Living Area Regulation / Terrace Area

According to the Wohnflächenverordnung, terraces can be included in the living space calculation at 25% to 50%. My question is, do terraces only count if they have a roof, or can a normal terrace in the garden on the ground floor (a slab, without a roof) also be included?

Terrace is terrace - as you mentioned, to be considered with a maximum of 50%.

My question is, do the terraces only count if they have a roof or can a normal terrace in the garden on the ground floor (a slab, without a roof) also be included?

No, a roof is not necessary.
Yes, a normal terrace is to be credited.

Attention:
1. The Living Space Ordinance originally applies only to price-bound housing (social housing). However, it has been extended by case law. There is simply nothing else, except old DIN standards.
2. 25% crediting is the rule!
3. 50% is the exception, which must be contractually justified/agreed! Be it rent or condominium ownership (e.g., due to location, equipment, sunshine, view, noise or quiet). Only then are they effective.

my lender explicitly wanted a living area calculation, was not satisfied with just the floor area. So much for "only for social housing". I then created it myself.

No, roofing is not necessary. Yes, a normal terrace is to be credited.

Attention:
1. The Living Space Ordinance originally only applies to price-bound housing (social housing). However, it has been extended by case law. There is simply nothing else except old DIN standards.
2. 25% crediting is the rule!
3. 50% is the exception, which must be contractually justified/agreed upon! Whether rent or condominium (e.g. due to location, features, sunlight, view, noise or quiet). Only then are they effective.

Thank you very much for your detailed answer. The house I am going to buy is located in noise level area II. Can I therefore argue that the terrace on the ground floor should not be credited at 50% because the quality is not good enough?

My lender explicitly wanted a living space calculation and was not satisfied with the floor area. So much for "only for social housing".

That’s why I wrote at the beginning "originally":

§ 1 Living Space Ordinance - Scope, Calculation of Living Space
(1) If the living space is calculated according to the Housing Promotion Act, the provisions of this ordinance are to be applied.
(...)

For the rest, it is then analogously applied if nothing else applies. It makes no difference in the matter.

The house I will buy is located in noise level zone II. Can I therefore argue that the terrace on the ground floor should not be calculated at 50% because the quality is not good enough?

Can you: yes.
Successful: rather no – at least not in negotiations. It may then possibly be sold to the next interested party.
No one is forced to buy; no one forces the seller to sell. Supply and demand determine the price.
Property is sold based on the object – and not by square meters in bulk. However, size is a value-forming factor.

After a purchase, however, it looks different, defect warranty law applies. Then it depends ... What was agreed, according to what is it to be calculated, is there a difference between actual and target, etc.?