Servo Motor Sizing Calculator

Size servo systems for belts, screws, and indexed moves. Review torque, speed, and inertia instantly. Built for accurate motion planning across demanding machines daily.

Enter Motion and Drive Details

Drive Mechanism

Load Mass (kg)

Move Distance (mm)

Move Time (s)

Acceleration Time (s)

Dwell Time (s)

External Process Force (N)

Friction Coefficient

Incline Angle (deg)

Pulley Radius (mm)

Screw Lead (mm/rev)

Gear Ratio

Use motor speed divided by load speed.

Overall Transmission Efficiency (%)

Motor Rotor Inertia (kg·m²)

Safety Factor

Include holding torque during dwell

Example Data Table

Parameter	Example Value	Notes
Mechanism	Timing Belt / Pulley	Useful for fast linear transfer axes.
Load Mass	25 kg	Includes fixture and carried payload.
Move Distance	600 mm	Total indexed travel per move.
Move Time	0.8 s	Complete motion time excluding dwell.
Acceleration Time	0.15 s	Symmetrical acceleration and deceleration.
External Process Force	40 N	Seal drag, tooling drag, or cable pull.
Pulley Radius	25 mm	Pitch radius at the driven pulley.
Gear Ratio	3 : 1	Motor runs three times faster than load.
Efficiency	90%	Use realistic drivetrain efficiency.
Typical Outcome	Peak, RMS, rpm, and power	Use these values to shortlist servo models.

Formula Used

1) Motion profile

Trapezoidal profile: Vmax = Distance / (Move Time − Accel Time)

Triangular profile: Vmax = 2 × Distance / Move Time

Acceleration: a = Vmax / Accel Time

2) Linear forces

Friction force: Ff = μ × m × g × cos(θ)

Gravity component: Fg = m × g × sin(θ)

Steady force: Fs = External Force + Ff + Fg

Acceleration force: Fa = m × a

3) Torque conversion

Belt / pulley output torque: Tout = F × r

Screw output torque: Tout = (F × Lead) / (2π)

Motor torque: Tmotor = Tout / (Gear Ratio × Efficiency)

4) Inertia reflection

Belt reflected load inertia: Jload = m × r²

Screw reflected load inertia: Jload = m × (Lead / 2π)²

Motor-side reflected inertia: Jref = Jload / Gear Ratio²

5) RMS and peak torque

Peak torque: highest absolute segment torque

RMS torque: square-root of time-weighted torque squares across the full cycle

Recommended torque: calculated torque × safety factor

How to Use This Calculator

Select the mechanism type: belt/pulley or screw drive.
Enter the total moving mass, travel distance, total move time, and acceleration time.
Add steady process force, friction coefficient, and incline angle if gravity affects motion.
Enter the transmission geometry: pulley radius or screw lead.
Provide gear ratio, drivetrain efficiency, motor rotor inertia, dwell time, and safety factor.
Enable holding torque during dwell when the axis must resist gravity or process load at standstill.
Click Calculate Servo Size to display peak torque, continuous torque, speed, inertia ratio, and power above the form.
Use the CSV and PDF buttons to save the finished sizing summary.

FAQs

1) What does this calculator size?

It estimates motor speed, peak torque, RMS torque, reflected inertia, and power for linear servo axes driven by belts or screws.

2) Why is RMS torque important?

Peak torque handles short bursts. RMS torque represents heating over the cycle, so it is critical for continuous motor selection.

3) When should I use holding torque during dwell?

Enable it when the axis must resist gravity, process force, or static load while stopped. Horizontal low-load conveyors may not need it.

4) What is a good inertia ratio?

Many servo systems tune well at ratios below 5:1. Ratios up to 10:1 can work, but tuning becomes more demanding.

5) Should I include gearbox efficiency?

Yes. Efficiency affects required torque. Ignoring it can understate motor demand, especially with gearheads, screws, and multiple mechanical stages.

6) Does this support vertical axes?

Yes. Enter the incline angle. A vertical lift can be modeled close to 90 degrees, which adds a strong gravity component.

7) Why add a safety factor?

Safety factor covers unknown losses, wear, higher friction, control margin, and real machine variation. It helps prevent undersized selections.

8) Is this final motor selection data?

It is a sizing estimate. Final selection should also verify overload curve, thermal limits, drive current, encoder needs, and available motor families.