How to Calculate Holding Torque for a Stepper Motor

Undersizing a stepper motor doesn't usually show up as a dramatic failure — it shows up as skipped steps you don't notice until the part comes out wrong. Here's how to size torque properly before that happens.

MOTOR ENGINEERING KNOWLEDGE Published October 5, 2026 · 8 min read · By Apexwell Engineering Team

Holding torque is the maximum torque a stepper motor can resist at zero speed, at rated current, before the rotor gets forced out of its commanded position. Sizing it correctly means adding up every real torque demand on the shaft — friction, gravity, and the torque needed to accelerate the load — and then applying a safety margin, rather than picking a motor because its frame size looks about right.

Why this calculation matters more than it looks

A stepper motor that's slightly undersized on holding torque doesn't usually stall outright. Instead it silently loses a step here and there under load, particularly during acceleration, and an open loop system has no way to know it happened. On a 3D printer this shows up as a slightly misaligned layer; on a CNC axis it shows up as a part that's out of tolerance in a way that's hard to trace back to the motor at all. Getting the torque calculation right at the design stage is far cheaper than debugging it after the fact.

Holding torque, detent torque, pull-in, and pull-out — what's the difference

Stepper motor datasheets use several torque terms that sound similar but describe different conditions:

Term	What it means
Holding torque	Maximum torque the motor can resist at zero speed with rated current applied, before the rotor is forced out of position
Detent torque	Torque the motor resists at zero speed with no current applied, from magnetic cogging alone — much lower than holding torque
Pull-in torque	Maximum load torque the motor can start and accelerate from a stop at a given step rate without losing steps
Pull-out torque	Maximum torque the motor can maintain once already running at a given speed, before it stalls

For sizing purposes, holding torque is the number to design against, since it represents the motor's maximum resistance at the moment it matters most — standing still or moving slowly under full load.

The basic holding torque formula

Required holding torque is the sum of every torque demand on the shaft, with a safety factor applied on top:

Required torque = (Load torque + Acceleration torque + Friction torque) × Safety factor

Load torque depends on how the load connects to the motor. For a direct-drive rotational load it's simply force times radius. For a lead-screw-driven linear stage, which is the most common case in 3D printers, CNC axes, and linear actuators, the formula is:

T_load = (F × lead) / (2π × η) — where F is the force needed to move the load in newtons, lead is the screw's lead in meters per revolution, and η is the lead screw's mechanical efficiency, typically 0.85–0.95 for a ball screw and lower for a lead screw with plain threads.

Acceleration torque accounts for the fact that the load needs to speed up, not just move at constant velocity:

T_accel = J_total × α — where J_total is the combined moment of inertia of the load, coupling, and screw as reflected back to the motor shaft, and α is the required angular acceleration in radians per second squared.

Worked example: sizing a motor for a linear stage

Take a linear stage that needs to move a load requiring 20 N of force, driven by a 5 mm lead ball screw at 90% efficiency, accelerating to 200 mm/s in 0.1 seconds, with a combined reflected inertia of 0.00005 kg·m²:

Step	Calculation	Result
1. Load torque (lead screw friction)	T_load = (F × lead) / (2π × η) = (20 N × 0.005 m) / (2π × 0.9)	≈ 1.8 N·cm
2. Angular acceleration	α = Δω / Δt, where ω = 2π × v / lead = 2π × 0.2 / 0.005	≈ 2,513 rad/s² over 0.1 s
3. Acceleration torque	T_accel = J_total × α = 0.00005 kg·m² × 2,513 rad/s²	≈ 12.6 N·cm
4. Raw required torque	T_load + T_accel = 1.8 + 12.6	≈ 14.3 N·cm
5. Apply safety factor	14.3 N·cm × 1.5	≈ 21.5 N·cm minimum holding torque

A 21.5 N·cm minimum requirement comfortably fits within the holding torque range of a mid-frame NEMA 17 stepper motor (13–65 N·cm), which is why NEMA 17 shows up so often in exactly this kind of application.

How much safety margin to add

● A 30–50% safety margin (multiplying raw required torque by 1.3–1.5) is standard for applications with well-understood, repeatable loads, such as a 3D printer axis or a known indexing mechanism.

● A 50–100% margin (1.5–2.0x) is more appropriate when the load has some uncertainty — friction that varies with wear, occasional jams, or a load mass that isn't precisely known at design time.

● Running a motor consistently near its rated holding torque with little margin increases the risk of step loss under normal manufacturing variation between motor units, not just under unusual load conditions.

Common mistakes when specifying torque

● Sizing off detent torque instead of holding torque. Detent torque with no current applied is far lower than rated holding torque and is not a usable design number for load capacity.

● Ignoring acceleration torque entirely. For fast point-to-point moves, acceleration torque frequently exceeds steady-state load torque and can't be skipped in the calculation.

● Not accounting for torque loss at speed. Holding torque is a zero-speed rating — a motor's usable torque drops as step rate increases, so the move's target speed needs to be checked against the motor's torque-speed curve, not just its holding torque figure.

Where this connects to our own product line

Every Apexwell stepper motor datasheet publishes holding torque, detent torque, and a full torque-speed curve so this calculation can be checked against real numbers rather than typical ranges. If your calculated torque comes out close to a motor's rated limit, or if step loss under load is a risk you'd rather design out entirely, our closed loop stepper motors add encoder feedback that detects and corrects missed steps instead of relying on the calculation being exactly right.

Send us your load, lead screw, and motion profile and our engineers can run this calculation against our torque-speed curves directly.

Frequently Asked Questions

What is the difference between holding torque and pull-out torque?

Holding torque is measured at zero speed with the motor energized and stationary. Pull-out torque is measured while the motor is already running at a given speed — it is always lower than holding torque, and drops further as speed increases.

How much safety margin should I add to my calculated torque?

A 30–50% margin is standard for well-understood, repeatable loads. Increase to 50–100% when friction, wear, or load mass carries meaningful uncertainty at design time.

Does holding torque change with speed?

Holding torque itself is a zero-speed specification and does not change. However, a stepper motor's usable torque while moving falls off as step rate increases, which is why the torque-speed curve — not the holding torque number alone — needs to be checked against the application's target speed.

What happens if I undersize a stepper motor's holding torque?

The most common symptom is silent step loss under load or during acceleration, which an open loop system cannot detect on its own. This shows up as positioning error that accumulates over time rather than an obvious motor failure.