OSHA teaching model
90 dBA criterion · 5 dB exchange
- Allowed duration
- 4 h
- Entered dose
- 100%
A result above 100% means the entered duration exceeds this model's allowed duration.
Type to filter links. Tab to a result. Escape closes results.
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Interactive formula desk
See why Q = V × A
Move one input at a time. Velocity changes airflow directly; duct diameter changes area by the square of the radius.
A = π × (12 ÷ 24)² = 0.785 ft²
Q = 2,000 × 0.785
1,571 cfm
The 24 converts diameter in inches to radius in feet: divide by 12 for feet, then by 2 for radius. This idealized exercise does not account for system losses or field measurement uncertainty.
Interactive formula desk
Compare noise dose models
Use the same exposure in both columns. The different criterion and exchange rate explain why the results are not interchangeable.
T = 8 ÷ 2^((L − criterion) ÷ exchange)
Dose % = 100 × exposure hours ÷ T
100% dose
NIOSH recommended model
85 dBA criterion · 3 dB exchange
- Allowed duration
- 0.79 h
- Entered dose
- 504%
A result above 100% means the entered duration exceeds this model's allowed duration.
This is a constant-level comparison for study. It does not assess impulse noise, hearing-protection attenuation, extended shifts, or mixed exposures. Apply the governing source and employer program in practice.
Interactive formula desk
Build a complete 8-hour TWA
The second duration adjusts automatically so the two periods always account for the full shift. Enter both concentrations in the same unit.
Full-shift exposure timeline8.0 h accounted
P1
3 h
3 h
P2
5 h
5 h
C₁T₁ = 80 × 3 = 240
C₂T₂ = 40 × 5 = 200
(240 + 200) ÷ 8
55 entered concentration unit
Zero exposure is explicit
Set a period concentration to zero when the worker is unexposed during that time; never treat a blank as zero.
Units must match
Do not average ppm with mg/m³ or combine different substances as if they were one concentration.
This arithmetic model demonstrates time weighting only. Compare the result with the correct substance-specific limit and governing source separately.
Interactive formula desk
See why flatter slings raise tension
This symmetric two-leg model measures each sling angle from the horizontal. It is not the included angle between both legs.
T = (W ÷ 2) ÷ sin(θ)
(1,000 ÷ 2) ÷ sin(60°)
Calculator must be in DEG mode.
Vertical share
500 lb
Tension / leg
577 lb
Angle multiplier
1.15×
The selected angle keeps the geometric multiplier comparatively moderate.
Teaching geometry only: equal legs, balanced load, and static conditions. Verify sling ratings, hitch reductions, hardware, load control, center of gravity, dynamic effects, and the approved lift plan.
Interactive formula desk
Stack the fall-clearance terms
Change each allowance and watch the required vertical space grow. The model uses the same four-term teaching sum as the Math Desk card.
L + D + H + C
6 + 3.5 + 6 + 1
16.5 ft
teaching clearance sum
- Lanyard
- 6 ft
- Deceleration
- 3.5 ft
- D-ring to feet
- 6 ft
- Safety margin
- 1 ft
This is a simplified teaching sum, not a system design. Actual clearance depends on the selected equipment, anchorage position, connector extension, harness stretch, worker geometry, swing-fall exposure, manufacturer instructions, and applicable requirements.
TRIR
3.20 cases per 100 full-time workers
N × 200,000 ÷ hours worked. Zero cases is valid; hours must be positive.
Calculator execution trace
Formula
TRIR = (recordable cases × 200,000) ÷ hours worked
Substitute
(4 × 200,000) ÷ 250000
- Step 1Type [4] → Press [×] → Type [200000] → Press [=]
- Step 2Press [÷] → Type [250000] → Press [=]
Interpret
Report the result as cases per 100 full-time workers; do not convert it to a percent.
DART rate
1.60 cases per 100 full-time workers
Days-away, restricted or transfer cases × 200,000 ÷ hours. Same base as TRIR; different case definition.
Calculator execution trace
Formula
DART rate = (DART cases × 200,000) ÷ hours worked
Substitute
(2 × 200,000) ÷ 250000
- Step 1Type [2] → [×] → [200000] → [=]
- Step 2Press [÷] → Type [250000] → Press [=]
Interpret
Use only cases involving days away, restriction, or job transfer; do not substitute all recordable cases.
