The numbers you need before you size anything
- Pressure determines how much force or torque a circuit can deliver.
- Flow determines how fast an actuator moves.
- Effective area is what turns pressure into cylinder force, so retract force is lower than extend force.
- Power is the pressure-flow product, but the real motor size must include losses.
- Metric units keep UK sizing work cleaner: bar, L/min, kW, N and mm.
- Efficiency and heat usually decide whether the final design is tidy or oversized.
What the equation is really telling you
At its core, the relationship is not complicated: if pressure rises, force capability rises; if flow rises, speed rises; if both rise, required power rises quickly. That is the practical meaning behind the fluid power equation. In UK engineering work I prefer bar, L/min, kW and mm because that keeps the arithmetic readable and matches most current catalogues.
Parker Hannifin’s metric sizing formula for pump input power is essentially power = pressure x flow / 600, which is the quickest sanity check I use before I move into detailed sizing. For cylinders, the same logic becomes force = pressure x area, so bore size matters far more than stroke when I am checking static load capacity.
Hydraulics and pneumatics share the same basic maths, but they do not behave identically. Oil is far less compressible than air, so hydraulic systems usually give a more direct force response, while pneumatic systems demand more care with pressure drop, valve capacity and timing. Once you see that distinction, the rest of the calculation chain becomes much easier to trust.The next step is to look at the three quantities that actually control the result, because most sizing errors start there rather than in the algebra itself.
The three variables that decide the outcome
Three variables do the heavy lifting in almost every fluid power calculation: pressure, flow and effective area or displacement. If any one of them is wrong, everything downstream is wrong as well. I treat them as a set, not as separate catalog values.
| Variable | What it does | Common trap | Practical check |
|---|---|---|---|
| Pressure | Sets force or torque capability | Using pump relief pressure instead of actual working pressure | Measure or estimate the pressure at the actuator or pump inlet to the circuit section you care about |
| Flow | Sets speed | Assuming theoretical pump flow is the same as delivered flow | Allow for leakage, throttling and pressure drop at operating temperature |
| Effective area or displacement | Converts fluid energy into motion | Using bore area for both extension and retraction | Use full piston area on extend stroke and annulus area on retract stroke |
That table looks basic, but it is where most bad assumptions live. In practice, pressure is rarely the whole story, because a circuit can carry enough pressure on paper and still miss the target once flow losses, fittings and valve behaviour are included. Flow tells you how quickly the system can work; area tells you how much of that energy becomes usable motion.
For production systems, especially the ones tied into automation or machine-vision timing, I also look at how stable those variables are over the duty cycle. A formula that works at steady state can still be wrong for fast indexing, intermittent loading or warm-up conditions, which is why I never stop at one number alone.
The cleanest way to see those variables in action is a cylinder example, because the geometry is easy to visualise and the force result is immediate.
How I size cylinder force without guessing
For linear actuators, force is the easiest place to see the formula in action. Static push force comes from the full piston area; pull force uses the annulus area after the rod is removed from the calculation. Stroke length does not change the force itself, but it does change the oil volume that must move, which then affects cycle time and pump flow.| Example | Calculation | Result |
|---|---|---|
| 100 mm bore, extend stroke at 210 bar | Area = π x 1002 / 4 = 7,854 mm2; force = 210 x 7,854 / 10,000 | 165 kN push force |
| 100 mm bore with a 50 mm rod, retract stroke at 210 bar | Annulus area = 7,854 - 1,963 = 5,891 mm2; force = 210 x 5,891 / 10,000 | 124 kN pull force |
The gap between push and pull is the bit people forget. A cylinder that looks generous on extension can be noticeably weaker on retraction, especially when the rod diameter is large or the application has side load. That is why I size against the weaker direction first and then confirm the stronger direction still has enough margin.
I also check the mechanical limits around the calculation: rod buckling on long strokes, mount stiffness, side load and the pressure setting of the relief valve. None of those change the equation, but all of them change whether the force you calculated is actually available on the machine.
Once the linear side makes sense, the next question is usually how much pump and motor power the circuit needs to support it.
