Cryogenic Boil-Off Rate Calculator

Introduction to heat-leak-driven cryogen boil-off

A cryogenic vessel does not lose liquid because of time passing. It loses liquid because heat gets in. Every watt that crosses the vacuum jacket, travels down the neck tube, sneaks along a support strap or radiates onto the cold surface is absorbed by the fluid at its boiling point, and the fluid pays for that energy by evaporating. The whole of cryogenic storage engineering follows from that single sentence, and so does this calculator: it estimates the heat leak into your vessel in watts, then divides that heat leak by the latent heat of vaporisation of the fluid to get a boil-off mass rate.

That is deliberately different from the way boil-off is usually presented on the web. It is common to see a calculator that asks for a "typical boil-off percentage per day" and then decays the inventory exponentially. Both halves of that approach are wrong in ways that matter. The percentage is not a physical property of anything — it is an output of a heat-leak measurement on a particular vessel, at a particular ambient temperature, with a particular fill level and vent arrangement. And the decay is not exponential, because the heat leak does not shrink in proportion to the liquid remaining. A dewar that loses 1.8 litres of nitrogen on its first day loses very nearly 1.8 litres on its hundredth day too, right up until it runs dry.

This page therefore asks you for the things that genuinely set the answer: which cryogen, how large the vessel is, what shape it is, how good the insulation is, how thick it is, how warm the room is, and how much extra heat arrives through necks, supports and instrumentation. It returns the heat leak in watts with a breakdown, the boil-off in kilograms per hour and per day, the liquid loss in litres per day, the normal evaporation rate as a percentage of rated capacity per day, the volume of gas released at room temperature, the hold time before the vessel empties, and an optional oxygen-deficiency check for the room the vessel stands in.

How to use the vessel, insulation and environment inputs

Work down the form in order. The first group describes what is in the vessel and how big it is.

• Cryogenic fluid. Choose nitrogen, helium, oxygen, methane (as a first-pass stand-in for lean LNG), normal hydrogen or argon. Each option loads its normal boiling point, latent heat of vaporisation, saturated liquid density and room-temperature gas density from NIST saturation data at one standard atmosphere. A custom option is provided for fluids not listed; it demands positive values for all three properties, because a zero latent heat would make the boil-off rate infinite.
• Vessel capacity and unit. Enter the rated capacity in litres, cubic metres or US gallons. Capacity is what sets the geometry and therefore the surface area, and it is the denominator of the normal evaporation rate.
• Current fill level. A percentage of rated capacity. This does not change the heat leak in the model — it only sets how much liquid you actually have, and therefore the hold time.
• Vessel shape. Choose a sphere, a vertical cylinder with a height-to-diameter ratio of two (the common proportions of a laboratory storage dewar), or supply your own outer surface area in square metres if you have it from a drawing. The surface area is derived from capacity for the first two options rather than being guessed, and the calculator shows you the area it used so you can sanity check it.

The second group describes the thermal path from the room into the liquid.

• Heat-leak model. "Measured apparent conductivity" is the right choice for evacuated multilayer insulation, evacuated powder and vacuum-jacketed vessels, because the conductivity quoted for those systems is an apparent or effective value that already contains solid conduction, residual gas conduction and radiation. "Bulk insulation plus radiation" is the right choice for foam jackets, unevacuated vessels and bare cold surfaces, where a genuine solid conductivity and a separate Stefan-Boltzmann radiation term are physically distinct.
• Apparent thermal conductivity. In milliwatts per metre per kelvin, because cryogenic insulation values are small and the literature quotes them that way. Good evacuated multilayer insulation sits near 0.05 to 0.3 mW/m·K; evacuated aerogel and glass bubbles fall in the single-digit range; foam and unevacuated fill are tens of milliwatts per metre per kelvin.
• Insulation thickness. In millimetres, and it must be greater than zero. A thickness of zero has no physical meaning in the Fourier expression and the calculator rejects it rather than returning an infinite heat leak.
• Effective emissivity. Only used by the radiation model. It is the combined emissivity of the cold surface and its surroundings, between 0 and 1. Polished metal is a few hundredths; oxidised or painted surfaces approach 0.9.
• Ambient temperature. In degrees Celsius or kelvin. It must be above the boiling point of the fluid, otherwise there is no heat flowing inwards to boil anything.
• Additional parasitic heat leak. In watts, added directly to the total. This is where you put the neck tube, the support straps, instrumentation leads, transfer line stubs and any known measured residual. On a real laboratory dewar these paths are frequently larger than the heat that crosses the insulation blanket.

