 Formulas Index: AC Synchronous Speed: Frequency: Number of Poles: Horsepower: Motor Slip: Brush DC Calculating Motor Speed, RPM: =V-(Tt/Kt+I0)/Ke×Rt ಏ 1000 Where: V= supply voltage, V; Tl = load torque, oz-in.; Kt = motor torque constant, oz-in./A; I0 = motor no-load current, A; Rt = motor terminal resistance, Ohms; Ke = motor voltage constant, V/1,000 rpm. It is possible to solve for an unknown quantity (voltage or current) when speed is known. Determining Speed and Current Flow: W = (VS – I x Rmt) / KE and I = TL / KT + INL Where: W = Speed, VS = Supply Voltage, Rmt = Motor Terminal Resistance, I = Current, T = Load Torque, KE = Back – EMF Constant Brushless DC Output Power = Torque*(No load speed)/1351.2 Rated Current = Torque/Torque Constant Back EMF = V/KRPM Efficiency: Motor Efficiency = Pout/Pin, Pout = (Vin - Iin * Rm) * (Iin - Io)        V = Voltage        Pout = Output power        Pin = Input power Couplings Torque is generated by force acting on a rotating body; it is the product of an acting force and the effective length of its lever arm. The formula is: T = F*r T Torque [Nm] F Force [N] r Lever arm [m] The above equation describes the relation between the force and the length of the lever arm. With Motor Couplings, a certain torque can either be achieved with a large outer diameter of the Motor Couplings and a low acting force, or with a small outer diameter and a high acting force. But in practice this relationship will be a proportional increase. Encoders The relationship between the encoder CPR frequency and the speed of the motor (RPM) is given by the following equation: f = (cycles/rev)*(rev/sec)/1000 = kHz RPM = Revolution per Minute CPR = Cycles per Revolution Distance Conversion: (PPR) / (2*pi*radius of shaft) = pulses per inch (Pulses per inch)^-1 = inch per pulse Gearboxes Motor Torque x Gear Ratio = Torque at the Wheel Input Shaft Speed (RPM) / Gear Ratio = Output Shaft Speed Gear Ratio = Teeth on one gear : Teeth on a second gear      Example: If one gear has 60 teeth and a second gear has 20 teeth the gear ratio would be 3:1 Stepper Step angle calculation:        φ=( (N_s-N_r)/(N_s*N_r ))*360°        φ = Step Angle Ns = Number of teeth on stator Nr = Number of teeth on rotor Steps per second = rpm * steps per revolution                                                         60