How to calculate pump and motor power in metric units
Power sizing is where metric units pay off. In a UK design file, I want bar, L/min and kW on the same line so nobody has to reverse a conversion at the wrong moment. The cleanest first-pass formula is still the pressure-flow product.
| Calculation | Formula | What it means |
|---|---|---|
| Hydraulic power | kW = bar x L/min / 600 | Theoretical power required at the fluid side |
| Pump flow | L/min = rpm x cm3/rev / 1000 | Theoretical flow before leakage |
| Pump input torque | N·m = bar x cm3/rev / (20 x π) | Useful when checking shaft load |
| Imperial cross-check | hp = psi x gpm / 1714 | Legacy reference if you inherit mixed-unit data |
Here is the part that matters in real sizing: at 180 bar and 25 L/min, the theoretical hydraulic power is 7.5 kW. If overall efficiency is 85%, the electrical input rises to about 8.8 kW. On a 400 V, 50 Hz machine, that gap is often enough to push a design from a 7.5 kW motor into an 11 kW frame once starting duty and ambient heat are included.
I would not treat that as overdesign. I would treat it as the difference between a machine that runs comfortably and one that sits on the edge of thermal trouble. The number is useful precisely because it looks neat at first and then becomes less neat once the real circuit is added.
That brings us to the part most spreadsheets hide: losses, heat and the gap between theoretical and usable power.
Where efficiency turns a neat answer into a real one
The formula on its own is theoretical. Real systems lose energy through leakage, friction, pressure drop and throttling, and those losses show up as heat. If I ignore that layer, the calculation looks elegant but the machine usually runs hot, noisy or underpowered.
| Efficiency type | What it affects | Why it matters |
|---|---|---|
| Volumetric efficiency | Actual flow and speed | Internal leakage reduces delivered flow, especially as temperature rises |
| Mechanical efficiency | Force, torque and shaft load | Friction steals part of the input before it reaches the load |
| Overall efficiency | Input power sizing | Combines the two effects and is the number I use for motor selection |
Long pipe runs, small fittings, throttling valves and dirty filters can do more damage than the nameplate data suggests. Oil temperature matters too, because viscosity shifts leakage and friction in both directions depending on the circuit. When I do not yet have measured data, I usually leave a margin rather than pretending the first calculation is exact.
That logic is also why modern power units increasingly use variable-speed drives, load-sensing control and better monitoring instead of simply adding size. The industry has learned that it is usually cheaper to avoid wasting power than to absorb the waste after the fact.
Even with the right efficiency allowance, there are a few repeat mistakes that can still spoil the result, and they are worth naming directly.
The mistakes I see most often in UK projects
The biggest avoidable errors are rarely exotic. They are usually unit mistakes, wrong assumptions about pressure or a missed distinction between extension and retraction. I see the same ones again and again when a design moves from drawing board to procurement.
- Mixing bar and psi or L/min and gpm inside the same calculation sheet.
- Using pump pressure instead of actuator pressure and forgetting pressure drop across the circuit.
- Applying bore area to retract force even though the rod removes part of the effective area.
- Confusing theoretical flow with actual flow at working temperature and pressure.
- Ignoring duty cycle and assuming the system can sit at peak load continuously.
- Skipping the thermal check and assuming the oil will stay in the same viscosity band all day.
In British plants, the unit mismatch is often the most expensive one because legacy drawings and European catalogues still get mixed with imperial references. My fix is simple: standardise every calculation sheet to one unit system before I touch the numbers, then convert only at the end if a supplier needs it.
Once those mistakes are out of the way, the final step is less about maths and more about confirming the design against the real machine.
The checklist I use before I sign off a design
Before I treat a sizing calculation as finished, I run a short sign-off check. It is not glamorous, but it saves far more time than it costs.
- Confirm the worst-case direction separately for extend and retract.
- Convert all data to one unit system before calculating anything.
- Add realistic efficiency and temperature margins instead of assuming ideal conditions.
- Check supply voltage, starting current and thermal duty on the actual site.
- Validate the first machine with measured pressure and flow, not just a spreadsheet.
If the machine will live inside a connected plant, I would also expose pressure and flow data to the control or IoT layer. That turns the calculation from a one-time design exercise into something you can monitor, compare and improve after commissioning. For me, that is where fluid power becomes genuinely useful: not just as an equation, but as a measurable part of a smarter system.
Used properly, the formula helps you avoid underpowered cylinders, overheated oil and motors that are one frame too small. Used badly, it only creates confidence in the wrong number. I always prefer the version that can be checked on the machine, because that is the one that survives contact with production.
