Beedy Academy · Calculators

Free process safety and OHS calculators

12 prevention calculations: mixture LEL, confined spaces, exposure limits, ventilation, noise, stored energy and falls. They do not replace regulations.

Flammable atmospheres and confined spaces

LEL of a gas mixture (Le Chatelier)

FormulaLEL_m = Σyᵢ ÷ Σ(yᵢ ÷ LELᵢ) · %LEL = C ÷ LEL_m × 100

Gas 1: share of the fuel mixture (y₁)%

Gas 1: LEL (LEL₁)% vol

Gas 2: share of the fuel mixture (y₂)%

Gas 2: LEL (LEL₂)% vol

Gas 3: share of the fuel mixture (y₃)%

Gas 3: LEL (LEL₃)% vol

Measured mixture concentration in air (C)% vol

Mixture LEL (LELm)—% vol

Concentration as % of mixture LEL—% LEL

10 % of the mixture LEL—ppm

For fuel gases that behave alike (hydrocarbons) in air. Usual LELs: methane 5.0, ethane 3.0, propane 2.1, butane 1.8, hydrogen 4.0 % vol. A detector calibrated on one gas does not read a mixture directly (response factors). Does not replace regulations, gas detectors, permits or site procedures.

Confined space: ventilation purge time

Formulan = K × ln(C₀ ÷ C) · t = n × V ÷ Q

Space volume (V)m³

Blower airflow (Q)m³/min

Initial concentration (C₀)ppm

Target concentration (C)ppm

Mixing safety factor (K)

Air changes required (n)—

Purge time (t)—min

Well-mixed model, clean supply air, no ongoing source; C₀ and C in the same unit (ppm or % LEL). K from 1 (ideal) to 3 or more depending on the shape of the space and duct position. Always test at several heights before entry and keep ventilating. Does not replace regulations, gas detectors, permits or site procedures.

Oxygen after an inert gas release

FormulaO₂ = O₂,₀ × e^{−Vg ÷ V} · O₂* = O₂,₀ × (1 − Vg ÷ V) · Vg(19.5 %) = V × ln(O₂,₀ ÷ 19.5)

Room volume (V)m³

Inert gas released (Vg)m³

Initial oxygen (O₂,₀)% vol

O₂, well mixed—% vol

O₂, worst case (O₂*)—% vol

Inert gas that brings O₂ down to 19.5 %—m³

Well mixed: the gas enters gradually and the excess flows out. Worst case: the gas pushes the air out without mixing (heavy gas, low point). Liquid nitrogen: about 0.7 m³ of gas per litre. A common minimum for entry is 19.5 % O₂. Does not replace regulations, gas detectors, permits or site procedures.

Exposure to contaminants and ventilation

ppm ↔ mg/m³ conversion

Formulamg/m³ = ppm × M ÷ Vm · ppm = mg/m³ × Vm ÷ M

Concentration in ppmppm

Concentration in mg/m³mg/m³

Molar mass (M)g/mol

Molar volume (Vm)

The ppm value in mg/m³—mg/m³

The mg/m³ value in ppm—ppm

For gases and vapours only (not dusts or fumes). ACGIH TLVs and most North American limits are at 25 °C and 1 atm; EU limits are at 20 °C. Does not replace regulations, gas detectors, permits or site procedures.

8-hour time-weighted average (TWA)

FormulaC_8h = (C₁t₁ + C₂t₂ + C₃t₃ + C₄t₄) ÷ 8 · % = C_8h ÷ OEL × 100

Concentration, period 1 (C₁)ppm | mg/m³

Duration, period 1 (t₁)h

Concentration, period 2 (C₂)ppm | mg/m³

Duration, period 2 (t₂)h

Concentration, period 3 (C₃)ppm | mg/m³

Duration, period 3 (t₃)h

Concentration, period 4 (C₄)ppm | mg/m³

Duration, period 4 (t₄)h

Exposure limit, 8-h TWA (OEL)ppm | mg/m³

8-hour TWA (C8h)—ppm | mg/m³

Share of the exposure limit—%

Total time sampled—h

Unmeasured time counts as zero exposure: only enter 0 if that is true. For shifts longer than 8 h the limit must be adjusted as your regulation requires. Ceiling and short-term limits (STEL) still apply. Does not replace regulations, gas detectors, permits or site procedures.

Mixture exposure (additive effects)

FormulaEm = C₁ ÷ L₁ + C₂ ÷ L₂ + C₃ ÷ L₃

Substance 1: concentration (C₁)ppm | mg/m³

Substance 1: exposure limit (L₁)ppm | mg/m³

Substance 2: concentration (C₂)ppm | mg/m³

Substance 2: exposure limit (L₂)ppm | mg/m³

Substance 3: concentration (C₃)ppm | mg/m³

Substance 3: exposure limit (L₃)ppm | mg/m³

Mixture exposure index (Em)—

Only add substances that act on the same organ or system. Em > 1 means the mixture limit is exceeded, even if each substance is below its own limit. Concentration and limit in the same unit. Does not replace regulations, gas detectors, permits or site procedures.

