Hydraulic Accumulator Calculator — Real-Gas Sizing, Precharge & PED Category

Governing standard: Real-gas nitrogen sizing (Span et al. 2000 equation of state)· Slow, fast or slow-charge / fast-discharge cycles on real N₂ over the temperature range · PED 2014/68/EU Annex II category · EN 14359 (accumulator construction standard) is background only, not implemented

Page last updated 21 October 2026

Video walkthrough (6:16)

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A lot of accumulator calculators use the ideal gas law. Between 90 and 400 bar, nitrogen doesn't behave that way. It's stiffer.

The ideal law overstates the oil you get by 4 to 58 percent, and it's on the unsafe side every time.

This is the MechanixCalc accumulator calculator. It sizes bladder, piston, diaphragm and bellows accumulators on real nitrogen, and shows every check with its source. So let's size one properly, and see what changes.

Here's the job. A press needs 10 litres of oil, between 150 and 250 bar. The shop runs from 10 °C in winter to 50 °C beside the power pack in summer.

A bladder accumulator, nitrile bladder, hydraulic oil. The usual choice.

First question. Where does the precharge go? For energy storage, the makers' rule is no more than 90 % of the minimum pressure, at the hottest temperature. Here, 135 bar at 50 °C.

Why the hot end? Gas pressure rises with temperature. Set it on a cool day, and by summer the precharge is above your minimum pressure. Then the bladder closes on the poppet at the bottom of every stroke.

Nobody fills an accumulator at 50 °C, though. So the tool gives you the workshop number. At 20 °C, with the oil side drained, fill to 119.4 bar. And there's a gauge table for whatever day you check it.

The other side of that coin. On a 10 °C morning the same charge reads 114 bar, and the accumulator gives less oil. So the size is taken at the cold end.

Next question. How fast does it run?

If the oil came and went slowly, the gas would stay at room temperature. That's the slow, isothermal case. 36.5 litres of gas.

Cycle it fast, back to back, and the gas heats on the way in and cools on the way out. It's a stiffer spring. 62 litres.

But a press does neither. It charges, then sits there, and the gas settles back to room temperature. Then the cylinder takes the oil in one fast stroke, and the gas expands and chills. 72 litres.

Same machine. Same 10 litres. 36 or 72, just from how fast it runs. That's double the vessel.

If you know your real cycle times, the timed model sits in between. About 65 litres with these times. When in doubt, take slow charge, fast discharge. It's the conservative one.

And for comparison, the catalogue short-cut, a fast compression straight from the precharge, says 48 litres. For a press that sits charged and fires, that's a third too small.

Now the checks. Precharge, fine. Pressure ratio, 2.2 to 1 against a limit of 4. Fine.

But one says CHECK.

After the press has sat charged, a fast discharge drops the gas to −28 °C. A standard nitrile bladder is good to −15 °C.

The bladder wall won't follow the gas all the way down. But do that every stroke, and nitrile goes brittle and cracks. And it's the expansion that does it, not the weather.

The tool gives you the ways out. A lower pressure ratio, a slower discharge, or a low-temperature compound. And it says to confirm with the maker. Which is what you'd do anyway.

So let's take one. Low-temperature nitrile, good to −35 °C.

And the check clears.

72 litres of gas. So you order an 80-litre accumulator. And you'd be short.

The number on the nameplate isn't the gas volume. The bladder and the poppet take up room, and a datasheet can list as little as 85 % of it as gas. 80 litres can mean as little as 68 litres of gas. So the tool recommends the next size up, 100. And the datasheet's effective gas volume is the number that counts.

Which brings up the question you get on site. There's an 80-litre unit already on the shelf. Will it do?

If this press cycled back to back, yes. 11 litres.

But it sits charged and fires. Taking 85 % as gas, it gives 9.4. About half a litre short at the cold end. Put in the datasheet's real gas volume before you write it off.

The 100-litre unit gives 11.8. With the low-temperature bladder, that's the one to buy.

Before you sign it off, the safety step. On the gas side this is a PED category IV vessel. The test pressure has to be at least 393 bar.

