Forward Kinematics

Turn the joints, and the hand follows. Forward kinematics maps a robot arm's joint angles to exactly where its tip ends up in space.

Forward KinematicsLive

joint angles → end effector

Controls

Presets

Joint 1 angle (°)

Joint 2 angle (°)

Joint 3 angle (°)

Forward kinematics computes where a robot arm's tip ends up from its joint angles. Each link rotates relative to the previous one, so the transforms chain together. It is fast and unique — every set of angles gives exactly one end-effector position — which is why controllers use it constantly.

▶ Run in Python

Data Inspector

End X172.2

End Y110.4

Reach204.6

Links3

Governing equation

x = i \sum L_{i} cos (j \leq i \sum θ_{j}) = 172.2, y = i \sum L_{i} sin (j \leq i \sum θ_{j}) = 110.4

Reading this result: Reach 205 sits near the 210 maximum: the three links are nearly collinear, so the arm is almost fully extended.

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How it works

Forward kinematics chains together the rotation of each link to compute the end-effector position from the joint angles. It is fast and always has a single answer, which is why robot controllers evaluate it thousands of times per second to know where the tool is.

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Frequently asked questions

Is this forward kinematics robot arm tool really free?▾

Yes. Forward Kinematics runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

Can I save or share my simulation?▾

Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.

How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.