8-hour TWA and mixture calculator
8-hour time-weighted average
| Level (ppm or mg/m³) | Hours | Remove |
|---|---|---|
- Formula: E = (C₁T₁ + C₂T₂ + ... + CₙTₙ) ÷ 8
- Multiply each level by its hours: 150 × 2 + 75 × 2 + 50 × 4
- Add them up: 300 + 150 + 200 = 650
- Divide by 8 hours (always 8, even if sampled time is 8 h): 650 ÷ 8
- Answer: 81.25
- Compare: 81.25 is not over the limit of 100.
Mixture of chemicals
| Level (ppm) | Limit (ppm) | Remove |
|---|---|---|
- Formula: Em = C₁ ÷ L₁ + C₂ ÷ L₂ + ... + Cₙ ÷ Lₙ
- Divide each level by its limit: 500 ÷ 1,000 + 45 ÷ 200 + 40 ÷ 200
- Add the fractions: 0.5 + 0.225 + 0.2 = 0.925
- Answer: 0.925, which is not over 1, so the mixture is within the limit.
Formulas and sources
- E = (C₁T₁ + C₂T₂ + ... + CₙTₙ) ÷ 8
- Em = C₁ ÷ L₁ + C₂ ÷ L₂ + ... + Cₙ ÷ Lₙ (must not be over 1)
The formula comes from
29 CFR 1910.1000(d)(1)(i)(opens ecfr.gov in a new tab)“The cumulative exposure for an 8-hour work shift shall be computed as follows: E = (Ca Ta + Cb Tb + . . .Cn Tn) ÷ 8 Where: E is the equivalent exposure for the working shift. C is the concentration during any period of time T where the concentration remains constant. T is the duration in hours of the exposure at the concentration C.”
The formula comes from
29 CFR 1910.1000(d)(2)(i)(opens ecfr.gov in a new tab)“In case of a mixture of air contaminants an employer shall compute the equivalent exposure as follows: Em = (C1 ÷ L1 + C2 ÷ L2) + . . .(Cn ÷ Ln) Where: Em is the equivalent exposure for the mixture. C is the concentration of a particular contaminant. L is the exposure limit for that substance specified in subpart Z of 29 CFR part 1910. The value of Em shall not exceed unity (1).”
Formulas and calculators on the BCSP exams
- BCSP gives you no formula sheet, and you can't bring one.
- When a question needs a formula, the formula is written into the question, unless the question is testing whether you know that formula.
- You get an on-screen calculator that works like the TI-30XS, plus a whiteboard. You can't bring your own calculator.
- On the ASP, Mathematical Calculations is its own domain, worth 10% of the exam (ASP11 blueprint).
BCSP on formulas
BCSP, What to Expect When Sitting for a BCSP Exam (item 7)(opens bcsp.org in a new tab)“For any question requiring a mathematical formula, the formula will be included within the exam question (unless the question is specifically testing your knowledge of a formula). You will not be provided or permitted to bring a formula sheet.”
BCSP on calculators
BCSP, What to Expect When Sitting for a BCSP Exam (item 6)(opens bcsp.org in a new tab)“You will be provided an on-screen calculator, emulating the TI-30XS scientific calculator. You will also have access to a white board and dry erase marker. The testing center will not provide a physical calculator or permit candidates to bring their own.”
FAQ
How do you calculate an 8-hour TWA for a chemical?
Multiply each measured level by the hours at that level, add the results, and divide by 8: E = (C₁T₁ + C₂T₂ + ...) ÷ 8. OSHA's example: 2 hours at 150 ppm, 2 hours at 75 ppm and 4 hours at 50 ppm gives (300 + 150 + 200) ÷ 8 = 81.25 ppm.
Do I divide by 8 even if the shift is shorter or longer?
Yes. OSHA's formula always divides by 8. Unexposed time counts as zero, and a 10-hour shift is still divided by 8, which raises the result.
How do you check a mixture of chemicals?
Divide each chemical's level by its own limit and add the fractions: Em = C₁ ÷ L₁ + C₂ ÷ L₂ + .... If the total is more than 1, the mixture is over the limit. OSHA's example: 500 ÷ 1,000 + 45 ÷ 200 + 40 ÷ 200 = 0.925, so it's within the limit.
This tool is for study and estimates. It doesn't replace a sampling plan or an industrial hygienist's review. Need to switch units first? Use the ppm to mg/m³ calculator.