Attack rate
5.00 %
New cases ÷ population at risk × 100. Cases cannot exceed the population.
Calculator execution trace
Formula
Attack rate % = (new cases ÷ population at risk) × 100
Substitute
(15 ÷ 300) × 100
- Step 1Type [15] → [÷] → [300] → [=]
- Step 2Press [×] → [100] → [=]
Interpret
Report a percentage for the defined population and period. The numerator cannot exceed the population at risk.
Relative risk
2.50 (unitless)
Ie ÷ Iu. Association, not proof of causation. Unexposed risk must be greater than zero.
Calculator execution trace
Formula
Relative risk = risk in exposed ÷ risk in unexposed
Substitute
0.05 ÷ 0.02
- Step 1Type [0.05] → [÷] → [0.02] → [=]
Interpret
A value above 1 indicates higher observed risk in the exposed group; it does not by itself prove causation.
Rectangular dike
1122 gal
L × W × H × 7.48 gal/ft³. Compare to the tank or scenario volume; this does not add freeboard policy.
Calculator execution trace
Formula
Volume (gal) = L × W × H × 7.48
Substitute
10 × 10 × 1.5 × 7.48
- Step 1Type [10] → [×] → [10] → [×] → [1.5] → [=]
- Step 2Press [×] → [7.48] → [=]
Interpret
The geometry returns gross gallons only. Apply displacement, freeboard, and governing containment requirements separately when the scenario supplies them.
8-hour TWA
55.0 in the entered concentration unit
(C1 × T1 + C2 × T2) ÷ 8. Use the same substance and concentration unit. Both periods must cover the full 8-hour shift.
Calculator execution trace
Formula
TWA = ((C₁ × T₁) + (C₂ × T₂)) ÷ 8
Substitute
((80 × 3) + (40 × 5)) ÷ 8
- Step 1Type [80] → [×] → [3] → [=]
- Step 2Press [+] → Type [40] → [×] → [5] → [=]
- Step 3Press [÷] → Type [8] → Press [=]
Interpret
Keep both concentrations in the same unit and confirm the time periods total exactly eight hours.
Q = VA (round duct)
1571 cfm
Radius is diameter / 24 feet. Diameter-as-radius is the trap.
Calculator execution trace
Formula
Q = V × π × (d ÷ 24)²
Substitute
2000 × π × (12 ÷ 24)²
- Step 1Type [12] → [÷] → [24] → [=]
- Step 2Press [x²] → [×] → [π] → [=]
- Step 3Press [×] → Type [2000] → Press [=]
Interpret
Dividing the diameter in inches by 24 converts it to a radius in feet before area is calculated.
Noise duration
OSHA 90 dBA / 5 dB model
4.000 h
NIOSH 85 dBA / 3 dB model
0.794 h
T = 8 ÷ 2^((level − criterion) ÷ exchange rate). This constant-level exercise does not assess mixed exposures, impulse noise or hearing protection.
Calculator execution trace
Formula
T = 8 ÷ 2^((L − criterion) ÷ exchange rate)
Substitute
OSHA: 8 ÷ 2^((95 − 90) ÷ 5) · NIOSH: 8 ÷ 2^((95 − 85) ÷ 3)
- Step 1OSHA: Type [95] → [−] → [90] → [÷] → [5] → [=]
- Step 2Press [2] → [xʸ] → [Ans] → [=], then [8] → [÷] → [Ans] → [=]
- Step 3NIOSH: repeat using criterion [85] and exchange rate [3]
Interpret
Keep each criterion paired with its own exchange rate. The two durations answer different exposure-model questions.
NIOSH RWL
25.5 lb
RWL = 51 × HM × VM × DM × AM × FM × CM. HM is 0 if H ≥ 25 in. 51 lb is not the RWL unless every multiplier is 1. Two-handed lifts only. Look up FM and CM; do not invent table values.
