Formulas and Conversion Factors Basic FormulasFluid Pressure =Force (Pounds)Unit Area (Square Inches)

Fluid Flow Rate=Volume (Gallons)Unit Time (Minute)

Fluid Power in Horsepower =Pressure (PSI) x Flow (GPM)1714

U.S. Gear Drive Formulas

Torque (in-lb) =hp x 63025 / rpm

Horsepower (hp)=in-lb x rpm / 63025

Pitch Dia=Teeth / Diametral Pitch

Thermal input (Watts) =hp x (1 - eff) x 745.7

Output Torque = Input Torque x Ratio x Gear Drive Efficiency

Output rpm = Input rpm / Ratio

Metric Gear Drive Formulas

Nm = kW x 9549RPM

kW = Nm x RPM9549

Thermal input (Watts) =kW x (1-eff)556.08

Output TQ = Input TQ x Ratio x Gear Drive Efficiency

Output rpm = Input rpm / Ratio

Back to Top U.S. Motor Formulas

hp =gpm x psi / 1714

hp = in-lb x rpm / 63025

in3 =(in-lb x 6.283) / (psi x eff)

in-lb = psi x in3 x eff / 6.283

in-lb =hp x 63025 / rpm

gpm =rpm x in3 / 231

rpm =gpm x 231 / in3

eff = (in-lb x 6.283) / (psi x in3)

in-lb =gpm x psi x eff x 36.77 / rpm

psi =(in-lb x 6.283) / (in3 x eff)

Back to Top Metric Motor Formulas

kW =L/min x bar / 70148.25

kW = Nm x rpm / 9549

cm3 = (Nm x 170.7) / (bar x eff)

Nm =bar x cm3 x eff / 170.7

Nm = kW x 9549 / rpm

L/min =rpm x cm3 / 125.25

rpm =L/min x 125.25 / cm3

eff =(Nm x 170.7) / (bar x cm3)

Back to TopPump Formulas

Pump Outlet Flow = RPM x Pump Displacement (Cu. In./Rev.)231

Pump Input Power in Horsepower = Flow Rate Output (GPM) x Pressure (PSI)1714 x Efficiency (Overall)

Overall Efficiency = Output HorsepowerInput Horsepowerx 100

Overall Efficiency = Volumetric Eff. x Mechanical Eff.

Volumetric Efficiency = Actual Flow Rate Output (GPM)Theoretical Flow Rate Output (GPM)x 100

Mechanical Efficiency = Theoretical Torque to DriveActual Torque to Drivex 100

Back to TopMetric to U.S. Conversion

kW = 1.341 hp

bar =14.5 psi

Nm = 8.8496 in-lb

daNm =88.496 in-lb

kg-m =86.796 in-lb

L/min =.2642 gpm

cm3 = .061 in3

L =2.114 Pints

C = (F - 32) / 1.8

Torque and horsepower relations:T = HP x 5252 RPMHP = T x RPM 5252RPM = HP x 5252 TTorque values are in foot pounds. Hydraulic (fluid power) horsepower:HP = PSI x GPM 1714PSI is gauge pressure in pounds per square inch, GPM is oil flow in gallons per minute. Velocity of oil flow in pipe:V = GPM x 0.3208 AV is oil velocity in feet per second, GPM is flow in gallons per minute, A is inside area of pipe in square inches. Charles' Law for behaviour of gases:T1V2 = T2V1, or T1P2 = T2P1T1, P1 and V1 are initial temperature, pressure and volume, and T2, P2 and V2 are final conditions. Boyle's Law for behaviour of gases:P1V1 = P2V2P1, V1 are initial pressure and volume; P2 and V2 are final conditions. Circle Formulae:Area = r2, or D2 4Circumference = 2r, or Dr is radius, D is diameter, inches; is 3.14 Heat equivalent of fluid power:BTU per hour = PSI x GPM x 1 Hydraulic Cylinder Piston travel speed:S = CIM AS is piston travel speed, inches per minute, CIM is oil flow into cylinder, cubic inches per minute, A is piston area in square inches. Thrust or force of any cylinder:T = A x PSIT is thrust or force, in pounds, A is piston area in square inches, PSI is gauge pressure.Force for piercing or shearing sheet metal:F = P x T x PSIF is force required, in pounds, P is perimeter around area to be sheared, in inches, T is sheet thickness in inches; PSI is the sheer strength rating of the material in pounds per square inch. Side load on pump or motor shaft:F = (HP x 63024) (RPM x R)F is the side load, in pounds, against shaft; R is the pitch radius of sheave on pump shaft, in inches; HP is driving power applied to shaft. Effective force of a cylinder working at an angle to direction of the load travel:F = T x sin AT is the total cylinder force, in pounds; F is the part of the force which is effective, in pounds, A is the least angle, in degrees, between cylinder axis and load direction. Heat radiating capacity of a steel reservoir:HP = 0.001 x A x TDHP is the power radiating capacity expressed in horsepower; A is surface area, in square feet; TD is temperature difference in F between oil and surrounding air. Burst pressure of pipe or tubing:P = 2t x S OP is burst pressure in PSI, t is wall thickness, in inches; S is tensile strength of material in PSI; O is outside diameter, in inches. Relationship between displacement and torque of a hydraulic motor:T = D x PSI 24T is torque in foot pounds, D is displacement in cubic inches per revolution, PSI is pressure difference across motor, is 3.14

