Servo Load Torque
T = F × d
Quick answer
This calculator solves T = F × d for Torque. With Force 0.5, Moment Arm 10 mm, the result is 5 mN·m. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The torque required to move a load through a rotary actuator (servo motor, RC servo, stepper) equals the force at the load multiplied by the moment arm (perpendicular distance from the rotation axis to the force application point). This is the fundamental relationship for sizing servo motors in robotic arms, CNC machines, pan-tilt mechanisms, and any rotary actuation system. The force includes the weight of the load (F = m × g for gravity) plus any process forces (cutting, pressing, accelerating). Dynamic loads require additional torque for acceleration: T_accel = J × α.
Variables
- T — Required torque (N·m)
- F — Applied force (N)
- d — Moment arm length (m)
Practical Notes
For gravity loads: F = mass × 9.81 m/s². A 1 kg load at 0.1 m arm length requires T = 1 × 9.81 × 0.1 = 0.981 N·m. RC servos are rated in kg·cm: 1 kg·cm = 0.098 N·m. Standard RC servos provide 1-3 kg·cm (0.1-0.3 N·m), high-torque servos 10-25 kg·cm (1.0-2.5 N·m). Always include a safety factor of 1.5-2× to account for friction, dynamic loads, and manufacturing tolerances.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| T | Torque | N·m | N·m, mN·m |
| F | Force | — | — |
| d | Moment Arm | mm | mm, cm, m, km |
Step by step
- 1. What you know: Force 0.5, Moment Arm 10 mm
- 2. The relation: T = F × d
- 3. Substitute: F = 0.5, d = 10 mm
- 4. Result: Torque = 5 mN·m
Worked examples
Minimum range
Given: Force 0.025, Moment Arm 0.1 mm
Result: Torque = 0.0025 mN·m
Low range
Given: Force 0.25, Moment Arm 1 mm
Result: Torque = 0.25 mN·m
Typical
Given: Force 0.5, Moment Arm 10 mm
Result: Torque = 5 mN·m
High range
Given: Force 0.8, Moment Arm 10 cm
Result: Torque = 80 mN·m
Maximum range
Given: Force 8, Moment Arm 1 m
Result: Torque = 8 N·m
Solving for each variable
Solve for Torque
Force 0.025, Moment Arm 0.1 mm → 0.0025 mN·m
Solve for Force
Torque 5 mN·m, Moment Arm 0.1 mm → 50
Solve for Moment Arm
Torque 5 mN·m, Force 0.025 → 20 cm
How Torque changes with Force
| Force (input) | Torque (result) |
|---|---|
| 0.05 | 0.5 mN·m |
| 0.125 | 1.25 mN·m |
| 0.25 | 2.5 mN·m |
| 0.375 | 3.75 mN·m |
| 0.5 | 5 mN·m |
| 0.75 | 7.5 mN·m |
| 1 | 10 mN·m |
| 2 | 20 mN·m |
| 3.5 | 35 mN·m |
| 5 | 50 mN·m |
The same result in other units
| Unit | Value |
|---|---|
| N·m | 0.005 |
| mN·m | 5 |
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<p><a href="https://vbatpower.com/formulas/servo-torque-load/">Servo Load Torque</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Servo Load Torque?
Use T = F × d. With Force 0.5, Moment Arm 10 mm, Torque works out to 5 mN·m.
What is the formula for Servo Load Torque?
The formula is T = F × d. The torque required to move a load through a rotary actuator (servo motor, RC servo, stepper) equals the force at the load multiplied by the moment arm (perpendicular distance from the rotation axis to the force application point).
How do you find Force when you know the other values?
Rearrange for Force: with Torque 5 mN·m, Moment Arm 0.1 mm, Force is 50.
How do you find Moment Arm when you know the other values?
Rearrange for Moment Arm: with Torque 5 mN·m, Force 0.025, Moment Arm is 20 cm.
What units does Servo Load Torque use?
Torque is shown in N·m, mN·m. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Motors & Mechanical formulas →Need more features?
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