Calculator execution trace
Formula
RWL = 51 × HM × VM × DM × AM × FM × CM
Substitute
H=20, V=30, D=10, A=0, FM=1, CM=1
- Step 1Calculate HM [10 ÷ max(20, 10)], VM [1 − .0075 × |30 − 30|]
- Step 2Calculate DM [.82 + 1.8 ÷ max(10, 10)], AM [1 − .0032 × 0]
- Step 3Type [51] → multiply HM, VM, DM, AM, [1], and [1] → [=]
Interpret
FM and CM must come from the NIOSH tables. A computed teaching value does not replace task-specific ergonomic assessment.
FMEA RPN
160 (unitless)
S × O × D. Ranks FMEA rows. It is not a fault-tree probability.
Calculator execution trace
Formula
RPN = severity × occurrence × detection
Substitute
8 × 4 × 5
- Step 1Type [8] → [×] → [4] → [×] → [5] → [=]
Interpret
Use RPN to compare rows within the selected FMEA scheme. It is a ranking product, not a probability.
ppm → mg/m³
57.3 mg/m³
mg/m³ = ppm × MW ÷ 24.45 at 25 °C. Do not use 22.4 when the stem is 25 °C.
Calculator execution trace
Formula
mg/m³ = ppm × molecular weight ÷ 24.45
Substitute
50 × 28 ÷ 24.45
- Step 1Type [50] → [×] → [28] → [=]
- Step 2Press [÷] → [24.45] → [=]
Interpret
The 24.45 molar-volume constant applies to the stated 25 °C teaching condition. Confirm temperature and pressure assumptions before converting.
ROI
300 %
(Gain − Cost) ÷ Cost × 100. This is not payback years.
Calculator execution trace
Formula
ROI % = ((gain − cost) ÷ cost) × 100
Substitute
((80000 − 20000) ÷ 20000) × 100
- Step 1Type [(] → [80000] → [−] → [20000] → [)]
- Step 2Press [÷] → [20000] → [×] → [100] → [=]
Interpret
ROI is a percentage based on net gain. Keep it separate from payback time and confirm which benefits and costs the scenario includes.
Payback
2.00 years
Cost ÷ annual benefit. Do not call this an ROI percent.
Calculator execution trace
Formula
Payback period = initial cost ÷ annual benefit
Substitute
20000 ÷ 10000
- Step 1Type [20000] → [÷] → [10000] → [=]
Interpret
The result is years under a simple constant-benefit assumption. It is not an ROI percentage or discounted cash-flow analysis.
Expected value
10000 (same unit as consequence)
P × consequence. A ranking aid, not a complete risk evaluation.
Calculator execution trace
Formula
Expected value = probability × consequence
Substitute
0.2 × 50000
- Step 1Type [0.2] → [×] → [50000] → [=]
Interpret
Keep probability between 0 and 1 and report the consequence unit. Expected value is a decision aid, not a complete risk judgment.
Noise dose
OSHA 90 / 5 dB
100 %
NIOSH 85 / 3 dB
504 %
Dose % = 100 × hours ÷ allowed duration. Allowed duration comes from the same criterion and exchange rate as the duration card. Two-period mixed exposures are on the mixed-exposure card, not this one.
Calculator execution trace
Formula
Dose % = 100 × exposure hours ÷ allowed duration
Substitute
100 × 4 ÷ T(95)
- Step 1First calculate T for [95 dBA] using one complete model
- Step 2Type [100] → [×] → [4] → [÷] → Type the calculated [T] → [=]
Interpret
A result above 100% exceeds the entered model's allowed duration. Never use an OSHA duration in a NIOSH dose or vice versa.
Air changes / hour
6.0 ACH
ACH = cfm × 60 ÷ volume. This is a room-average rate, not proof of mixing or capture.
Calculator execution trace
Formula
ACH = airflow (cfm) × 60 ÷ room volume
Substitute
1000 × 60 ÷ 10000
- Step 1Type [1000] → [×] → [60] → [=]
- Step 2Press [÷] → [10000] → [=]
Interpret
ACH is a room-average exchange rate. It does not demonstrate effective mixing, contaminant removal, or local capture.
Two-leg sling
577 lb per leg
T = (W ÷ 2) ÷ sin(θ). θ is from the horizontal, not the included angle. A flatter sling raises tension. Equal legs only.
