| Joint | Holding torque | Servo rating needed | Smallest fit |
|---|---|---|---|
| Enable JavaScript to calculate. | |||
Robot arm torque calculator
Enter your link lengths and masses to see the holding torque each joint needs with the arm stretched out flat — the worst case — and which common hobby servo covers it.
Results
How the calculation works
A servo has to hold everything beyond it against gravity, and the lever arm is longest when the arm is stretched out horizontally. So the calculator works out that worst case for each joint by adding up mass × horizontal distance for every part further out:
- the payload and gripper act at the end of the arm;
- each link acts at its midpoint;
- each servo acts at the joint it drives, so the wrist servo loads the elbow and shoulder, and the elbow servo loads the shoulder.
With the default values — 12 cm upper arm, 12 cm forearm, 8 cm to the payload, a 100 g payload and a 60 g gripper — the wrist needs about 1.3 kg·cm, the elbow 3.8 kg·cm and the shoulder 7.3 kg·cm just to hold position. Doubled for safety, the shoulder wants a servo rated for about 15 kg·cm: more than an MG996R delivers, and exactly why capable arms use 20 kg-class servos at the shoulder.
The base rotation joint isn't included: it turns about a vertical axis, so gravity doesn't load it the same way. Size it for the arm's inertia and put a bearing under the turntable — the robotic arm design guide covers both.
Servo ratings used
| Servo | Stall torque | At higher voltage |
|---|---|---|
| SG90 | 1.8 kg·cm @ 4.8 V | 1.8 kg·cm @ 4.8 V |
| MG90S | 1.8 kg·cm @ 4.8 V | 2.2 kg·cm @ 6.6 V |
| MG996R | 9.4 kg·cm @ 4.8 V | 11 kg·cm @ 6 V |
| DS3218 | 19 kg·cm @ 5 V | 21.5 kg·cm @ 6.8 V |
Ratings are the manufacturers' published stall torque (Tower Pro for SG90, MG90S and MG996R; DSServo for DS3218). Cheaper clones are often weaker than the official figure, which is one more reason to keep the safety factor.
If the numbers come out too high
Every centimetre of reach multiplies the load, so the cheapest fix is almost always geometric: shorten the links, move heavy servos toward the base, or lighten the gripper. After that, raise the servo supply to 6 V if your servos allow it, add a counterweight or spring behind the shoulder, or move the shoulder to a geared stepper motor. The reach and payload guide explains the trade-off in more depth, and choosing servo motors covers the servo classes.
Frequently asked questions
How much torque does a robot arm servo need?
Multiply every mass beyond the joint by its horizontal distance from the joint and add them up — that is the holding torque with the arm stretched out flat, the worst case. Then choose a servo whose stall torque is at least twice that figure. The shoulder always needs the most because it carries everything; wrist and gripper servos can be far smaller.
How is robot arm torque calculated?
Torque = mass × distance. For each joint, add up the payload and gripper at the end of the arm, each link acting at its midpoint, and each servo mounted further out, each multiplied by its distance from that joint. With masses in grams and distances in centimetres the result is in g·cm; divide by 1,000 for kg·cm.
How do I convert kg·cm to N·m?
Multiply by 0.0981. So 10 kg·cm is about 0.98 N·m. Hobby servo datasheets use kg·cm (sometimes written kg/cm), while stepper motors and industrial actuators are usually rated in N·m or N·cm.
Why use a safety factor of 2?
Servo ratings are stall torque — the point where the motor stops turning — measured at a specific voltage. Real arms also accelerate, which adds load, and a servo held near its stall torque runs hot and wears quickly. A factor of 2 keeps each servo comfortably inside its range; use 2.5–3 for fast motion or a heavy gripper.