Stepper Motor Torque Calculator

Calculator Inputs

Choose an application, enter your load, then calculate torque.

All fields support decimals.

Application type

Pick the mechanism that matches your design.

Gear ratio (motor:output)

Use 3 for 3:1 reduction. Use 1 for direct.

Gear efficiency (%)

Typical: 85-95 for belts, 60-90 for gears.

Start speed (RPM)

Set 0 if starting from rest.

Target speed (RPM)

Start speed (mm/s)

Target speed (mm/s)

Acceleration time (s)

Time to ramp from start to target speed.

Load mass (kg)

Used for friction and incline terms.

Incline angle (degrees)

0 for horizontal. Positive for uphill motion.

Friction coefficient (mu)

0.02-0.2 typical depending on guides and bearings.

External force (N)

Any extra linear load: springs, cutting, preload.

Inertia input mode

Use direct inertia if you already have J.

Effective radius (m)

For a drum or pulley radius driving the load.

Load inertia J (kg*m^2)

Reflected through gearing inside the calculator.

Motor inertia (kg*m^2)

Optional; improves acceleration estimate.

Coupling inertia (kg*m^2)

Include pulleys, hubs, couplers if known.

External torque at output (Nm)

Any constant resisting or assisting torque.

Lead (mm/rev)

Travel per revolution. Example: 8 mm/rev.

Screw efficiency (%)

Acme: 20-40. Ball screw: 85-95.

Pulley diameter (mm)

Used for force-to-torque and steps/mm.

Drive efficiency (%)

Belts are often 90-98 in good condition.

Full steps per rev

Common: 200 (1.8 deg) or 400 (0.9 deg).

Microstep setting

Common: 8, 16, 32. Higher reduces torque ripple.

Holding torque (Nm)

Used if Kt and current are not provided.

Torque constant Kt (Nm/A)

Optional: use motor datasheet value.

Phase current (A)

Enter RMS or rated current consistently with Kt.

Derating (%)

Typical 40-70% depending on speed and heating.

Safety factor

Recommended: 1.3-2.0 for many systems.

Reset

After calculation, downloads appear in the results card.

Example Data Table

Sample scenarios showing typical inputs and estimated torque outcomes.

Scenario	Mechanism	Mass	Speed	Accel time	Transmission	Estimated required torque
Light rotary index	Rotary, radius 0.02 m	2 kg	300 RPM	0.5 s	1:1, 90%	~ 0.10-0.25 Nm
Vertical lift stage	Lead screw, 8 mm/rev	5 kg	60 mm/s	0.6 s	2:1, 90%, screw 35%	~ 0.6-1.2 Nm
Belt gantry move	Belt, 20 mm pulley	3 kg	200 mm/s	0.4 s	1:1, 90%	~ 0.2-0.6 Nm

Formula Used

Rotary

omega = RPM * 2*pi / 60
alpha = (omega_target - omega_start) / t_accel
J_ref = J_output / gear^2
T_accel = J_total * alpha
T_motor_for_load = T_output / (gear * eta_gear)
T_required = T_accel + T_motor_for_load

Output load torque may include gravity, friction, and any external torque.

Linear

a = (v_target - v_start) / t_accel
F_total = m*a + m*g*sin(theta) + mu*m*g*cos(theta) + F_external
T_screw = F_total * lead / (2*pi * eta_screw)
T_pulley = (F_total * r_pulley) / eta_drive
T_motor = T_output / (gear * eta_gear)

Use a safety factor for transients, resonance, and speed-related torque drop.

How to Use This Calculator

Select your mechanism: rotary, lead screw, or belt drive.
Enter speed targets and acceleration time for your motion profile.
Provide load mass and incline angle if gravity matters.
Set friction and any external force or torque.
Enter gear ratio and efficiencies to reflect losses.
Optionally add holding torque or Kt and current for margin.
Click Calculate Torque to view results above the form.
Use the buttons to download CSV or PDF reports.

FAQs

1) Why does required torque increase with acceleration?

Acceleration requires extra torque to change speed. In rotary systems, torque follows T = J*alpha. In linear systems, force follows F = m*a, which then converts to torque through screws or pulleys.

2) What gear ratio should I enter?

Enter motor revolutions per output revolution. Use 3 for a 3:1 reduction. Reductions lower motor torque needs but increase motor speed, which can reduce stepper torque at high RPM.

3) How do I pick efficiency values?

Use realistic losses. Belts and good bearings often exceed 90%. Spur gears may be 85-95%. Lead screws can be 20-40% for sliding threads, while ball screws are often above 85%.

4) Why is holding torque not enough for sizing?

Holding torque is measured at zero speed. At higher speeds, inductance and driver limits reduce current and torque. Use this tool’s derating plus a motor torque-speed curve for accurate sizing.

5) What safety factor is sensible?

Common values are 1.3-2.0. Use higher values for unknown friction, shock loads, vertical lifting, or if resonance and missed steps are costly. Always validate with testing.

6) How do microsteps affect torque?

Microstepping improves smoothness and resolution, but incremental holding torque per microstep is lower. Full-step torque capability stays similar, yet usable dynamic torque still depends heavily on speed and driver current.

7) How do I interpret steps per mm?

Steps per mm indicate positioning resolution. For lead screws, it’s (steps/rev * microsteps) / lead. For belts, it’s (steps/rev * microsteps) / circumference. Practical accuracy also depends on stiffness and backlash.

8) Does this include motor rotor inertia and resonance?

Rotor inertia can be entered in rotary mode. Resonance is not directly modeled; it depends on mechanics and drive settings. Use conservative derating and safety factor, and consider damping or different microstep settings.