Motor Torque Calculator
Calculate required motor torque from load mass, speed, acceleration, and gear ratio for robotic joint actuators.
About this calculator
Required Motor Torque sums three separate torque components computed at the joint and then reflects the total through the Gear Ratio before applying a Safety Factor margin. Gravity Torque (worst case, arm horizontal) and Friction Torque both scale directly with Load Mass and Arm Length, since a heavier load farther from the joint pivot creates more moment arm regardless of how fast the arm moves. Acceleration Torque is different: it comes from the load's rotational inertia (which grows with Arm Length squared) combined with angular acceleration (Max Tip Speed divided by both Arm Length and Acceleration Time), and the arm-length terms partially cancel in that product, leaving Acceleration Torque scaling with Load Mass, Arm Length, and Max Tip Speed but shrinking as Acceleration Time lengthens -- a slower, gentler ramp to speed needs less peak torque than snapping to the same speed quickly.
Gear Ratio divides the total joint-side torque down to what the motor itself must produce, so a higher reduction ratio always lowers Required Motor Torque for the same physical task, at the cost of the motor needing to spin faster (Motor Speed rises with Gear Ratio in exactly the inverse relationship). Friction Coefficient and Safety Factor apply only to torque, never to speed -- Motor Speed depends purely on Max Tip Speed, Arm Length, and Gear Ratio. The gravity-torque term assumes the worst-case horizontal arm position; an arm that never operates fully horizontal would see lower peak torque than this calculator reports, which is intentional headroom rather than an error.
Inputs
Results
Required Motor Torque
0.86 N·m
How to Use This Calculator
- Enter load mass (kg), robot arm length (mm), and maximum tip speed (m/s).
- Set acceleration time (sec) to achieve maximum speed and friction coefficient at the joint.
- Enter gear ratio if a gearbox is used between motor and load.
- Review required motor torque (N·m), gravity torque, acceleration torque, and friction torque components.
- Select a servo motor with rated torque exceeding the required value including a safety margin.
How the result changes with Gear Ratio
| Gear Ratio | Required Motor Torque |
|---|---|
| 25 | 1.72 N·m |
| 38 | 1.13 N·m |
| 75 | 0.57 N·m |
| 125 | 0.34 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
- Identify Input Parameters7 parametersLoad Mass = 5, Arm Length = 400, Max Tip Speed = 2, Acceleration Time = 0.5, Friction Coefficient = 0.05, Gear Ratio = 50, Safety Factor = 1.5 = 7 input(s) provided
- Calculate Required Motor TorqueRequired Motor Torque0.858 = 0.858
- Calculate Gravity TorqueGravity Torque19.62 = 19.62
- Calculate Acceleration TorqueAcceleration Torque8 = 8
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 increasing the Gear Ratio lower the Required Motor Torque?
The gearbox multiplies the motor's torque by the reduction ratio before it reaches the joint, so for the same joint-side torque demand a higher Gear Ratio means the motor itself has to produce proportionally less. The tradeoff is Motor Speed, which rises by that same ratio -- a higher reduction always trades motor torque for motor speed, never gets both for free.
Why doesn't Friction Coefficient affect Motor Speed?
Motor Speed is pure kinematics -- it depends only on how fast the arm tip needs to move (Max Tip Speed), how long the arm is (Arm Length), and the Gear Ratio reflecting that rotation to the motor shaft. Friction Coefficient only enters the separate torque calculation, describing how much extra force is needed to overcome joint resistance, not how fast anything is rotating.
Why does a longer Acceleration Time reduce Acceleration Torque?
Acceleration Torque is proportional to angular acceleration, which is angular velocity divided by Acceleration Time -- reaching the same top speed over a longer window means a gentler rate of speed change and therefore less torque needed to produce it. Snapping to full speed instantly demands far more peak torque than ramping up smoothly over a full second or more.
Does this calculator assume the worst-case arm position?
Yes, for Gravity Torque. It uses the horizontal-arm case, which produces the maximum possible gravitational moment about the joint since the full weight acts at the farthest lever arm. If your application's arm never swings fully horizontal, the actual peak torque demand will be somewhat lower than this calculator's Required Motor Torque figure, which is intentional safety margin rather than an overestimate to correct.
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