Write the formula, align units, state assumptions and interpret the result before selecting an answer. These five examples show methods and reporting conventions; verify the governing definition for your workplace or exam question.
1. Total recordable incident rate (TRIR)
TRIR = (recordable cases × 200,000) / hours worked
Apply: Identify the OSHA-recordable cases and actual hours for the same period. Multiply cases by 200,000, then divide by hours.
Worked example: 3 cases and 400,000 hours → (3 × 200,000) / 400,000 = 1.5 cases per 100 full-time workers.
Check: The 200,000-hour base represents 100 workers at 40 hours for 50 weeks; it is a normalization, not the site's headcount. BLS incidence-rate method.
2. Days-away, restricted or transferred rate (DART)
DART = (qualifying DART cases × 200,000) / hours worked
Apply: Count qualifying cases, not lost days. Use the same period and hours denominator as the incident-rate comparison.
Worked example: 2 DART cases and 400,000 hours → (2 × 200,000) / 400,000 = 1.0.
Check: DART counts cases involving days away, restricted work or job transfer; do not substitute the total recordable count. BLS DART calculation.
3. Fatal accident rate (FAR; IOGP convention)
FAR = (fatalities × 100,000,000) / hours worked
Apply: Confirm the reporting convention first. Count fatalities and hours from the same defined population and period, then apply the 100-million-hour base.
Worked example: 1 fatality in 20,000,000 hours → (1 × 100,000,000) / 20,000,000 = 5 fatalities per 100 million hours.
Check: Organizations use different fatality-rate bases. Label the IOGP convention and never compare unlike denominators without converting them. IOGP definition.
4. Ideal steady-state dilution ventilation
Q = G / (Ctarget − Cin)
Apply: Express generation G in mass/time and both concentrations in the same mass/volume unit. Subtract supply concentration from the target; divide G by that positive difference.
Worked example: G = 120 mg/min, Ctarget = 10 mg/m³, Cin = 2 mg/m³ → Q = 120 / 8 = 15 m³/min.
Check: This simplified mass balance assumes a well-mixed space at steady state. It is not a complete ventilation design or a substitute for source capture and exposure assessment. NIOSH ventilation reference.
5. Two-leg symmetric sling tension
T per leg = W / (2 × sin θ), where θ is measured from horizontal
Apply: Find the supported load W, confirm two equal legs and a centered load, measure each leg's angle from horizontal, then compute tension and check the rated configuration.
Worked example: W = 2,000 lb at θ = 30° → T = 2,000 / (2 × 0.5) = 2,000 lb per leg.
Check: As the angle becomes flatter, tension rises. Account for the actual center of gravity, hardware, dynamic effects and manufacturer's rated sling-angle capacities. OSHA sling-angle tables.