The last input is optional: the volume of the room the vessel stands in, in cubic metres. If you supply it, the calculator estimates how long the evolved gas would take to drive the oxygen concentration of a sealed, unventilated, perfectly mixed room down to the 19.5 % threshold that OSHA defines as oxygen deficient.

The boil-off formula: heat leak divided by latent heat

Start with the geometry, because surface area is the lever that everything else pulls on. For a sphere of internal volume the radius and outer area follow directly:

Formula: r = ((3V)/(4π))^1/3, A = 4 π r^2

For a vertical cylinder with a fixed height-to-diameter ratio , the volume relation inverts to give the diameter, and the total area is two end caps plus the side wall:

Formula: D = ((4V)/(πα))^1/3, A = (π D^2) / 2 + π D H

Heat crossing the insulation obeys the one-dimensional Fourier conduction law, written for cryogenic insulation testing by NASA's Cryogenics Test Laboratory as . With the warm boundary at ambient temperature and the cold boundary pinned at the saturation temperature of the boiling fluid :

Formula: Q_ins = (k_e A(T_amb − T_sat)) / t

The cold boundary really is pinned. As long as saturated liquid and its vapour coexist at the vent pressure, the fluid cannot warm up; all the incoming energy goes into the phase change. That is what makes a cryogenic vessel such a clean thermal measurement, and it is why boil-off calorimetry is the reference method in ASTM C1774 for measuring insulation performance in the first place.

When the insulation is a genuine bulk solid rather than an evacuated reflective blanket, radiation onto the cold surface is a separate and frequently dominant path. It follows the Stefan-Boltzmann law with the effective emissivity of the surface pair:

Formula: Q_rad = ε σ A (T_amb^4 − T_sat^4)

The Stefan-Boltzmann constant used here is the exact SI value , which has been exact since the 2019 redefinition of the SI base units fixed the Planck, Boltzmann and elementary charge constants. Note the fourth powers: at 293 K the ambient term is about 7.39 × 10⁹ K⁴ while the 77 K nitrogen term is only 3.58 × 10⁷ K⁴. The cold surface radiates back essentially nothing, so radiation heat leak is set almost entirely by the room, not by the cryogen.

Total heat leak adds the parasitic term covering neck, supports and instrumentation, and the boil-off mass rate is that total divided by the latent heat of vaporisation:

Formula: Q_tot = Q_ins + Q_rad + Q_par, m ˙ = Q_tot / h_fg

Everything reported afterwards is unit bookkeeping on that one mass rate. Dividing by saturated liquid density gives the volumetric loss; dividing that by rated capacity gives the normal evaporation rate; dividing by the room-temperature gas density gives the volume of gas that has to go somewhere.

Formula: V˙_l = (m ˙) / ρ_l, NER = 100 ⁢ V˙_l / V_cap, V˙_g = (m ˙) / ρ_g

Because is constant, the inventory falls in a straight line and the hold time is a simple division rather than a logarithm:

Formula: V(t) = max (0, V_0 − V˙_l t), t_hold = V_0 / V˙_l

Worked example: a 240-litre liquid nitrogen storage dewar

Take a full 240 L vertical cylindrical liquid nitrogen dewar, height-to-diameter ratio two, wrapped in 25 mm of evacuated multilayer insulation with a measured apparent conductivity of 0.10 mW/m·K, standing in a 20 °C laboratory, with 1.5 W of measured parasitic heat leak down the neck and support straps.

