# Hydraulic Pump Flow and Input Horsepower Calculator > Source: https://netray.co/tools/hydraulic-pump-flow-and-input-horsepower-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Converts pump displacement, shaft speed, pressure and efficiencies into delivered GPM, hydraulic horsepower, required motor input power, torque and annual electricity cost. ## Category engineering-plm ## Industry Hydraulic Equipment Manufacturing ## Audience - Design engineer - Estimator - Maintenance engineer ## Tool **Kind:** calculator **Currency:** $ **Inputs:** #### Pump displacement **Key:** disp **Type:** number **Default:** 2.4 **Min:** 0.01 **Step:** 0.05 **Unit:** cu in/rev **Help:** Geometric displacement per revolution from the pump nameplate or datasheet. #### Shaft speed **Key:** rpm **Type:** number **Default:** 1750 **Min:** 1 **Step:** 50 **Unit:** rpm **Help:** Actual full-load motor speed. A 4-pole 60 Hz motor runs near 1750 rpm. #### Operating pressure **Key:** psi **Type:** slider **Default:** 2500 **Min:** 100 **Max:** 5000 **Step:** 50 **Unit:** psi **Help:** Pressure at the pump outlet while working. #### Volumetric efficiency **Key:** vol_eff **Type:** number **Default:** 94 **Min:** 50 **Max:** 100 **Step:** 0.5 **Unit:** % **Help:** Piston pumps are commonly 92 to 97 percent at rated pressure, gear pumps 85 to 93 percent. #### Overall efficiency **Key:** ov_eff **Type:** number **Default:** 88 **Min:** 40 **Max:** 98 **Step:** 0.5 **Unit:** % **Help:** Volumetric times mechanical efficiency. Must not exceed the volumetric figure. #### Operating hours per year **Key:** hours **Type:** number **Default:** 4000 **Min:** 0 **Step:** 100 **Unit:** h #### Electricity rate **Key:** rate **Type:** number **Default:** 0.11 **Min:** 0 **Step:** 0.01 **Unit:** $/kWh **Outputs:** #### Theoretical flow **Key:** gpm_th **Expr:** disp * rpm / 231 **Format:** decimal **Description:** GPM = displacement (cu in/rev) x rpm / 231 cu in per US gallon. #### Delivered flow **Key:** gpm **Expr:** gpm_th * vol_eff / 100 **Format:** decimal **Primary:** true **Description:** Theoretical flow reduced by internal leakage (volumetric efficiency). #### Hydraulic horsepower **Key:** hhp **Expr:** gpm * psi / 1714 **Format:** decimal **Description:** Useful fluid power leaving the pump: GPM x psi / 1714. #### Required input horsepower **Key:** ihp **Expr:** gpm * psi / (1714 * ov_eff / 100) **Format:** decimal **Primary:** true **Description:** Shaft power the motor or engine must supply, divided by overall efficiency. #### Input power **Key:** kw **Expr:** ihp * 0.7457 **Format:** decimal **Description:** Shaft input in kW (1 hp = 0.7457 kW). #### Input torque **Key:** torque **Expr:** ihp * 5252 / rpm **Format:** decimal **Description:** Torque in lb-ft = hp x 5252 / rpm. #### Implied mechanical efficiency **Key:** mech_eff **Expr:** if(gt(vol_eff, 0), ov_eff / vol_eff * 100, 0) **Format:** percent **Description:** Overall divided by volumetric. A value over 100 percent means the inputs are inconsistent. #### Annual energy cost at shaft **Key:** cost **Expr:** kw * hours * rate **Format:** currency **Description:** Shaft kW only. Add motor losses (typically 4 to 10 percent) for the meter figure. **Chart:** #### Horsepower vs operating pressure **Type:** line **X:** psi **From:** 200 **To:** 4500 **Steps:** 30 **Series:** - hhp - ihp **Disclaimer:** Uses standard US customary formulas. Real pumps lose efficiency at partial displacement, high viscosity and low speed. Confirm against the manufacturer's efficiency curves before sizing a motor. ## Content **Intro:** This calculator turns a pump nameplate into the numbers you need for a motor, a flow budget and a power bill. Enter displacement, speed, pressure and the two efficiencies and it returns delivered GPM, hydraulic horsepower, required input horsepower, torque and yearly shaft energy cost. **Sections:** #### How to use it **Body:** Start with displacement per revolution and the real operating