How to use this calculator
- Enter usable oil volume. Enter the oil volume the accumulator must deliver between maximum and minimum pressure.
- Enter pressures. Enter gas precharge, minimum system pressure and maximum charging pressure as gauge pressures.
- Pick the exponent. Use 1.0 for slow/isothermal discharge or about 1.4 for rapid/adiabatic discharge.
- Read the gas volume. Use the required gas volume as the nominal accumulator size, then check manufacturer limits.
How it works
A bladder or piston accumulator stores oil by compressing nitrogen. The gas follows a polytropic relation: P · Vⁿ = constant Between minimum pressure P₁ and maximum pressure P₂, the deliverable oil volume is the change in gas volume: ΔV = V₀[(P₀/P₁)^(1/n) − (P₀/P₂)^(1/n)] The calculator rearranges this to solve the required precharge gas volume V₀.
Hydraulic gauges read gauge pressure, but the gas law must use absolute pressure. Internally the calculator adds atmospheric pressure to P₀, P₁ and P₂ before applying the equation.
Worked example
Verified against the live calculator
Need 1.0 L of oil between 100 bar minimum pressure and 200 bar maximum pressure,
with 90 bar nitrogen precharge and a rapid-discharge exponent n = 1.4. The pressure
term is about 0.361, so V₀ = 1.0 / 0.361 ≈ 2.77 L. The calculator
reports a required gas volume of about 2.8 L, then shows the gas
volumes at the low and high pressure ends of the cycle.
Frequently asked questions
How do I size a hydraulic accumulator?
For a gas-charged accumulator, use the polytropic gas law. The usable oil volume is ΔV = V₀[(P₀/P₁)^(1/n) − (P₀/P₂)^(1/n)], so V₀ = ΔV divided by that pressure term. The calculator adds atmospheric pressure to the gauge inputs before solving.
What precharge pressure should I use?
A common first pass is about 80–90% of the minimum working pressure, but the correct value depends on bladder limits, temperature and the manufacturer. Too high a precharge can leave no oil at minimum pressure; too low a precharge over-compresses the gas.
What polytropic exponent should I use?
Use n = 1.0 for a slow discharge where heat can flow into the gas, and about n = 1.4 for a rapid discharge that is closer to adiabatic. Many real cycles land between those values.
Does the calculator use gauge or absolute pressure?
You enter gauge pressure because that is what hydraulic gauges show. The equation itself uses absolute pressure, so the calculator adds atmospheric pressure internally.
Method & assumptions
- Gas is nitrogen and follows a single polytropic exponent over the stroke.
- Inputs are gauge pressure; the calculation uses absolute pressure.
- Does not check bladder extrusion, minimum gas volume, temperature swing, mounting orientation, safety factors or shell ratings.
- Use the result as a first-pass size, then verify against the accumulator manufacturer data sheet.