11.2 Exposure Quantification: Dose Equations, Average Daily Dose (ADD) & Lifetime Average Daily Dose (LADD)
Key Takeaways
- The RAGS-style oral intake equation is Intake = C × IR × EF × ED / (BW × AT), with the result in mg/kg-day when C, IR, and AT are in consistent units.
- Average daily dose (ADD) for noncancer uses averaging time AT = ED × 365 days; lifetime average daily dose (LADD) for cancer uses AT = 70 years × 365 days so the same intake is spread over a lifetime.
- RAGS Part A teaching defaults include adult body weight 70 kg, adult water 2 L/day, child soil 200 mg/day, residential 350 days/year and 30 years, and occupational 250 days/year and 25 years.
- The 2011 EPA Exposure Factors Handbook recommended mean adult body weight is 80 kg; live assessments should take current handbook age bins rather than inventing replacement precision around the RAGS teaching set.
- A worked residential water example at 3.5 mg/L, 2 L/day, 70 kg, and daily exposure for 30 years gives ADD = 0.10 mg/kg-day and LADD ≈ 0.043 mg/kg-day.
From a concentration to a milligram-per-kilogram-day dose
Handbook III.B.3 B expects you to turn an environmental concentration into a dose. For oral (and, with extra terms, dermal) Superfund-style work, EPA Risk Assessment Guidance for Superfund (RAGS) Part A still supplies the teaching equation every DABT candidate is expected to unpack:
Intake = (C × IR × EF × ED) / (BW × AT)
When C is mg per kg (soil) or mg per L (water), IR is kg/day or L/day, EF is days/year, ED is years, BW is kg, and AT is days, intake has units of mg/kg-day. That unit is what an oral reference dose (RfD) is written in. Independent OpenExamPrep material in this section covers each term, the average daily dose (ADD) versus lifetime average daily dose (LADD) choice of AT, the classic RAGS teaching defaults, and why the current Exposure Factors Handbook (EFH) should replace those defaults in live work. It is not an ABT product and does not claim official approval, review, or partnership with ABT or EPA.
Inhalation is the exception you should flag now. Classic RAGS Part A converted air into a mg/kg-day “intake” using an inhalation rate. Superfund RAGS Part F moved inhalation risk to an exposure concentration (mg/m³) compared with an RfC, because Agency inhalation toxicity values are concentrations, not oral RfDs. Section 11.3 develops that dosimetry. Do not force an air concentration through the oral intake equation merely to produce a familiar unit.
| Symbol | Meaning | Teaching units |
|---|---|---|
| C | Concentration at the exposure point | mg/kg (soil), mg/L (water), mg/m³ (air, if you are still in the old intake form) |
| IR | Contact or intake rate | kg soil/day, L water/day, m³ air/day; dermal uses area × adherence |
| EF | Exposure frequency | days/year |
| ED | Exposure duration | years |
| BW | Body weight | kg |
| AT | Averaging time | days |
| ADD | Average daily dose (noncancer) | mg/kg-day, AT = ED × 365 |
| LADD | Lifetime average daily dose (cancer) | mg/kg-day, AT = 70 y × 365 d/y |
Dermal uses the same averaging structure with extra contact terms: DAD = (C × SA × AF × ABS × EF × ED) / (BW × AT), where SA is surface area, AF is a soil-adherence factor, and ABS is an absorption fraction. You still report mg/kg-day. The oral equation is the one to memorize cold; the dermal extras are how soil on skin becomes a dose instead of a concentration.
ADD versus LADD: the averaging-time fork
Averaging time is not a free stylistic choice. It is how you match the dose to the toxicity value.
- Noncancer / ADD. Effects are treated as depending on the dose during the period of exposure. AT = ED × 365 days. If someone drinks the water for 30 years, you average over those 30 years, not over a lifetime they have not yet lived. ADD then compares with an RfD or similar chronic noncancer value.
- Cancer / LADD. EPA oral cancer slope factors are defined as risk per mg/kg-day averaged over a 70-year lifetime. AT = 70 years × 365 days/year = 25,550 days. The same milligrams ingested over 30 years are spread over 70 years, so LADD is smaller than ADD by the factor ED/70 when EF and the rest of the inputs match.
If exposure is every day (EF = 365), the 365 in the numerator and in AT cancel for ADD and you recover the compact form ADD = C × IR / BW. That cancellation is a check, not a reason to drop EF from the written equation when frequency is 350 or 250 days/year.
RAGS Part A teaching defaults—and the handbook that replaced them
Exam items still speak RAGS. Live Superfund and many EPA program assessments are supposed to speak EFH. Know both, and label which set you are using.
