A lot of test-takers seem to stress out about the math on the ARE 5.0 exams, especially the rounding. In this post I’ll cover some of the most common code math issues and how to round for each one.
Short answer:
(almost) Always Round Up
Long Answer:
In most cases the code will set the minimum requirement for something, so you can't use less than that number, i.e. you can't use fewer toilets, or a smaller exit door or claim your occupant load is smaller than the space requires (more on this later!) Sometimes the code sets a maximum, like for riser height, in which case you need to round the number of risers up, so that each one isn't too tall. And sometimes the maximum actually is the maximum, like for allowable building area, which you can not exceed.
The trick here is to try not to memorize this stuff. Instead, try to learn and understand what the code is trying to accomplish in a specific section. After doing the calculations, does using a lower or higher number still satisfy what the code wants to happen? And get comfortable reading the actual code. A lot of times the rules will be written right into the code so there’s no guesswork.
Let's cover four common items you might see on the ARE.
STAIR RISERS
ROUND UP
WHAT THE CODE WANTS:
The code wants people egressing from a space to not have to take really big steps.
EXPLANATION:
The 2018 IBC sets the maximum riser height at 7” See the 2018 International Building Code, section 1011.5.2. Stair riser height “shall be 7 inches maximum.”
EXAMPLE:
How many risers are needed for a 10 ft floor-to-floor height?
First, divide 120″ by 7″. This results in 17.14 risers. Since you can’t build a fraction of a riser, you need to round to a whole number. If you round down to 17 risers, each riser would end up being 120/17 = 7.06 inches. This is above the 7” code maximum, so you can’t round down. You need to round up to create 18 risers, with each one being 6.67 inches high.
OCCUPANCY
ROUND UP.
Perhaps the most confusing of the code rounding scenarios. This one is complicated by the fact that you have probably done different things on different projects, split up building areas in weird ways and maybe even calculated the occupancy of hallways and bathrooms…then had it accepted by your AHJ. On the ARE, try to remember to just go with what's in the code, and in this case, it's easy. You have to round up.
WHAT THE CODE WANTS TO HAPPEN:
The code wants you to provide enough exit access for the people who might be in a space.
EXPLANATION:
You determine occupancy by finding the floor area of a space and dividing by the occupant load factor. This is 2018 IBC Section 1004. Per section 1004.5, the “occupant load shall not be less than…” the number you get when you calculate the occupant load. This means you must round your occupant load UP.
EXAMPLE:
What is the occupancy for a 1,725 sf (net) daycare? Per 2018 IBC Table 1004.5 the occupant load factor for daycares is 35 net. 1725 / 35 = 49.28. Since you must round up, the required occupant load is 50.
Note that the occupant load is not meant to see how many people you’re allowed to have in a space…it is the code dictating how much egress size you have to provide. You can’t build a 1,725 sf daycare and claim only 10 people will use it. The occupant load calculation means you are required to provide egress for 50 people.
BUILDING AREA
ROUND DOWN
WHAT THE CODE WANTS TO HAPPEN:
The code wants to limit the size of the building to a safe size, given the occupancy and the construction type.
EXPLANATION:
This one should be fairly easy, but Chapter 5 is used to calculate the maximum building height, stories and areas. If something is a Maximum, you can not go bigger. From 503.1, “Unless otherwise specifically modified…building height, number of stories, and building area shall not exceed the limits specified…”
BATHROOMS
ROUND UP
WHAT THE CODE WANTS TO HAPPEN:
For you to provide enough places for people to go
EXPLANATION:
Section 2902 has the requirements for Minimum Plumbing Facilities. Table 2902.1 has the Minimum Number of Required Plumbing Fixtures. It’s a minimum, so anything less would be illegal! This means you will have to round UP in order to meet the code requirements.
EXAMPLE:
How many toilets and sinks are required for an art gallery with an occupant load of 530? See the math below, but a couple quick notes first:
- It is most common to take the total occupant load and divide by two to find the number of male and female occupants. By exception you can claim a distribution that is not 50:50, like for an all-male boarding school or a convent, etc.
- The requirements from Table 2902.1 list separate facilities for men and women. Shared or single-use facilities are covered in the exceptions and depend on the program and the total occupant load.
THE MORE YOU KNOW
This has been a public service announcement from Hyperfine Architecture. Got a request for future blog or YouTube topics? Send me an email! And while you're here, check out my ARE 5.0 Study Material.
