Forward Kinematics Position Calculator

Work out forward kinematics position instantly with clear inputs, formula shown and shareable results.

About Forward Kinematics Position Calculator

Forward kinematics chains the links: x = L1 cos(t1) + L2 cos(t1 + t2), y = L1 sin(t1) + L2 sin(t1 + t2). Note the second angle is relative to the first link, which is the usual robot convention, so the tool orientation is the sum of the joint angles.

Formula

Two-link FK

x = L1 cos(t1) + L2 cos(t1+t2); y = L1 sin(t1) + L2 sin(t1+t2)

Worked example

With the default values below, Forward Kinematics Position Calculator returns Tool X position of 324.51. Change any input above and every figure here is recalculated in your browser.

Inputs used

Link 1 length: 300 mm
Link 2 length: 250 mm
Shoulder angle: 30 °
Elbow angle: 45 °

Results

Tool X position: 324.51 mm
Tool Y position: 391.48 mm
Distance from origin: 508.49 mm
Tool orientation: 75.00 °

Step by step

1Values used
2Two-link FK
3Tool X position= 324.51 mm
4Tool Y position= 391.48 mm
5Distance from origin= 508.49 mm
6Tool orientation= 75.00 °

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Are joint angles absolute or relative?

Relative here: theta2 is measured from the first link, not from the base frame. Mixing the conventions is the most common source of kinematics errors.

Why is forward kinematics easier than inverse?

It is a direct evaluation with a unique answer. Inverse kinematics must solve for angles and generally has multiple or no solutions.