Well-established RAGS Part A / Superfund teaching values:
- Adult body weight 70 kg; young child (roughly ages 1–6) 15 kg
- Adult drinking water 2 L/day; child 1 L/day
- Child soil/dust ingestion 200 mg/day; adult 100 mg/day (indoor worker soil often 50 mg/day in later Superfund tables)
- Adult inhalation 20 m³/day (sometimes 15 m³/day as an indoor-only split)
- Residential 350 days/year and 30 years; occupational 250 days/year and 25 years
- Cancer averaging time 70 years (25,550 days)
Current EFH, used carefully. The 2011 Exposure Factors Handbook, Table 8-1, recommends a mean adult body weight of 80 kg, not 70 kg. Age-binned child means also differ (for example, 3 to <6 years is tabulated at 18.6 kg, not the RAGS 15 kg child). Long-term mean adult inhalation rates in the 2011 Chapter 6 tables sit near 16 m³/day for several adult age bins (15.7 m³/day for 21 to <31 years; 16 m³/day for 31 to <51 years), not the RAGS 20 m³/day teaching default. Chapter 3 (water) was updated in 2019 and Chapter 5 (soil and dust) in 2017; central-tendency soil-plus-dust rates are lower than the RAGS 200 mg/day child default and are tabulated by age. Do not invent a single replacement number for every RAGS default and treat it as official. Pull the current chapter for the age and percentile you actually need. EPA also warns that if a toxicity value was derived assuming 70 kg, changing only the exposure-side body weight can create an inconsistency that has to be thought through—not ignored and not “fixed” by a homemade factor.
Soil milligrams to kilograms. 200 mg/day = 200 / 1,000,000 = 0.0002 kg/day. Forgetting that conversion inflates oral soil dose by a million.
Worked example (residential tap water)
A residential adult drinks 2 L/day of water containing 3.5 mg/L of chemical X, every day for 30 years. Use the RAGS teaching adult body weight 70 kg and EF = 365 days/year so the arithmetic is transparent. (A RAGS residential frequency of 350 days/year would scale both ADD and LADD by 350/365.)
Numerator = C × IR × EF × ED
3.5 mg/L × 2 L/day = 7 mg/day
7 mg/day × 365 day/year = 2,555 mg/year
2,555 mg/year × 30 year = 76,650 mg ingested over the exposure window.
ADD averaging time = 30 year × 365 day/year = 10,950 days
Denominator = BW × AT = 70 kg × 10,950 day = 766,500 kg·day
ADD = 76,650 / 766,500 = 0.10 mg/kg-day
Check with the cancelled form: ADD = C × IR / BW = 3.5 × 2 / 70 = 7/70 = 0.10 mg/kg-day. The 365 and the 30 cancel because EF is 365 and AT uses the same ED.
LADD averaging time = 70 year × 365 day/year = 25,550 days
Denominator = 70 kg × 25,550 day = 1,788,500 kg·day
LADD = 76,650 / 1,788,500 = 0.04286 mg/kg-day, which rounds to 0.043 mg/kg-day at three decimal places.
Check: LADD = ADD × (ED / 70) = 0.10 × (30/70) = 0.10 × 0.4286 = 0.04286 mg/kg-day. Same ingested milligrams, longer averaging window, smaller daily dose for comparison with a lifetime slope factor.
If this were a noncancer problem, you would take 0.10 mg/kg-day to the RfD. If it were an oral cancer problem using an EPA slope factor, you would take 0.043 mg/kg-day to the slope factor. Using ADD in a lifetime cancer equation double-counts duration; using LADD against an RfD understates the dose during the years of exposure.
What the equation is not
It is not a PBPK model. It assumes a constant C, a constant IR, and complete mixing of the averaging window. It does not convert parent to metabolite. It does not know bioavailability unless you put an absorption fraction in IR or as a separate term. Peak one-day doses that drive acute effects are not LADDs. Probabilistic sampling of these same terms is section 11.4, not a different equation.
Scenario
A reviewer replaces 70 kg with 80 kg in the example above, keeps C, IR, EF, and ED unchanged, and reports ADD = 3.5 × 2 / 80 = 0.0875 mg/kg-day. The arithmetic is correct for that body weight. What is not automatic is using 80 kg in the exposure equation while leaving a slope factor or RfD that was derived as mg/kg-day assuming 70 kg—EPA’s EFH Chapter 8 highlight flags that inconsistency. A second reviewer computes LADD with AT = 30 × 365 because “the person only lived there 30 years.” That is an ADD, not a LADD, and it is the wrong input to a 70-year oral slope factor. A third reviewer converts the same water concentration to an inhalation “intake” with 20 m³/day to “cover showering” without a volatilization factor or an RfC comparison; shower inhalation belongs in an air concentration or a dedicated volatilization term, not a silent extra 20 m³ in the oral equation.
Traps
- Using ED × 365 as AT for a cancer LADD, or 25,550 days as AT for a 2-year noncancer ADD.
- Leaving soil IR in mg/day while C is in mg/kg.
- Treating 70 kg and 80 kg as interchangeable without saying RAGS teaching versus EFH 2011 recommended mean, and without checking the toxicity value’s assumed body weight.
- Forcing inhalation through mg/kg-day so it can sit next to an oral RfD when the toxicity value is an RfC in mg/m³.
- Inventing three-significant-figure EFH replacements from memory instead of opening the current handbook chapter.
A 30-year residential water exposure is being compared with an EPA oral cancer slope factor that is defined per lifetime mg/kg-day. Which averaging time produces LADD rather than ADD?
Using the RAGS-style water example in this section (3.5 mg/L, 2 L/day, 70 kg, EF = 365 days/year, ED = 30 years), what is the ADD, and what is the LADD rounded to three decimal places?
Which statement about default body weights and handbooks is accurate for exposure quantification?