Now a trap. Pressurise it on a cool morning, valve it off, and let the plant warm up to 50 °C. The trapped gas and oil climb to about 319 bar. The system relief can't see it, it's on the other side of the valve. And this vessel is set up for 275.

So it sits on a safety block. An isolating valve, a relief between that valve and the accumulator, and an unloading valve that dumps the oil at shut-down.

Through a 1.5 mm bleed orifice, that takes about four minutes. Then the oil side reads zero. The gas side doesn't. It still holds its precharge. Never take the accumulator off until the nitrogen is let down through the charging kit.

It also covers who inspects it and how often, and the nitrogen bottles to charge it.

Working in psi and gallons? One click, and every number follows.

All of it goes into the PDF. The method, every check with its source, the fill table, and that hot-day FAIL, in red, until you deal with it.

What it doesn't do: it doesn't design the shell. That's the vessel maker's job, under the construction standard, and the tool says so.

Real nitrogen. The right cycle. The cold end. The nameplate read properly. And the cold-gas check and the hot-day trap dealt with. Those are numbers you can put your name to. Size your next accumulator on MechanixCalc.com.

The MechanixCalc hydraulic accumulator calculator sizes bladder, piston, diaphragm and welded metal-bellows accumulators on real nitrogen: the reference equation of state of Span et al. (2000), the same one NIST uses. At hydraulic pressures nitrogen is noticeably stiffer than an ideal gas (Z = 1.05 at 200 bar, 1.19 at 350 bar), and the ideal law P·Vⁿ = const undersizes accumulators by 4–58 %. EN 14359, the European standard for gas-loaded accumulators, governs how the vessel itself is built and tested; it does not specify this application sizing, and the calculator does not implement it. Enter the pressures, the operating temperature range and either the fluid volume you need (to size a new accumulator) or the gas volume of one already installed (to check it). The precharge is defined at the maximum operating temperature, as the accumulator makers specify, and the size is taken at the temperature that delivers least — usually the cold end. The tool returns the gas volume, what the accumulator delivers at each end of the range, the gauge pressure to fill it to in the workshop, a precharge check table against temperature, the gas-temperature range of the cycle and every limit check with its source.

It is built for hydraulic systems and machine-design engineers who need a defensible accumulator selection for peak-flow buffering, emergency actuation, shock absorption, pulsation damping or thermal compensation, for service technicians who need the right precharge for an installed accumulator, and for anyone who must hand a reviewer a worked, method-stated calculation with the PED 2014/68/EU category and a branded PDF engineering report.

What this calculator does

Accumulator sizing on real nitrogen (Span et al. 2000 equation of state, proven against NIST data and maker examples) — bladder, piston, diaphragm and welded metal-bellows types
A nominal size is not its gas volume: the recommended size is the one whose effective gas volume (85 % of nominal, the smallest the makers publish) covers the requirement; a Check job takes the datasheet's effective gas volume
Four gas processes: slow (isothermal), fast continuous cycling (the steady real isentrope), slow charge or held charged with a fast discharge — the cycle of most presses, clamps and emergency strokes, and the conservative one — and a timed cycle: your charge, hold, discharge and rest times with the gas's thermal time constant (heat exchange through the shell)
Operating temperature range: the precharge is defined at the maximum temperature (the makers' rule), the size is taken at the temperature that delivers least, and the fill pressure at your workshop temperature is given with a check table
Check an installed accumulator: what it delivers over the temperature range, the precharge it should have and the gauge reading to fill it to
Every limit with its source: precharge ≤ 0.9 × P₁ at T_max, bladder p₂ : p₀ ≤ 4 : 1, diaphragm 4–10 : 1, bellows 20 : 1 and its stroke, piston precharge limits and seal friction, size ranges, bladder compound against the fluid and the temperatures, the gas cooling on a fast discharge (cold cracking) and the hot gas of the first charge
Installation: flow through each unit's own port against the makers' limits by size, piston speed against the seal, installation position, back-up nitrogen bottles with the gas-line velocity, the oil weight for the clamps
Flow duty: one peak event, a full duty cycle of phases (with the check that the pump covers the average demand) or emergency strokes; line loss with your length, bore and fluid
Other duties: pressure-shock absorber (Joukowsky), piston-pump pulsation damper and thermal expansion / contraction compensation — each with the catalogue short-cut alongside
Safety: PED 2014/68/EU category per Annex II Table 2, minimum hydrostatic test pressure, relief-valve Kdr·A for your pump flow, hot-day pressure against the relief setting, vessel cycles and the permissible fluctuation width against the maker's rating, the bleed-down time through the unloading orifice, and who inspects the vessel and how often (Germany BetrSichV, UK PSSR)
Service: the precharge read on site converted to the reference temperature with a verdict, pressure holding after a fast charge (gas cooling and leakage, time to the pressure switch), the nitrogen bottles to charge it (booster or reducer), the gas as a hydraulic spring (capacitance and natural frequency), shipping a charged accumulator
Energy per discharge on real nitrogen, peak power and the pump downsizing it allows
Branded PDF engineering report with the full method, the checks and their sources