Geometry first. With  m³ and , the diameter is 0.5346 m, the height 1.0691 m, and the outer area  m². Nitrogen boils at 77.355 K at one standard atmosphere, so the temperature difference is 293.15 − 77.355 = 215.795 K. The conduction term is then

Formula: Q_ins = (1.0 × 10^−4 ⁢ 2.2447 ⁢ 215.795) / 0.025 = 1.938 W

Adding the 1.5 W parasitic load gives a total heat leak of 3.438 W. Nitrogen's latent heat of vaporisation at the normal boiling point is 199.18 kJ/kg, so

Formula: m ˙ = (3.438 W) / (199180 J /kg) = 1.726 × 10^−5 kg /s = 1.49 kg /day

Dividing by the saturated liquid density of 806.08 kg/m³ gives 1.85 litres of liquid lost per day, which against the 240 L rated capacity is a normal evaporation rate of 0.77 % per day. That figure lands squarely inside the 0.5 % to 1 % band that manufacturers publish for well-maintained static storage dewars, which is the sanity check you want: the model reproduces the data sheet from first principles instead of taking the data sheet as an input. Hold time from full is 240 ÷ 1.85 = 130 days, and the vessel releases 1.28 m³ of nitrogen gas per day into the room at 20 °C.

Now change one thing. Keep the same 3.438 W of heat leak and put liquid helium in the vessel instead. The mass rate rises to 14.4 kg/day because helium's latent heat is only 20.56 kJ/kg, and because liquid helium is only 124.67 kg/m³ that mass is 115.9 litres per day — 48 % of the vessel emptying daily, a hold time of about two days. Nothing about the vessel changed; only the fluid did. This is why a helium cryostat is a fundamentally different machine from a nitrogen dewar, with vapour-cooled shields, a liquid nitrogen guard bath and an order of magnitude more attention paid to every conduction path. The comparison table the calculator prints after each run makes this explicit for all six fluids at your own computed heat leak.

Reading the normal evaporation rate, hold time and gas volume

The heat-leak breakdown is the first thing to look at. If the insulation term dominates and it is much larger than you expected, the usual culprits are a soft vacuum, a compressed blanket or an overstated thickness. Multilayer insulation is exquisitely sensitive to mechanical load: NASA's Cryogenics Test Laboratory reports that six MLI systems averaging 0.6 W/m² of heat flux under no load suffer a fifteenfold increase in heat flux under a mere 0.7 kPa (0.1 psi) of compression, roughly fortyfold at 7 kPa and more than a hundredfold at 70 kPa. A blanket squashed by a cable tie or a strap is not the blanket you specified.

If the parasitic term dominates, that is normal and healthy for a small laboratory dewar. Necks and supports are structural necessities and they conduct. It also tells you where to spend engineering effort: shrinking the neck cross-section or intercepting it with the cold vent gas will do far more for your hold time than adding insulation layers.

The normal evaporation rate is the number to compare against a data sheet, and the comparison is only fair at the conditions the manufacturer used: full vessel, standing still, vented to atmosphere, no cold load inserted, and an ambient temperature near 20 °C. Every real-world departure from that makes the true loss worse. Withdrawing liquid, inserting warm samples, opening the neck, moving the vessel and transferring through a warm line all inject energy that this steady-state model does not see.

The gas volume output is the one people forget. That 1.28 m³ per day is not a rounding error in a laboratory: in a small unventilated room it is a genuine asphyxiation hazard, and the calculator's optional room check quantifies it.

Cryogen property reference used by this calculator

Every fluid property below was taken from the NIST Chemistry WebBook thermophysical property database, evaluated on the saturation line and interpolated to exactly 101.325 kPa. The gas density column is the real-gas density of the same substance at 20 °C and 101.325 kPa, and the expansion ratio is simply the quotient of the two densities.

Two caveats on that table. The hydrogen row is normal hydrogen, the 75 % ortho equilibrium mixture; hydrogen stored as a liquid is catalytically converted to parahydrogen, which boils at about 20.28 K with a slightly lower latent heat. Worse, the spontaneous ortho-to-para conversion of unconverted normal hydrogen releases roughly 527 kJ/kg inside the tank, more than its own latent heat of 448.7 kJ/kg, which is why liquefiers use staged catalytic converters. The methane row is a stand-in for lean LNG and does not capture weathering of a real multicomponent mixture.

The helium row is the one worth staring at. Its latent heat is roughly one tenth of nitrogen's and its liquid density roughly one sixth, so per watt of heat leak liquid helium disappears about 63 times faster by volume than liquid nitrogen. That single ratio explains most of the architecture of low-temperature laboratories.