Rules of Thumb

Horsepower for driving a pump:For every 1 HP of drive, the equivalent of 1 GPM @ 1500 PSI can be produced. Horsepower for idling a pump:To idle a pump when it is unloaded will require about 5% of its full rated horsepower. Compressibility of hydraulic oil:Volume reduction is approximately 0.5% for every 1000 PSI pressure.Compressibility of water:Volume reduction is about 0.3% for every 1000 PSI pressure. Wattage for heating hydraulic oil:Each watt will raise the temperature of 1 gallon of oil by 1 F per hour. Flow velocity in hydraulic lines:Pump suction lines 2 to 4 feet/second; pressure lines up to 500 PSI, 10 to 15 feet/second; pressure lines 500 to 3000 PSI, 15 to 20 feet/second; pressure lines over 3000 PSI, 25 feet/second; all oil lines in air-over-oil system, 4 feet/second.

Formulae In SI Metric Units

Familiar fluid power formulae in English units are shown in the left column. When the industry converts to SI (International) units, these formulae will take the form shown in the right column.

English Units Metric Units

Torque, HP, Speed Relations in Hydraulic Pumps and Motors

T = HP x 5252 RPMHP = T x RPM 5252RPM = HP x 5252 T T = Torque, foot-lbs.RPM = Speed, revs/minHP = HorsepowerT = Kw x 9543 RPMKw = T x RPM 9543RPM = Kw x 9543 T T = Torque, Nm (Newton-meters)RPM = Speed, revs/minKw = Power in kilowatts

Hydraulic Power Flowing Through the Pipes

HP = PSI x GPM 1714 HP = HorsepowerPSI = Gauge pressure, lbs/sq. InchGPM = Flow, gallons per minuteKw = Bars x dm3/min 600 Kw = Powers in kilowattsBars = System pressuredm3/min = Flow, cu. dm/minute

Force Developed by an Air or Hydraulic Cylinder

T = A x PSI T = Force or thrust, in lbs.A = Piston area, square inchesPSI = Gauge pressure, lbs/sq. inchN = A x Bars x 10 N = Cylinder force in NewtonsA = Piston area, sq. centimetersBars = Gauge pressure

Travel Speed of a Hydraulic Cylinder Piston

S = V A S = Travel speed, inches/minuteV = Vol. of oil to cyl., cu.in/minA = Piston area, square inchesS = V 6A S = Travel speed, meter/secV = Oil flow dm3/minuteA = Piston area, square centimeters

Barlow's Formula - Burst Pressure of Pipe & Tubing

P = 2t x S O P = Burst pressure, PSIt = Pipe wall thickness, inchesS = Tensile str., pipe material, PSIO = Outside diameter of pipe, inchesP = 2t x S O P = Burst pressure, barst = Pipe wall thickness, mmS = Tensile str., pipe material, barsO = Outside diameter of pipe, mm

Velocity of Oil Flow in Hydraulic Lines

V = GPM x 0.3208 A V = Velocity, feet per secondGPM = Oil flow, gallons/minuteA = Inside area of pipe, sq. inchesV = dm3/min 6A V = Oil velocity, meters/seconddm3/min = Oil flow, cu.dm/minuteA = Inside area of pipe, sq.cm.