Method & formulas

Accumulator sizing — real-gas nitrogen

The precharged nitrogen is one fixed mass m = ρ₀·V₀, so its volume at any pressure is V(p) = V₀·ρ₀/ρ(p), with the density ρ from the Span et al. (2000) reference equation of state (an engineering method — EN 14359 covers the vessel's construction and testing, not this sizing). Slow cycles follow the isotherm at the ambient temperature; fast cycles cycled continuously follow the steady isentrope on which the small heat exchange with the shell balances over each cycle, whose real exponent rises from 1.4 at low pressure to about 2 at 200 bar. The ideal-gas shortcut P·Vⁿ = const ignores both effects and undersizes the vessel by 4–58 % at hydraulic pressures. The gas is precharged to P₀ with the accumulator fully charged to volume V₀. At the minimum system pressure P₁ the gas has expanded to V₁; at the maximum system pressure P₂ it has been compressed to V₂. The usable fluid volume ΔV delivered between P₁ and P₂ is V₁ − V₂, and the required total gas volume V₀ follows directly.

The precharge P₀ is defined at the maximum operating temperature — the accumulator makers' rule, P₀ = 0.9 × P₁ for energy storage, so the separator never touches the fluid port even on the hottest day. The sealed nitrogen then follows its real-gas isochore: colder, it reads a lower pressure and the accumulator delivers less. The calculator evaluates the cycle at both ends of the operating range and sizes on the end that delivers least (normally the cold one); it also gives the precharge to set at the workshop temperature. A precharge at or above P₁ at any operating temperature drives the separator onto the poppet valve every cycle — a failure the tool reports, never hides.

A third cycle sits between the two textbook limits: a pump that charges slowly (the gas has cooled back to ambient when the accumulator is full) and a consumer that draws fast (the gas expands on the isentrope from P₂). It delivers the least fluid per litre of the three and cools the gas the most — below the low limit of a standard nitrile bladder at moderate pressure ratios, the cold cracking the makers warn about — so it is the conservative choice whenever the discharge is fast.

One gas mass on real nitrogen

V₁ = V₀ · ρ₀/ρ₁ ; V₂ = V₀ · ρ₀/ρ₂ (never more than V₀)

where ρ₀ = nitrogen density of the charge (precharge P₀ at the maximum operating temperature); ρ₁, ρ₂ = density at P₁ and P₂ on the cycle's path at the governing temperature — the isotherm (slow), the steady isentrope of continuous fast cycling (fast), or the isotherm to P₂ then the isentrope from (P₂, T) to P₁ (slow charge, fast discharge) — all from the Span et al. (2000) equation of state, absolute pressures; V₀ = gas volume (L)

Required gas volume

V₀ = ΔV / [ρ₀/ρ₁ − ρ₀/ρ₂] at the temperature that delivers least

where ΔV = required usable fluid volume (L); all other symbols as above

Precharge at another temperature (sealed charge)

p₀(T) = p(ρ₀, T)

where the real-gas isochore of the charge — the ideal form is the makers' p₀,T = p₀,T_max · (T + 273)/(T_max + 273)

