Motors & Mechanical Formulas
Motor and mechanical formulas relate torque, speed, voltage, and power for rotating machines. These calculators help you size motors and drivers and predict performance under load. They bridge the electrical and mechanical sides of motion systems.
Motors & Mechanical Formula Calculators
- Motor Mechanical Power P = τ × ω Torque 5 mN·m, Angular Velocity 9.549 RPM → Power = 5 mW
- Motor Torque τ = Kt × I Torque Constant 11 mN·m, Current 2 mA → Torque = 0.022 mN·m
- Motor Speed n = (V − I×R) / Ke Supply Voltage 0.33 V, Current 2 mA, Winding Resistance 1 Ω, Back-EMF Constant 1 × 10⁻⁴ V/(rad/s) → n = 3280 rad/s
- Gear Ratio Output Torque τout = τin × N × η Input Torque 11 mN·m, Gear Ratio 0.025, Efficiency 5.5 % → Output Torque = 0.01513 mN·m
- Back-EMF Voltage Vemf = Ke × ω Back-EMF Constant 0.025 V/(rad/s), Angular Velocity 9.549 RPM → Back-EMF Voltage = 25 mV
- Motor Efficiency η = Pmech / Pelec Mechanical Output 10 mW, Electrical Input 22 mW → Efficiency = 45.45 %
- Rotational Dynamics τ = J × α Moment of Inertia 0.025 kg·m², Angular Acceleration 0.055 rad/s² → Torque = 1.375 mN·m
- Stepper Motor Step Angle θ = 360 / (steps × microstep) Full Steps/Rev 0.025, Microstep Divisor 0.055 → Step Angle = 261800 °
- BLDC Motor Kv to Kt Conversion Kt = 9.549 / Kv Velocity Constant (RPM/V) 0.055 → Torque Constant (N·m/A) = 173.6
- Shaft (Mechanical) Power P = τ × 2π × n / 60 Torque 5 mN·m, Speed (RPM) 0.025 → Mechanical Power = 13.09 µW
- Servo Load Torque T = F × d Force 0.025, Moment Arm 0.1 mm → Torque = 0.0025 mN·m
- PWM Motor Effective Voltage Veff = Vcc × D Supply Voltage 0.726 V, Duty Cycle 2.5 % → Effective Voltage = 18.15 mV
Worked result for every Motors & Mechanical formula
| Formula | Expression | Worked result |
|---|---|---|
| Motor Mechanical Power | P = τ × ω | Torque 5 mN·m, Angular Velocity 9.549 RPM → Power = 5 mW |
| Motor Torque | τ = Kt × I | Torque Constant 11 mN·m, Current 2 mA → Torque = 0.022 mN·m |
| Motor Speed | n = (V − I×R) / Ke | Supply Voltage 0.33 V, Current 2 mA, Winding Resistance 1 Ω, Back-EMF Constant 1 × 10⁻⁴ V/(rad/s) → n = 3280 rad/s |
| Gear Ratio Output Torque | τout = τin × N × η | Input Torque 11 mN·m, Gear Ratio 0.025, Efficiency 5.5 % → Output Torque = 0.01513 mN·m |
| Back-EMF Voltage | Vemf = Ke × ω | Back-EMF Constant 0.025 V/(rad/s), Angular Velocity 9.549 RPM → Back-EMF Voltage = 25 mV |
| Motor Efficiency | η = Pmech / Pelec | Mechanical Output 10 mW, Electrical Input 22 mW → Efficiency = 45.45 % |
| Rotational Dynamics | τ = J × α | Moment of Inertia 0.025 kg·m², Angular Acceleration 0.055 rad/s² → Torque = 1.375 mN·m |
| Stepper Motor Step Angle | θ = 360 / (steps × microstep) | Full Steps/Rev 0.025, Microstep Divisor 0.055 → Step Angle = 261800 ° |
| BLDC Motor Kv to Kt Conversion | Kt = 9.549 / Kv | Velocity Constant (RPM/V) 0.055 → Torque Constant (N·m/A) = 173.6 |
| Shaft (Mechanical) Power | P = τ × 2π × n / 60 | Torque 5 mN·m, Speed (RPM) 0.025 → Mechanical Power = 13.09 µW |
| Servo Load Torque | T = F × d | Force 0.025, Moment Arm 0.1 mm → Torque = 0.0025 mN·m |
| PWM Motor Effective Voltage | Veff = Vcc × D | Supply Voltage 0.726 V, Duty Cycle 2.5 % → Effective Voltage = 18.15 mV |
Variables used across Motors & Mechanical formulas
- P — Mechanical power output (W)
- τ — Torque (N·m)
- ω — Angular velocity (rad/s)
- Kt — Torque constant (N·m/A)
- I — Armature current (A)
- n — Rotational speed (rad/s, divide by 2π/60 to get RPM)
- V — Supply voltage (V)
- R — Winding resistance (Ω)
- Ke — Back-EMF constant (V/(rad/s))
- τout — Output torque (N·m)
- τin — Input torque from motor (N·m)
- N — Gear ratio (output teeth / input teeth)
- η — Gear train efficiency (0 to 1)
- Vemf — Back-EMF voltage (V)
- Pmech — Mechanical output power (W)
- Pelec — Electrical input power (W)
- J — Moment of inertia (kg·m²)
- α — Angular acceleration (rad/s²)
- θ — Angular displacement per microstep (degrees)
- steps — Full steps per revolution (typically 200 or 400)
- microstep — Microstep divisor (1, 2, 4, 8, 16, 32, etc.)
- Kv — Velocity (back-EMF) constant in RPM per volt
- T — Required torque (N·m)
- F — Applied force (N)
- d — Moment arm length (m)
- V_eff — Effective (average) voltage seen by the motor (V)
- V_cc — Supply voltage (V)
- D — PWM duty cycle (ratio 0 to 1)
Questions people ask about Motors & Mechanical
- Motor mechanical power — Motor Mechanical Power
- Motor mechanical power calculator — Motor Mechanical Power
- Output torque = motor torque × gear ratio × η — Gear Ratio Output Torque
- Stepper motor step angle formula — Stepper Motor Step Angle
Related Formula Categories
Browse the full formulas index for all 32 categories.