Calculator execution trace
Formula
Tension per leg = (load ÷ 2) ÷ sin(angle)
Substitute
(1000 ÷ 2) ÷ sin(60°)
- Step 1Confirm calculator angle mode is [DEG]
- Step 2Type [(] → [1000] → [÷] → [2] → [)]
- Step 3Press [÷] → [sin] → [60] → [)] → [=]
Interpret
The angle is measured from horizontal for this equal-leg model. A smaller angle increases leg tension.
Fall clearance
16.5 ft
L + D + H + C. Teaching sum only. It does not replace manufacturer instructions or a site clearance drawing.
Calculator execution trace
Formula
Clearance = lanyard + deceleration + D-ring height + safety margin
Substitute
6 + 3.5 + 6 + 1
- Step 1Type [6] → [+] → [3.5] → [+] → [6] → [+] → [1] → [=]
Interpret
This teaching sum does not include every system-specific allowance. Follow manufacturer instructions and the actual anchorage geometry.
Occupant load
133.3 persons (unrounded)
Area ÷ factor. Do not multiply. Occupancy rounding is a code step after this quotient.
Calculator execution trace
Formula
Occupant load = floor area ÷ area-per-person factor
Substitute
2000 ÷ 15
- Step 1Type [2000] → [÷] → [15] → [=]
Interpret
Calculate the quotient first. Apply the governing code's rounding and occupancy rules only after identifying the correct factor.
Kinetic energy
3106 ft-lbf
W v² ÷ (2 × 32.2). Translational only. Mass in slugs is not this card.
Calculator execution trace
Formula
KE = weight × velocity² ÷ (2 × 32.2)
Substitute
2000 × 10² ÷ (2 × 32.2)
- Step 1Type [10] → [x²] → [×] → [2000] → [=]
- Step 2Press [÷] → [(] → [2] → [×] → [32.2] → [)] → [=]
Interpret
This form uses weight in pounds-force and velocity in feet per second to return translational energy in ft-lbf.
Pressure force
1000 lbf
F = P × A. Gauge pressure times the loaded area. This is not stored energy in the vessel.
Calculator execution trace
Formula
Force = pressure × loaded area
Substitute
100 × 10
- Step 1Type [100] → [×] → [10] → [=]
Interpret
psi multiplied by square inches returns pounds-force. This static force is not the vessel's stored energy.
Mixed-exposure noise dose
OSHA 90 / 5 dB
100 %
NIOSH 85 / 3 dB
411 %
100 × Σ(C/T). Below-criterion periods add 0. Not impulse. Do not mix OSHA and NIOSH on the same line.
Calculator execution trace
Formula
Mixed dose % = 100 × ((C₁ ÷ T₁) + (C₂ ÷ T₂))
Substitute
100 × ((2 ÷ T at 95 dBA) + (4 ÷ T at 90 dBA))
- Step 1Calculate T₁ for [95 dBA] and T₂ for [90 dBA] using the same model
- Step 2Type [2] → [÷] → [T₁] → [+] → [4] → [÷] → [T₂] → [=]
- Step 3Press [×] → [100] → [=]
Interpret
Complete one OSHA line and one NIOSH line separately. Below-criterion handling follows the selected model.
Hood capture Q = VA
300 cfm
Q = V × (W × H / 144). Rectangle only. Diameter-as-radius stays on the round-duct card.
Calculator execution trace
Formula
Q = face velocity × (width × height ÷ 144)
Substitute
150 × (24 × 12 ÷ 144)
- Step 1Type [24] → [×] → [12] → [÷] → [144] → [=]
- Step 2Press [×] → [150] → [=]
Interpret
Dividing by 144 converts square inches to square feet. This rectangle exercise does not establish adequate capture velocity in the field.
Spill vs dike
600 gal spilled
1122 gal dike (from dike card sizes)
Spill = rate × minutes. Dike volume uses the Length/Width/Height fields on the rectangular-dike card (L×W×H×7.48). This does not add freeboard policy.
Calculator execution trace
Formula
Spill volume = leak rate × duration
Substitute
10 × 60
- Step 1Type [10] → [×] → [60] → [=]
Interpret
Compare spilled gallons with independently calculated containment capacity. Add displacement, freeboard, and regulatory criteria only when supplied.