Flow & pressure response

During peak demand the accumulator supplements the pump to deliver the required flow Q_peak: Q_acc = Q_peak − Q_pump, and ΔV = Q_acc × t_delivery / 60. For a whole machine cycle, the consumer flow of each phase is entered and the required ΔV is the deepest draw below full over a repeating cycle — and if the pump delivers less than the consumers take per cycle, no accumulator is big enough, which the calculator says. For an emergency supply, ΔV is the strokes the accumulator must make with the pump stopped plus the leakage while holding. The line check uses the line's own length, inside diameter and the fluid's density (Hagen–Poiseuille 64/Re below Re 2300; from Re 2300 up, the larger of 64/Re and the Haaland approximation).

Accumulator flow supplement

Q_acc = Q_peak − Q_pump [L/min]

where Q_acc = peak flow supplied by the accumulator (L/min); Q_peak = peak system demand (L/min); Q_pump = continuous pump output (L/min)

Darcy–Weisbach pressure drop

ΔP = f_D · (L / d) · (ρ · v²) / 2 [Pa]

where f_D = Darcy friction factor (64/Re below Re 2300, else max of 64/Re and Haaland); L = line length (m); d = pipe inside diameter (m); ρ = fluid density (kg/m³); v = mean flow velocity (m/s)

Energy storage and PED categorisation

The energy stored in an accumulator per cycle equals the work done on the gas. On real nitrogen this is exact from the equation of state: on the isentrope (fast) E = m·(u₂ − u₁), the internal-energy change; on the isotherm (slow) E = m·(a₂ − a₁), the Helmholtz-energy change — minus the atmosphere's share p_atm·ΔV for the energy delivered to the circuit. The mean-pressure shortcut ((P₁+P₂)/2)·ΔV is not used, because that chord lies above a convex gas curve and overstates the energy the store can actually deliver. The peak discharge power is the stored energy divided by the discharge time, and the peak-power reduction fraction (1 − P_avg / P_peak) quantifies the pump/motor downsizing benefit.

PED 2014/68/EU classes an accumulator by its nitrogen side, Annex II Table 2 (vessels for group 2 gases), from the maximum allowable pressure PS and the volume V — the calculator takes PS = max(P₂, P_sv), because PS cannot sit below the relief-valve setting. Above 1 L: up to PS·V = 50 bar·L the vessel is outside the categories (sound engineering practice, Art. 4(3)), Category I to 200, II to 1000, III to 3000, IV above (a vessel at PS ≤ 4 bar stays Category III); at 1 L or less: Art. 4(3) up to 1000 bar, Category III to 3000, IV above. The hydrostatic test pressure must be at least 1.43 × PS (Annex I §7.4), and the relief valve must pass the pump's full flow with a momentary surge of at most 10 % of PS (§7.3) — the calculator gives the certified Kdr·A the valve must have.

Stored energy on real nitrogen

E = m·(u₂ − u₁) − p_atm·(V₁ − V₂) (fast) ; E = m·(a₂ − a₁) − p_atm·(V₁ − V₂) (slow)

where m = ρ₀·V₀ = nitrogen mass (kg); u = specific internal energy, a = specific Helmholtz energy of N₂ at the states P₂ and P₁ (Span et al. 2000); p_atm = 1.01325 bar.

Worked example

Size a bladder accumulator for a slow (isothermal) cycle at a constant 20 °C: the system requires ΔV = 10 L of usable fluid between P₁ = 100 bar (min) and P₂ = 150 bar (max). Nitrogen precharge P₀ = 90 bar (= 0.9 × P₁, the makers' rule).

