Robot Arm Reach Calculator

Work out robot arm reach instantly with clear inputs, formula shown and shareable results.

About Robot Arm Reach Calculator

Maximum reach is the sum of the link lengths plus the tool offset and the shoulder offset. Equally important is the inner dead zone: the arm cannot fold past |L1 - L2|, so there is a sphere close to the base it can never enter, which is why parts are never placed directly under the shoulder.

Formula

Arm reach

max reach = L1 + L2 + tool + base offset; min reach = |L1 - (L2 + tool)|

Worked example

With the default values below, Robot Arm Reach Calculator returns Maximum reach from base centre of 1,070.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Upper arm length: 420 mm
Forearm length: 380 mm
Wrist and tool offset: 120 mm
Shoulder offset from base centre: 150 mm

Results

Maximum reach from base centre: 1,070.00 mm
Minimum reach (inner dead zone): 80.00 mm
Annular work envelope width: 990.00 mm
Approximate swept volume: 2.5647 m³

Step by step

1Values used
2Arm reach
3Maximum reach from base centre= 1,070.00 mm
4Minimum reach (inner dead zone)= 80.00 mm
5Annular work envelope width= 990.00 mm
6Approximate swept volume= 2.5647 m³

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 4 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

Why is there an inner dead zone?

The elbow cannot hyperextend, so with equal links the arm folds to zero but with unequal links a minimum radius remains that no joint combination can reach.

Is full reach usable?

No. At full extension the arm is singular, stiffness is lowest and payload capacity falls, so working reach is typically 80-90% of geometric reach.