Choosing a defensible insulation conductivity

The apparent thermal conductivity you type in is the least certain number in the calculation, and it is worth an order-of-magnitude sanity check before trusting the output. NASA's Kennedy Space Center Cryogenics Test Laboratory measures cryogenic insulation systems with liquid nitrogen boil-off calorimeters at boundary temperatures of 293 K and 78 K, following ASTM C1774, and reports effective conductivities spanning roughly 0.01 to 100 mW/m·K across the whole family of materials and vacuum levels.

You can derive the multilayer figure yourself from published NASA data rather than taking it on trust. Six MLI systems tested under no mechanical load averaged 0.6 W/m² of heat flux at a typical blanket thickness of about 22 mm over a 215 K temperature difference. Rearranging Fourier's law gives  W/m·K, that is 0.061 mW/m·K. The same source reports that 0.7 kPa of compression multiplies that heat flux fifteenfold, which is where the compressed row of the table comes from. Whenever your supplier can provide ASTM C1774 or ASTM C740 test data for the actual blanket you are installing, use their number instead of any table.

Expansion ratios and the oxygen-deficiency hazard

The expansion ratio column above is not a curiosity. Boil-off gas has to go somewhere, and in an enclosed room it goes into the air you are breathing. OSHA's respiratory protection standard, 29 CFR 1910.134(b), defines an oxygen-deficient atmosphere as one below 19.5 % oxygen by volume, and treats every such atmosphere as immediately dangerous to life or health. Normal air is about 20.9 % oxygen. Displacing air with an inert gas at constant pressure dilutes the oxygen fraction, so the volume of released gas that takes a perfectly mixed, unventilated room to the threshold is

Formula: V_g,19.5 = V_room (20.9 / 19.5 − 1) ≈ 0.0718 ⁢ V_room

For the worked example above, a 60 m³ room reaches the threshold after only 4.31 m³ of nitrogen gas, which at 1.28 m³ per day takes about 3.4 days of routine boil-off with the door shut. A single dropped or vented dewar does it in seconds. This is the reason CGA P-12, Safe Handling of Cryogenic Liquids, and essentially every institutional cryogen policy require ventilation and oxygen monitoring in rooms where cryogens are stored. Note also that the hazard inverts for liquid oxygen: an oxygen-enriched atmosphere above roughly 23.5 % dramatically increases the flammability of ordinary materials, so the calculator flags oxygen enrichment rather than deficiency when you select oxygen.

Limitations and assumptions behind this heat-leak estimate

This is a steady-state, single-node, one-dimensional model, and you should know exactly where it stops being true.

• Constant heat leak. The model assumes the full outer surface area participates at all fill levels. In reality the wetted area shrinks as the level drops while the vapour space warms, so late-life boil-off usually accelerates somewhat. Treat the hold time as an optimistic bound.
• Vent pressure fixed at one standard atmosphere. All properties are evaluated at 101.325 kPa. A pressure-building vessel held at 1 bar gauge has a higher saturation temperature, a lower latent heat and a smaller temperature difference, so its behaviour differs materially. Pressurised and supercritical vessels are outside this model.
• No liquid withdrawal, transfer or cold load. Cooling down a warm sample, a warm transfer line or a warm probe consumes cryogen directly, and that consumption is frequently larger than a whole day of standing boil-off. Add it separately.
• Flat plate geometry for the insulation. Fourier's law is applied with the outer area and a uniform thickness. For thick insulation on a small vessel the curvature correction matters, and the true area for conduction lies between the inner and outer surfaces.
• No double counting check across models. If you select the measured apparent conductivity mode you must not add a separate radiation term, because the measured value already contains it; the calculator enforces this by hiding the emissivity field in that mode.
• Steady state only. Cool-down transients, thermal stratification, tank rollover in LNG service, ortho-to-para conversion heat in hydrogen, and superfluid helium below the lambda point at 2.1768 K all have their own physics that this page does not attempt.
• Not a safety instrument. The oxygen-deficiency estimate assumes a sealed, perfectly mixed room with no ventilation and no stratification. Cold gas is denser than air and pools at floor level, which can produce dangerous local concentrations long before the well-mixed average reaches any threshold. Use a calibrated oxygen monitor, not arithmetic.

Within those assumptions the calculation is straightforward physics with no fitted parameters and no invented coefficients, which is precisely why it is worth doing this way rather than guessing a percentage.

Common questions about cryogenic boil-off calculations

Sources for the fluid properties, constants and insulation data