Given

Required usable volume ΔV10 L
Nitrogen precharge P₀90 bar
Minimum system pressure P₁100 bar
Maximum system pressure P₂150 bar
Gas processIsothermal at 20 °C (slow cycle)

Result

Total gas volume V₀34.8 L
Gas volume at P₁ (min)V₁ = 31.5 L
Gas volume at P₂ (max)V₂ = 21.5 L
Usable fluid deliveredΔV = 10.0 L ✓
Recommended nominal size50 L (85 % effective gas = 42.5 L ≥ 34.8 L)

The precharged nitrogen is one fixed mass, so its volume at any pressure is V(p) = V₀ · ρ₀/ρ(p). Gas pressures are ABSOLUTE: p = P + 1.013 bar.
Real-nitrogen densities at 20 °C (Span et al. 2000 / NIST): ρ₀ = 104.751 kg/m³ at 91.013 bar abs; ρ₁ = 115.974 at 101.013 bar abs; ρ₂ = 169.986 at 151.013 bar abs.
Ratios: r₁ = ρ₀/ρ₁ = 0.9032; r₂ = ρ₀/ρ₂ = 0.6162; r₁ − r₂ = 0.2870.
Total gas volume: V₀ = 10 / 0.2870 = 34.8 L. (The ideal gas law gives 33.5 L, a vessel that delivers only 9.6 L — 4 % short even at this moderate pressure; from 210 to 400 bar an ideal-gas-sized vessel delivers 9–37 % less than required (slow cycles 9–27 %, fast 19–37 %).)
Check gas volumes at the band limits: V₁ = 34.84 × 0.9032 = 31.5 L; V₂ = 34.84 × 0.6162 = 21.5 L; ΔV_check = V₁ − V₂ = 10.0 L ✓.
Choose the size by its EFFECTIVE gas volume, not its nominal number: the bladder and the poppet valve take up room, and the effective gas volume the makers list can be as low as 85 % of nominal. A nominal 40 L may hold only 34 L of gas — less than 34.8 L — so the next size, 50 L (≥ 42.5 L of gas), is the safe choice; a 40 L unit qualifies only if its datasheet effective gas volume is at least 34.8 L.

Illustrative example at one temperature — with an operating range the precharge is set at the hottest temperature and the cold end then governs, which makes V₀ larger; the calculator does both ends. For a fast discharge V₀ is larger still (the real isentrope is stiffer), and a slow charge with a fast discharge is the largest — the conservative basis when the consumer draws fast.

Frequently asked questions

Which standard does this accumulator calculator use?

No standard governs the sizing: the engine sizes on real nitrogen — the reference equation of state of Span et al. (2000), the one NIST uses — over your operating temperature range, along the isotherm (slow cycles), the isentrope (fast cycles) or a slow charge followed by a fast discharge. It does not use the ideal gas law, which undersizes accumulators by 4–58 % at hydraulic pressures. Every limit check names its source (the accumulator makers' catalogues and operating instructions). The PED category follows PED 2014/68/EU Annex II Table 2. EN 14359:2017+A1:2021 (gas-loaded accumulators for fluid power applications) is the construction and testing standard for the vessel; it does not specify this sizing and is not implemented. Panels without a governing standard (shock, pulsation, thermal duties, the cycle simulation) carry an in-product engineering-method note.

What is gas precharge and how is P₀ set?

The precharge P₀ is the nitrogen pressure in the accumulator with no oil in it. The accumulator makers define it at the MAXIMUM operating temperature: P₀ = 0.9 × P₁ for energy storage (0.6–0.9 × the mean pressure for shock absorbers, about 0.6 × the mean pressure for pulsation dampers), so the separator never touches the fluid port, even on the hottest day. The sealed nitrogen reads lower when colder, so the pressure you fill to in a cool workshop is lower than P₀ — the calculator gives that fill pressure and a table of what the gauge should read at each temperature.

How do I find the right precharge for an accumulator that is already installed?

Choose the Check job and enter the installed gas volume, the minimum and maximum working pressures and the temperature range. The calculator gives the recommended precharge at the maximum temperature, the gauge pressure to fill to at your workshop temperature, what the accumulator delivers at the cold and hot end of the range with your current precharge and with the recommended one, and whether the separator would touch the fluid port at any temperature. Check the precharge in the first week of operation, again after 3–4 months and then at least once a year, with the fluid side drained — with oil pressure present the gauge reads the system, not the gas.

Why does the operating temperature change the accumulator size?