Recommended Maximum Oil Velocity in Hydraulic Lines

fps = feet per secondPump suction lines - 2 to 4 fpsPres. lines to 500 PSI - 10 to 15 fpsPres. lines to 3000 PSI - 15 to 20 fpsPres. lines over 3000 PSI - 25 fpsOil lines in air/oil system - 4 fpsmps = meters per secondPump suction lines - .6 to 1.2 mpsPres. lines to 35 bar - 3 to 4 mpsPres. lines to 206.8 bar - 4 to 6 mpsPres. lines over 200 bar - 7 mpsOil lines in air/oil system - 1 mps

Material (common name)Density (in Kg/M^3)

Metals

Aluminum2,768

Beryllium1,868

Brass8,500

Cast Iron6,975

Chromium7,197

Copper8,940

Gold18,878

Lead11,349

Magnesium1,743

Molybdenum10,214

Nickel8,553

Phosphor Bronze8,858

Platinum21,452

Silver10,491

Stainless Steel7,861

Steel7,861

Tin7,308

Titanium4,512

Tungsten19,293

Zinc7,141

Woods (weight listed is average dried weight)

Acacia Blackwood660

Ash, White660

Balsa160

Basswood420

Beech, European720

Birch700

Bloodwood960

Bocote800

Brazilwood1,280

Bubinga880

Butternut450

Cedar, Western Red370

Chakte Kok640

Chechen850

Cherry, Black580

Cocobolo1,040

Douglas Fir520

Ebony, African1,000

Ebony, Gaboon1,193*

Ebony, Macassar1,090

Elm, American560

Goncalo Alves940

Hickory820

Holly800

Jarrah800

Jatoba900

Kiaat700*

Kingwood1,200

Koa660

Kwila963*

Lemonwood820

Lignum Vitae (Ironwood)1,310

Mahogany, Honduran640

Mahogany, Philippine (Lauan)382*

Makore620

Mango570

Maple, Hard720

Maple, Soft620

Oak, Red770

Oak, White770

Padauk720

Panga Panga930

Pink Ivory990

Poplar450

Purpleheart930

Redwood420

Rosewood, Brazilian850

Rosewood, East Indian830

Rosewood, Honduran940

Sapele620

Shedua748*

Snakewood1,295

Spruce, Sitka420

Teak640

Tulipwood960

Verawood1,218*

Walnut, Black640

Wenge880

Yellowheart860

Zebrawood740

Ziricote880

Plastics

ABS1,052

Acetal (Delrin)1,356

Acrylic1,163

Neoprene1,384

Polyamide (Nylon)1,100

Polycarbonate1,190

LDPE (Low-Density Polyethylene)913

HDPE (High-Density Polyethylene)941

Polypropylene913

PVC1,467

Teflon2,159

Other

Carbon Fiber1,743

Human Bone1,439

Water1,000

*Denotes my own measurements

Metal or AlloyDensity(kg/m3)

Actinium10070

Admiralty Brass8525

Aluminum2712

Aluminum - melted2560 - 2640

Aluminum - 11002720

Aluminum - 60612720

Aluminum - 70502800

Aluminum - 71782830

Aluminum bronze (3-10% Al)7700 - 8700

Aluminum foil2700 -2750

Antifriction metal9130 -10600

Antimony6690

Babbitt7272

Barium3594

Beryllium1840

Beryllium copper8100 - 8250

Bismuth9750

Brass - casting8400 - 8700

Brass - rolled and drawn8430 - 8730

Brass 60/408520

Bronze - lead7700 - 8700

Bronze - phosphorous8780 - 8920

Bronze (8-14% Sn)7400 - 8900

Brushed metal7860

Cadmium8640

Caesium1873

Calcium1540

Cast iron6800 - 7800

Cerium6770

Chemical Lead11340

Chromium7190

Cobalt8746

Constantan8920

Columbium8600

Constantan8880

Copper8940

Cupronickel8908 - 8940

Delta metal8600

Duralumin2790

Electrum8400 - 8900

Eroded metal7860

Europium5243

Gallium5907

Germanium5323

Gold19320

Hafnium13310

Hatelloy9245

Indium7310

Inconel8497

Incoloy8027

Iridium22650

Iron7850

Lanthanum6145

Lead11340

Light alloy based on Al2560 - 2800

Light alloy based on Mg1760 - 1870

Lithium534

Magnesium1738

Manganese7440

Manganese Bronze8359

Manganin8500

Mercury13593

Molybdenum10188

Monel8360 - 8840

Neodymium7007

Nichrome8400

Nickel8908

Nickel 208090

Nickel 2008890

Nickel silver8400 - 8900

Nickeline8770

Nimonic8100

Niobium8570

Osmium22610

Palladium12160

Phosphor bronze8900

Platinum21400

Plutonium19816

Red Brass8746

Silver10490

Sodium971

Solder 50/50 Pb Sn8885

Stainless Steel7480 - 8000

Steel7850

Tin7280

Titanium4500

Tungsten19600

Uranium18900

Vanadium5494

White metal7100

Wrought Iron7750

Zinc7135

Zirconium6570

Yellow Brass8470