Hydraulic Pump Flow Calculation

Flow is what makes a hydraulic actuator move. Get the flow calculation right and your cylinder extends at the speed the machine needs; get it wrong and the cycle is either sluggish or violently fast. This guide shows exactly how displacement and pump speed set flow, how to correct for volumetric efficiency, and how to turn litres-per-minute into a real cylinder speed in mm/s.

What flow is — and why it sets speed, not force

Flow is the volume of oil a pump delivers per unit time, measured in litres per minute (LPM or L/min). In a hydraulic system, flow governs how fast things happen: how quickly a cylinder extends, or how fast a hydraulic motor spins. It does not govern how hard they push.

Force and torque come from the other half of the picture — pressure acting on an area (force = pressure × area). Pressure builds up in response to the load resisting the flow. So the two variables are independent: flow buys you speed, pressure buys you force. Pushing more oil into a stuck cylinder will not move a heavier load; it only raises pressure until the load yields or the relief valve opens. If that distinction is new, read our companion guide on pressure vs flow.

The core flow formula

For a fixed-displacement pump — the gear pumps that sit on most hydraulic power packs — flow is set by how much oil the pump moves per revolution and how fast it is turned:

Each term:

• Q — delivered flow at the pump outlet, in litres per minute.
• V_g — the pump's geometric displacement: the volume of oil, in cubic centimetres, swept per revolution. This is a fixed property of the pump (e.g. 8, 12 or 25 cc/rev).
• n — drive speed in rpm, set by the electric motor. In India a 4-pole motor runs at roughly 1440 rpm on 50 Hz; a 2-pole runs near 2880 rpm.
• η_v — volumetric efficiency, a fraction between 0 and 1. Real pumps leak a little oil internally past their clearances, so actual flow is slightly below the theoretical V_g × n. This slip grows with pressure and temperature, and with thinner oil. For a typical gear pump ηv sits in the 90–95% range.
• The ÷ 1000 simply converts cc/rev × rev/min (cm³/min) into litres per minute.

Worked example — pump flow

Take a common combination: a 12 cc/rev gear pump driven by a 4-pole motor at 1440 rpm, with a volumetric efficiency of 95% (ηv = 0.95).

So this pump delivers about 16.4 L/min at the outlet. Note that the theoretical flow (before efficiency) would be 17.28 L/min — the roughly 0.9 L/min difference is the internal slip you would lose if you assumed a perfect pump.

From flow to cylinder speed

Once you know the flow into a cylinder, its extend speed follows directly. All the oil going in has to fill the swept volume, so speed is flow divided by the piston area:

Keep the units consistent. A handy shortcut for the mixed units used on the shop floor is:

Take our 16.4 L/min feeding a cylinder with an 80 mm bore. First the full-bore area:

So the rod extends at roughly 54 mm/s — a 500 mm stroke would take about 9 seconds.

The return stroke is faster. When the rod retracts, oil enters the rod side and pushes on the annulus area — the bore area minus the rod area — which is smaller. With a 40 mm rod, that area is π/4 × (80² − 40²) = 3770 mm², so the same 16.4 L/min gives about 72 mm/s. A cylinder always retracts faster than it extends at equal flow — plan your cycle time around the slower extend stroke, and watch that the faster return does not exceed a safe rod speed.

Fixed vs variable displacement

The formula above assumes fixed displacement — V_g is constant, so flow only changes if you change the drive speed. Gear and most vane pumps work this way, and they suit the great majority of hydraulic power packs: simple, robust and inexpensive.

A variable-displacement pump (typically a piston pump) can change its swept volume per revolution on the fly, so it can vary flow — and therefore actuator speed — at constant motor speed, and can throttle back to near-zero flow when the system is holding pressure. That saves energy and heat on machines with long idle-under-load phases, at higher cost and complexity. For most standard duty cycles a fixed-displacement pump plus correctly sized relief and flow controls is the practical choice.

Typical pump sizes for reference

The table below lists common nominal flows and the rough displacement each needs at 1440 rpm, with an indicative drive motor at around 120 bar. Treat these as typical starting points, not selections — actual pump and motor ratings depend on working pressure, duty cycle and oil.

Typical fixed-displacement pump sizes (indicative)

Nominal flow	Approx. displacement @ 1440 rpm	Indicative motor @ ~120 bar
6 LPM	~4.4 cc/rev	~1.5 kW (2 HP)
12 LPM	~8.8 cc/rev	~3 kW (4 HP)
25 LPM	~18 cc/rev	~5.5 kW (7.5 HP)
40 LPM	~29 cc/rev	~9.5 kW (12.5 HP)
63 LPM	~46 cc/rev	~15 kW (20 HP)

For the motor side of this table, see our guide on hydraulic motor sizing.

Common mistakes

• Confusing flow with pressure. Sizing a bigger pump to get "more power" without checking pressure is a classic error. Flow makes the actuator faster; it does nothing for the force it can push. If the machine is slow, add flow; if it stalls under load, that is a pressure and force problem.
• Ignoring volumetric efficiency. Using theoretical flow (V_g × n only) overstates delivery by 5–10%, and the gap widens at high pressure and temperature. Always apply ηv, and use the lower end of the range for hot, high-pressure duty.
• Forgetting the rod-side area. Calculating return speed or regeneration on the full bore instead of the annulus gives wrong cycle times — and can hide a rod speed that is actually too high. Always use the annulus area for the rod side.