The nitrogen is sealed: its mass is fixed by the precharge at the maximum temperature. When it is colder, the same gas is denser and its pressure lower, so between P₁ and P₂ it breathes less fluid. The calculator works out the cycle at both ends of the range on real nitrogen and sizes on the end that delivers least — usually the cold one. If the precharge reached P₁ at the hot end, the separator would be driven onto the poppet valve every cycle; the calculator reports that as a failure.

When should I use isothermal, adiabatic or slow charge / fast discharge?

Isothermal when both the charge and the discharge are slow (minutes) and the gas stays at the oil temperature. Fast continuous cycling when charge and discharge are fast (seconds) and back to back: the gas follows the real nitrogen isentrope, whose exponent is about 2 at 200 bar rather than the textbook 1.4, settling on the one whose heat exchange balances over the cycle. Timed when you know the charge, hold, discharge and rest times: the tool integrates the energy balance with the gas's thermal time constant τ (your measured value, or an estimate evaluated at 0.5·τ … 2·τ). Slow charge / fast discharge when a pump fills the accumulator slowly and a consumer draws from it fast — presses, clamps, emergency strokes. That cycle delivers the least fluid per litre and cools the gas the most, so it is the conservative choice whenever the discharge is fast; the calculator also checks the coldest gas temperature against the bladder compound's low limit (cold cracking).

What is the PED category and why does it matter?

The Pressure Equipment Directive (PED) 2014/68/EU classes an accumulator by its nitrogen side (Annex II Table 2, group 2 gases), from the maximum allowable pressure PS — the calculator uses PS = max(P₂, P_sv), since PS cannot sit below the relief-valve setting — and the volume V. Above 1 L: up to PS·V = 50 bar·L no category (sound engineering practice), Category I to 200, II to 1000, III to 3000, IV above; at 1 L or less: no category up to 1000 bar, III to 3000, IV above. The higher the category, the more the conformity assessment involves a notified body. The calculator also gives the minimum hydrostatic test pressure (1.43 × PS) and the relief-valve flow area your pump flow needs.

Can it size a shock absorber or a pulsation damper?

Yes. The Other duties step sizes a pressure-shock absorber for a valve closing in a line (Joukowsky pressure rise with the wave speed in an elastic pipe and the reflection time), a pulsation damper for a piston pump (the pump's flow ripple from its crank kinematics) and an accumulator for trapped fluid that heats or cools. Each uses real nitrogen and shows the catalogue short-cut alongside, so you can compare with a maker's catalogue. For a shock the real-gas volume is several times the short-cut: the line's supply keeps pushing at the operating pressure while the column stops, so only the work above that pressure absorbs its kinetic energy.

Why is the recommended accumulator size bigger than the gas volume I need?

Because a nominal size is not its gas volume. The bladder, the poppet valve and the piston take up room, so the effective gas volume the makers list is 85–95 % of the nominal size, depending on the type and series. The calculator recommends the smallest standard size whose effective gas volume (85 % of nominal — the smallest ratio the makers publish) covers the volume you need. When you check an installed accumulator, enter its effective gas volume from the datasheet, or leave the basis on nominal and the tool applies the same 85 %.

How long does it take to bleed an accumulator down at shut-down?

Machinery law requires stored energy to be released or isolated at shut-down (Machinery Directive 2006/42/EC, Annex I 1.6.3). The calculator gives the time for the accumulator to empty through the unloading valve's orifice (1.5 mm by default, editable) with the gas expanding until the separator seats, and the oil volume released. Check that time against your maintenance procedure; the pressure gauge must read zero before anyone opens the circuit. That gauge shows the oil side only: the gas side still holds its precharge, so let the nitrogen down through the charging kit before the accumulator is removed or its gas end opened.

My precharge reading is lower than the fill pressure — is the accumulator losing gas?

Not necessarily: the reading depends on the gas temperature. Enter the as-found reading and the temperature you read it at; the calculator converts it along the real-gas isochore to the reference temperature, compares it with the precharge the design needs and gives a verdict. Nitrogen slowly permeates through an elastomer bladder or diaphragm, so the makers ask for a check in the first week, after about three months and then at least yearly — with the fluid side drained.

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