What is the difference between forward and inverse kinematics?

Forward kinematics (FK) computes the end-effector position from known joint angles. Inverse kinematics (IK) does the reverse — it finds the joint angles needed to reach a desired position. This tool performs FK.

Are the angles absolute or relative?

Theta1 is measured from the positive x-axis (absolute). Theta2 is measured relative to the first link — this is the standard Denavit-Hartenberg convention for planar arms.

What units should I use?

Any consistent unit works for lengths (meters, cm, inches). Angles are entered in degrees and converted to radians internally.

Can I use this for 3D robot arms?

No — this tool only handles planar (2D) arms with two revolute joints. For 3D arms with more than 2 DOF you would need full Denavit-Hartenberg matrix multiplication.

What happens when the arm is fully extended?

When theta2 is 0° the arm is fully extended and the end-effector lies at (L1+L2, 0) rotated by theta1. The diagram reflects this configuration.

Forward Kinematics 2DOF

Enter two joint angles and two link lengths to instantly compute the end-effector position of a 2-link planar robot arm.

Robot Parameters

Link Lengths

L1 — First link length

L2 — Second link length

Joint Angles

θ1 — From positive x-axis

deg

θ2 — Relative to first link

deg

Results

Elbow Position (Joint 2)

x₁ —

y₁ —

End-Effector Position

x_ee —

y_ee —

Arm Reach

Distance from origin —

Max reach (L1+L2) —

Link 2 Absolute Angle

θ1 + θ2 —

In radians —

Arm Diagram

Axes in link-length units

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Summary

This tool solves the forward kinematics problem for a 2-degree-of-freedom (2-DOF) planar robot arm. Given the two joint angles (theta1, theta2) and link lengths (L1, L2), it applies the standard FK equations to compute the Cartesian (x, y) coordinates of the end-effector. Both the intermediate joint position (elbow) and the final end-effector position are displayed, along with a live diagram showing the arm configuration.

How it works

Enter the length of the first link (L1) in any consistent unit (e.g., meters or millimeters).
Enter the length of the second link (L2) in the same unit.
Enter the first joint angle (theta1) measured from the positive x-axis.
Enter the second joint angle (theta2) measured relative to the first link.
The tool applies the FK equations: x = L1*cos(theta1) + L2*cos(theta1+theta2) and y = L1*sin(theta1) + L2*sin(theta1+theta2).
The computed elbow and end-effector positions are shown numerically and as a scaled diagram.

Use cases

Verify robot arm configurations during mechanical design.
Teach and learn forward kinematics concepts in robotics courses.
Quickly prototype path-planning calculations before coding.
Debug joint-angle setpoints in robot control systems.
Calculate reachability of a 2-link arm for a given workspace point.
Visualize how changing joint angles affects end-effector placement.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu