Robot Reach Calculator
Calculate workspace envelope from arm link lengths and joint limits. Determine maximum and minimum reach, workspace area, and volume.
About this calculator
This calculator estimates a robot arm's reachable workspace from its link geometry and joint limits, useful for a first-pass check of whether a planned work cell layout falls within a candidate robot's physical reach before committing to detailed kinematic simulation. Maximum Reach is the simplest figure: the straight-line sum of all three link lengths, achieved only when the arm is fully extended in a straight line. Minimum Reach approximates the "dead zone" close to the robot's base that the end effector can never enter -- the distance left over when the arm folds back on itself as tightly as its geometry allows.
Workspace Area treats the reachable region between minimum and maximum reach as an annular sector (a ring-shaped wedge) swept through the base joint's angular range, and Workspace Volume extends that flat area into three dimensions using a simplified vertical-sweep factor. All of these are simplified geometric approximations, not a substitute for the robot manufacturer's actual reach envelope diagram or a full inverse-kinematics simulation, since real industrial arms have additional joint constraints, singularities, and self-collision limits this calculator's simple link-length model doesn't capture.
Inputs
Results
Maximum Reach
850 mm
≈ 10 credit cards
How to Use This Calculator
- Enter the length of each robot arm link (mm or m) — typically found in the URDF or datasheet.
- Set joint angle limits (degrees) for each joint in your robot configuration.
- Review maximum reach, minimum reach (inner dead zone), workspace area (mm²), and volume (mm³).
- Verify all work station positions fall within the reach envelope before finalizing cell layout.
How the result changes with Link 1 Length
| Link 1 Length | Maximum Reach |
|---|---|
| 200 | 650 mm |
| 300 | 750 mm |
| 600 | 1,050 mm |
| 1,000 | 1,450 mm |
What each input means
- Link 1 Length
- Length of the first arm link (shoulder to elbow).
- Link 2 Length
- Length of the second arm link (elbow to wrist).
- Link 3 Length
- Length of the wrist/end-effector offset.
- Joint Min Angle
- Minimum rotation angle of the base joint.
- Joint Max Angle
- Maximum rotation angle of the base joint.
How this is calculated
Worked example, using the default values
- Identify Input Parameters5 parametersLink 1 Length = 400, Link 2 Length = 350, Link 3 Length = 100, Joint Min Angle = -170, Joint Max Angle = 170 = 5 input(s) provided
- Calculate Maximum ReachMaximum Reach850 = 850
- Calculate Minimum ReachMinimum Reach0 = 0
- Calculate Workspace AreaWorkspace Area2143700.65 = 2143700.65
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does increasing Link 1 Length always increase Maximum Reach?
Maximum Reach is simply the sum of Link 1, Link 2, and Link 3 lengths -- the distance the end effector can reach when the arm is fully extended in a straight line -- so lengthening any one link by a given amount lengthens Maximum Reach by that same amount, regardless of the other links' lengths.
What does Minimum Reach actually represent?
It approximates the inner "dead zone" near the robot's base that the end effector physically cannot enter, computed as Link 1 minus Link 2 minus Link 3 (floored at zero). This is a simplified estimate of how far the arm can fold back on itself -- it does not model the exact folded geometry or joint-angle constraints a full kinematic simulation would, so treat it as an approximate inner boundary rather than an exact one.
Why is Workspace Volume just an approximation rather than an exact figure?
Workspace Volume multiplies the calculated Workspace Area (a 2D annular sector swept through the joint's angular range) by the total arm length and a fixed 0.6 vertical-sweep factor, which assumes the arm's actual vertical reach is roughly 60% of its horizontal reach. Real robot arms have additional joints and orientation constraints that shape their true 3D workspace very differently, so treat this figure as a coarse sizing check, useful for comparing candidate arms at a glance but not for finalizing a work cell around the manufacturer's actual reach envelope.
Does widening the joint angle range increase Workspace Area?
Yes -- Workspace Area is directly proportional to the angular range between Joint Min Angle and Joint Max Angle, since a wider sweep covers proportionally more of the annular ring between Minimum Reach and Maximum Reach. Widening the joint limits (within the robot's actual mechanical range) always increases the area this calculator reports, holding link lengths fixed.
Should I use this to finalize a robot cell layout?
No -- use it only for an early, rough screening of whether a candidate robot's reach is in the right ballpark for your planned work cell. Final layout decisions should rely on the manufacturer's certified reach envelope diagram and, ideally, a full inverse-kinematics simulation, since this calculator's link-length model ignores joint interference, singularities, and payload-dependent reach derating.
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