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Motor Torque Calculator

Calculate required motor torque from load mass, speed, acceleration, and gear ratio for robotic joint actuators.

Inputs

lb
mm
m/s
s

Results

Required Motor Torque

0.86 N·m

Gravity Torque19.62 N·m
Acceleration Torque8 N·m
Friction Torque0.98 N·m
Motor Speed2,387 RPM
Power Required214.5 W
How to Use This Calculator
  1. Enter load mass (kg), robot arm length (m), and maximum tip speed (m/s).
  2. Set acceleration time (sec) to achieve maximum speed and friction coefficient at the joint.
  3. Enter gear ratio if a gearbox is used between motor and load.
  4. Review required motor torque (N·m), gravity torque, acceleration torque, and friction torque components.
  5. Select a servo motor with rated torque exceeding the required value including a safety margin.

How the result changes with Gear Ratio

Gear RatioRequired Motor Torque
510.84 N·m
1760.24 N·m
3250.13 N·m
4500.1 N·m

What each input means

Load Mass
Total mass at the joint output including arm and payload.
Arm Length
Distance from the joint to the center of mass of the load.
Max Tip Speed
Maximum linear speed at the arm tip.
Acceleration Time
Time to accelerate from zero to maximum speed.
Friction Coefficient
Joint friction coefficient (typically 0.02-0.10).
Gear Ratio
Reduction ratio of the gearbox (e.g., 50:1).
Safety Factor
Safety multiplier for torque sizing (typically 1.3-2.0).

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Load Mass = 5, Arm Length = 400, Max Tip Speed = 2, Acceleration Time = 0.5 = 7 input(s) provided
  2. Calculate Required Motor Torque
    Required Motor Torque
    0.858 = 0.858
  3. Calculate Gravity Torque
    Gravity Torque
    19.62 = 19.62
  4. Calculate Acceleration Torque
    Acceleration Torque
    8 = 8

Engine last updated . Checked against 1 independently-derived test — how we verify calculators.

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