on price, energy usage, usable area etc.

 

But as @JohnMo says, the ground and associated groundworks is the big one.

 

A house can be designed so that it can be extended upwards at a later date, but not many people want to pay for the extra structural work at the beginning.

[Kelvin]

Long corridors waste a significant amount of space. As does a stairwell in the middle of a house unless you want to make a feature of the entrance and stairs. We mostly designed out the internal corridors as there were two, one upstairs and one downstairs stairs, both pokey and dark. The neat feature of our stair design is it hidden behind the kitchen wall so takes up very little floorspace and creates a big cupboard off our kitchen and a wardrobe under the stairs off the guest bedroom. The 45° roof pitch and ridge beam also gives you a lot of flexibility in how you finish the upstairs ceiling both in height and style. We also removed the coomb storage on one side of the upstairs and made the other side slightly wider. Consequently the two upstairs rooms feel big and airy. A room in roof design creates quite a neat compact looking house on the outside and plenty of extra space on the inside. 

Edited November 4 by Kelvin

[G and J]

4 hours ago, Oz07 said:

Did anyone understand any of this 🤯

Yes.

 

Did it help in any way?  Ah, now there’s a question….

[saveasteading]

Land.

The cost and layout of a plot may be decisive.

With expensive land, go up.

With views, it depends if you need an upper floor to see them.

Then there is the roof structure and finish. The cost varies a lot depending on structure and finish.

I'm surprised uo see some large single storeys being built on commercial developments in the SE.  They seem to be in prime positions so the cost will be huge. London money.

[saveasteading]

4 hours ago, SteamyTea said:

1^st year engineering mathematics

School for me. I really wish they had made me understand it fully, and the uses,  rather than how to pass the exams.

[G and J]

11 minutes ago, Kelvin said:

Long corridors waste a significant amount of space. As does a stairwell in the middle of a house unless you want to make a feature of the entrance and stairs. We mostly designed out the internal corridors as there were two, one upstairs and one downstairs stairs, both pokey and dark. The neat feature of our stair design is it hidden behind the kitchen wall so takes up very little floorspace and creates a big cupboard off our kitchen and a wardrobe under the stairs off the guest bedroom. The 45° roof pitch and ridge beam also gives you a lot of flexibility in how you finish the upstairs ceiling both in height and style. We also removed the coomb storage on one side of the upstairs and made the other side slightly wider. Consequently the two upstairs rooms feel big and airy. A room in roof design creates quite a neat compact looking house on the outside and plenty of extra space on the inside. 

When we built our current house we received many comments about wasting space in the hall.  We could easily have made it much smaller but we liked the gallery landings (which makes it sound much grander than it is) and the sense of space it gave, and we were happy to have less space in other rooms to compensate.  I think in the vast majority of cases the site and the preferences of the dudes that the house is being built for dominate the design, which is how it should be.

[ProDave]

17 minutes ago, Kelvin said:

Long corridors waste a significant amount of space. As does a stairwell in the middle of a house unless you want to make a feature of the entrance and stairs.

I definitely agree with remove corridors but we found a stairwell right in the middle of the house worked very well.  Straight in from front door into a small hall area giving access to all downstairs rooms from the one small hall.  Up the stairs, 180 degree turn at the half landing, and the upstairs landing is directly above the hall, and gives access to all upstairs rooms.  Nice and compact and efficient.

 

The only one we struggled with downstairs was how to get a utility room and downstairs WC without a corridor or having to pass through one to get to the other.  Simple answer combined utility and WC all in one room.  Not to everyone's taste I agree but it works well.

[joe90]

20 minutes ago, ProDave said:

Simple answer combined utility and WC all in one room.

Yes my plant cupboard was In the downstairs cloakroom with a washing machine In it as well.

[Kelvin]

1 hour ago, G and J said:

When we built our current house we received many comments about wasting space in the hall.  We could easily have made it much smaller but we liked the gallery landings (which makes it sound much grander than it is) and the sense of space it gave, and we were happy to have less space in other rooms to compensate.  I think in the vast majority of cases the site and the preferences of the dudes that the house is being built for dominate the design, which is how it should be.

Our previous house had a particularly huge entrance hallway that was 10m x 5.5m with a 5m ceiling height. The staircase went up the middle to a galleried walkway to the bedrooms either side of the house. The staircase itself was a bit cheap but it certainly had a wow factor when you walked into the house. It also had two long corridors downstairs that took you off to the two wings of the house with all the other rooms. But it was an awful lot of wasted space. We did eventually put a big dining table in it so was great for family dinners. The house we built is half the size but we use all of it so oddly it feels bigger than the previous house. 

[SteamyTea]

27 minutes ago, Kelvin said:

Our previous house had a particularly huge entrance hallway that was 10m x 5.5m

That is bigger than the total floor area of my house.

[Kelvin]

16 minutes ago, SteamyTea said:

That is bigger than the total floor area of my house.

And the council house I grew up in.
 

The house was stupidly big and as nice as it was I never felt comfortable in it. 

[JohnMo]

1 hour ago, Kelvin said:

hallway that was 10m x 5.5m with a 5m ceiling height

That's bigger many new houses! And that's just the hall

[Crofter]

For context, the first house I built was 43m² internal, and the possible next one would be similar but with a second bedroom. I'm not sure if splitting such a small house over two floors works...