Calculators and formula sheet

Every formula the exams use, as a working calculator that shows the sum, not just the answer. Change any box and the working updates. For study only, never for dive planning.

Depth to pressure · Boyle's law · Gas in a cylinder or bank · Consumption and duration · Bailout duration · D050 emergency gas · Partial pressure and depth limits · Equivalent air depth · Gas density · Mixing two gases · Topping up a bank · Joining two banks · Chamber pressurisation and lock gas · Initial depth on the rich gas · Charles' law (temperature) · Vent, blowdown and joining chambers · Joining two chambers · Saturation consumables · CO2 tubes and analysers · Buoyancy and lift · Lift bag volume change · Working load limit · Hot water temperature at the diver · Ohm's law · Formula sheet

Depth to pressure
Absolute = depth/10 + 1
Boyle's law
P1 x V1 = P2 x V2 (absolute)
Gas in a cylinder or bank
Free gas = water capacity x gauge pressure
Consumption and duration
Consumption = rate x absolute; duration = gas / consumption
Bailout duration
Usable pressure = fill - (absolute + 10)
D050 emergency gas
Divers x minutes x rate x absolute pressure
Partial pressure and depth limits
PP = absolute x fraction; max depth = (limit/fraction - 1) x 10
Equivalent air depth
EAD = N2% x (depth + 10)/79 - 10
Gas density
Sum of PP x (O2 1.4102, N2 1.2346, He 0.1764)
Mixing two gases
A = final x (final% - B%)/(A% - B%)
Topping up a bank
Final = start x (start% - add%)/(final% - add%)
Joining two banks
Weighted average by gas volume
Chamber pressurisation and lock gas
Gas = volume x depth/10
Initial depth on the rich gas
[(PO2 req - present) x 1000 - D x low%]/(rich% - low%)
Charles' law (temperature)
P2 = P1 x T2/T1 (kelvin, absolute)
Vent, blowdown and joining chambers
Vent: PO2 x Pnew/Pold. Blowdown: + depth added/10 x fraction
Joining two chambers
Weighted by volume
Saturation consumables
0.72 m3 O2 and 6 kg soda lime per diver per day
CO2 tubes and analysers
True % = scale/absolute; mbar = scale x 10
Buoyancy and lift
Upthrust = volume x 1.03
Lift bag volume change
Boyle: V2 = V1 x P1/P2
Working load limit
WLL = breaking strain / factor
Hot water temperature at the diver
Drop (C) = length (m) / flow (l/min)
Ohm's law
I = V / R

Formula sheet

Pressure and volume
  • Gauge (bar) = depth / 10; absolute = depth / 10 + 1
  • fsw: absolute (ata) = depth / 33 + 1
  • Boyle: P1 x V1 = P2 x V2 (absolute)
  • Free gas = water capacity x gauge pressure
  • Usable gas = WC x (start - end pressure)
Diver gas
  • Consumption = rate x absolute (35 working, 40 emergency l/min)
  • Duration = usable gas / consumption
  • Bailout usable pressure = fill - (absolute + 10)
  • D050 bailout: 1 min per 10 m of excursion at 40 l/min
Partial pressure and mixes
  • PP = absolute x fraction; % = PP / absolute x 100
  • Max depth = (limit / fraction - 1) x 10
  • EAD = N2% x (depth + 10) / 79 - 10
  • Density = PO2 x 1.4102 + PN2 x 1.2346 + PHe x 0.1764 g/l
Mixing
  • Gas A = final x (final% - B%) / (A% - B%)
  • Top-up final = start x (start% - add%) / (final% - add%)
  • Joined banks: weighted average by gas volume
Chambers
  • Pressurisation gas = volume x depth/10 (gauge)
  • Rich gas depth = [(PO2 req - present) x 1000 - D x low%] / (rich% - low%)
  • Charles: P2 = P1 x T2 / T1 (kelvin, absolute)
  • Vent: PO2 x Pnew / Pold; blowdown: + depth/10 x fraction
  • Join: (V1 x PO2 1 + V2 x PO2 2) / (V1 + V2)
  • Lock gas = pi r² L x depth/10
Life support
  • Metabolic O2 = divers x days x 0.72 m3
  • Soda lime = divers x days x 6 kg
  • Decompression O2 = ln(absolute) x PO2 x volume
  • CO2 tube: true % = scale / absolute; mbar = scale x 10
  • SEP = true % x absolute
Lifting and buoyancy
  • Upthrust = volume x 1.03 (seawater)
  • Weight in water = weight in air - upthrust
  • WLL = breaking strain / 5 (general) or / 8 (man-riding)
Other
  • Hot water drop (C) = umbilical length (m) / flow (l/min); over 45 C scalds
  • Ohm's law: I = V / R
  • Kelvin = C + 273; 1 m3 = 1,000 l; 1% = 10,000 ppm; 1 bar = 1,000 mbar