Dilution ventilation for a solvent (ACGIH method)

FormulaG = Lₑ × ρ × Vm ÷ M · Q = K × G × 10⁶ ÷ L

Solvent evaporated (Lₑ)L/h

Liquid density (ρ)kg/L

Molar mass (M)g/mol

Exposure limit (L)ppm

Mixing factor (K)

Molar volume (Vm)

Vapour generated (G)—m³/h

Required airflow (Q)—m³/h

Required airflow (Q)—m³/s

Required airflow (Q)—cfm

Method from the ACGIH Industrial Ventilation manual: K from 1 (very good mixing) to 10 (poor mixing). Dilution is not suitable for highly toxic substances or large sources: use local exhaust instead. Does not replace regulations, gas detectors, permits or site procedures.

Noise

Adding sound levels (dB)

FormulaL = 10 × log₁₀(10^L₁/10 + 10^L₂/10 + 10^L₃/10 + 10^L₄/10)

Source 1 (L₁)dBA

Source 2 (L₂)dBA

Source 3 (L₃)dBA

Source 4 (L₄)dBA

Total level (L)—dBA

Increase over the loudest source—dB

Two equal sources: +3 dB. A source 10 dB quieter adds less than 0.5 dB. Leave 0 for an unused source. Does not replace regulations, gas detectors, permits or site procedures.

Noise dose and 8-hour exposure level

FormulaTᵢ = 8 ÷ 2^{(Lᵢ − Lc) ÷ q} · D = Σ tᵢ ÷ Tᵢ × 100 · L_EX,8h = 10 log₁₀(Σ tᵢ 10^Lᵢ/10 ÷ 8) · TWA = Lc + q × log₂(D ÷ 100)

Level, period 1 (L₁)dBA

Duration, period 1 (t₁)h

Level, period 2 (L₂)dBA

Duration, period 2 (t₂)h

Level, period 3 (L₃)dBA

Duration, period 3 (t₃)h

Criterion level (Lc)

Exchange rate (q)

Noise dose (D)—%

Daily exposure level (LEX,8h)—dBA

Dose-based TWA level (TWA)—dBA

Most jurisdictions use 85 dBA with a 3 dB exchange rate; some use 90 dBA and 5 dB. With 3 dB, LEX,8h and TWA are almost equal. No threshold level is applied. Does not replace regulations, gas detectors, permits or site procedures.

Sound level at another distance

FormulaL₂ = L₁ − 20 × log₁₀(r₂ ÷ r₁) · r_t = r₁ × 10^{(L₁ − Lt) ÷ 20}

Measured level (L₁)dBA

Measurement distance (r₁)m

New distance (r₂)m

Target level (Lt)dBA

Level at r₂ (L₂)—dBA

Distance to reach Lt (rt)—m

Point source in a free field: −6 dB each time the distance doubles. Indoors, reverberation reduces the drop: measure to confirm. Does not replace regulations, gas detectors, permits or site procedures.

Stored energy and work at height

Stored energy of a pressurised gas vessel

FormulaE = P₁ × V ÷ (γ − 1) × [1 − (Pₐ ÷ P₁)^{(γ − 1) ÷ γ}] · P₁ = P + Pₐ, Pₐ = 101.325 kPa · TNT = E ÷ 4184

Gauge pressure (P)kPa

Vessel volume (V)m³

Gas (γ)

Stored energy (E)—kJ

TNT equivalent—kg

Isentropic expansion of an ideal gas (the method used for pneumatic tests, e.g. ASME PCC-2). An order of magnitude to set an exclusion zone; a hydrostatic test stores far less energy. 1 kg of TNT = 4184 kJ. Does not replace regulations, gas detectors, permits or site procedures.

Fall arrest clearance required

FormulaTFC = FF + DD + HS + H + SM · M = Dₐ − TFC

Free fall (FF)m

Deceleration distance (DD)m

Harness stretch and D-ring shift (HS)m

D-ring to feet height (H)m

Safety margin (SM)m

Available clearance (Dₐ)m

Required clearance (TFC)—m

Remaining margin (M)—m

Distances measured from the D-ring height at the start of the fall down to the first obstruction. Take the deceleration distance from the energy absorber label; add swing fall if the anchor is offset. Does not replace regulations, gas detectors, permits or site procedures.

Learning and checking tools. The ranges shown are general guidance: always follow your plant's procedures, permits and set points. Nothing is sent anywhere: the calculations run in your browser.