speed, not the synchronous speed. Set the operating pressure to the pressure the pump sees while working, not the relief valve setting, unless the machine spends its cycle at relief. Enter efficiencies from the pump datasheet at that pressure and viscosity. If you do not have data, piston pumps near 92 to 97 percent volumetric and 85 to 92 percent overall are a reasonable starting point. The chart sweeps pressure so you can see how horsepower grows linearly with pressure at fixed flow. **Bullets:** - Displacement in cubic inches per revolution - Use full-load motor speed, usually 1750 rpm on a 4-pole 60 Hz motor - Overall efficiency must be at or below volumetric efficiency - Use average pressure for the energy cost, peak pressure for the motor size #### The formulas behind the numbers **Body:** Theoretical flow in US GPM is displacement times rpm divided by 231, since one US gallon is 231 cubic inches. Delivered flow multiplies by volumetric efficiency. Hydraulic horsepower is GPM times psi divided by 1714, a constant that comes from unit conversion of foot-pounds per minute. Input horsepower divides hydraulic horsepower by overall efficiency. Torque in pound-feet is horsepower times 5252 divided by rpm. Kilowatts are horsepower times 0.7457. All of these are standard fluid power relationships found in pump manufacturer catalogs. #### Worked example and how to read it **Body:** A 2.4 cu in/rev piston pump at 1750 rpm has 18.2 theoretical GPM. At 94 percent volumetric efficiency it delivers about 17.1 GPM. At 2500 psi that is 25 hydraulic horsepower, and at 88 percent overall efficiency the shaft needs about 28.4 hp, so a 30 hp motor is the first standard size above it. The gap between hydraulic and input horsepower is heat that the reservoir or cooler must reject, which is why this tool pairs well with a heat load check. #### Common mistakes **Body:** Sizing the motor on rated pressure for a machine that mostly idles at low pressure wastes capital, but sizing on average pressure for a machine with long holds at relief can trip the motor. Using nameplate rpm of a synchronous speed overstates flow by roughly 3 percent. Forgetting that variable displacement pumps at partial stroke have worse efficiency can understate input power. Always confirm cold-start viscosity, because high viscosity at startup raises torque well above the running figure. **Cta:** If pump and motor data live in your ERP asset records or maintenance system, Netray can build a private assistant that answers sizing and energy questions from your own equipment data. **Faq:** #### Why is the constant 1714 used? **Answer:** It folds unit conversions together: 1 hp is 33,000 ft-lb per minute, and one GPM at one psi equals 0.583 ft-lb per second of work after converting gallons and square inches. The result is that hp equals GPM times psi divided by 1714. #### What efficiency should I enter if I have no datasheet? **Answer:** For axial piston pumps use roughly 94 percent volumetric and 88 percent overall at rated conditions. Gear pumps run lower, near 90 and 80 percent. Ask the supplier for curves at your operating pressure and oil temperature for any purchase decision. #### Does the motor size equal the input horsepower? **Answer:** Pick the next standard motor above the peak input horsepower, then check service factor, starting torque and duty cycle. Heavily cycled machines may justify sizing on the RMS load, but verify with the motor vendor. #### How do I convert the result to metric? **Answer:** Multiply GPM by 3.785 for L/min, psi by 0.06895 for bar, and kW is already shown. Metric pump kW also equals L/min x bar / (600 x overall efficiency as a decimal). ## Search terms hydraulic pump flow calculator, hydraulic horsepower calculator, pump displacement to gpm, hydraulic pump input power, gpm psi 1714 formula, hydraulic pump torque calculator, hydraulic power unit motor size, hydraulic pump energy cost --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json