Servo Sizing Calculator
Size servo motors by checking inertia ratio, RMS torque, and speed requirements for optimal motion control performance.
About this calculator
Matching a servo motor to its load is mostly about inertia matching: if the load's rotational inertia at the motor shaft is too large relative to the motor's own rotor inertia, the system becomes hard to control precisely and can oscillate or resonate. This calculator first reflects Load Inertia through the Gear Ratio -- a gearbox reduces the inertia seen at the motor by the square of the ratio, so a 10:1 gearbox cuts reflected inertia by 100x -- to get Reflected Load Inertia, then divides that by Motor Rotor Inertia to get the Inertia Ratio, the key sizing number most servo manufacturers publish guidance for. A ratio under about 3:1 is considered excellent, up to 5:1 is good, up to 10:1 is acceptable for less demanding applications, and above 10:1 risks instability.
Separately, RMS Torque estimates the effective continuous torque demand from Peak Torque Required and Duty Cycle (the percentage of time the motor spends at peak load), which should stay at or below the Motor Continuous Torque rating. Because Gear Ratio reduces reflected inertia by its square rather than linearly, it is normally the single most effective lever for fixing a poor inertia ratio, more so than swapping in a larger motor.
Inputs
Results
Inertia Ratio
1:1
How to Use This Calculator
- Enter load inertia (kg·cm²) reflected at the motor shaft and the gear ratio.
- Set motor rotor inertia (kg·cm²) from the motor manufacturer's specification.
- Enter peak torque required (N·m) and motor continuous torque rating and duty cycle (%).
- Review inertia ratio — values above 10:1 indicate potential stability issues; target below 5:1.
- Check RMS torque and bandwidth (Hz) to confirm the servo meets dynamic response requirements.
- Enter motor max RPM and required motor RPM, then check the Continuous Torque Check and Speed Check outputs to confirm the motor is not overloaded on either axis.
How the result changes with Gear Ratio
| Gear Ratio | Inertia Ratio |
|---|---|
| 5 | 4:1 |
| 7.5 | 1.78:1 |
| 15 | 0.44:1 |
| 25 | 0.16:1 |
What each input means
- Load Inertia
- Total load inertia at the gearbox output shaft.
- Gear Ratio
- Gearbox reduction ratio (e.g., 10:1).
- Motor Rotor Inertia
- Motor rotor inertia from the motor datasheet.
- Peak Torque Required
- Maximum torque needed during acceleration/deceleration.
- Motor Continuous Torque
- Motor continuous torque rating from datasheet.
- Duty Cycle
- Percentage of time the motor is under peak load.
- Motor Max RPM
- Maximum rated speed of the servo motor.
- Required Motor RPM
- Required motor shaft speed for the application.
How this is calculated
Worked example, using the default values
- Identify Input Parameters8 parametersLoad Inertia = 50, Gear Ratio = 10, Motor Rotor Inertia = 0.5, Peak Torque Required = 5, Motor Continuous Torque = 3, Duty Cycle = 50, Motor Max RPM = 3000, Required Motor RPM = 2000 = 8 input(s) provided
- Calculate Inertia RatioInertia Ratio1 = 1
- Calculate Inertia MatchInertia MatchExcellent = Excellent
- Calculate Reflected Load InertiaReflected Load Inertia0.5 = 0.5
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the gear ratio have such a large effect on the inertia ratio?
A gearbox reduces the load inertia seen at the motor shaft by the SQUARE of the gear ratio, not just the ratio itself -- Reflected Load Inertia is Load Inertia divided by Gear Ratio squared. That means doubling the gear ratio cuts reflected inertia to a quarter, not a half, which is why increasing gear ratio is usually the most effective single change for fixing a poor Inertia Ratio.
What inertia ratio should I be targeting?
Most servo manufacturers consider a ratio under about 3:1 excellent, up to 5:1 good for most general-purpose applications, and up to 10:1 acceptable for less demanding or lower-bandwidth tasks -- above 10:1 risks control instability, resonance, and difficulty tuning the servo loop cleanly. This calculator's Inertia Match output labels your result against those same thresholds.
Does changing the duty cycle affect the required motor size?
Yes. RMS Torque is Peak Torque Required multiplied by the square root of Duty Cycle (as a fraction), so raising the percentage of time the motor spends at peak load raises the effective continuous torque demand the motor must sustain. A motor whose Motor Continuous Torque rating exceeds RMS Torque at your actual duty cycle is properly sized for continuous operation, not just peak bursts.
Does rotation speed affect the inertia ratio calculation?
No. Inertia Ratio and Reflected Load Inertia depend only on Load Inertia, Gear Ratio, and Motor Rotor Inertia -- Motor Max RPM and Required Motor RPM are checked separately and reported in the Speed Check output (a simple speed-sufficiency comparison, alongside the similar Continuous Torque Check for RMS Torque vs. Motor Continuous Torque) and don't factor into the inertia matching calculation at all.
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