Interactive Corner Radius Calculator
Choose the values you already know, then calculate radius, angle, arc length, and other corner geometry.
Quick Formula Reference
- R from chord + sagitta: R = (c² / 8s) + (s / 2)
- Setback relation: d = R tan(α/2)
- Chord from radius + angle: c = 2R sin(α/2)
- Sagitta from radius + angle: s = R(1 − cos(α/2))
- Arc length: L = R × α (in radians)
What Is a Corner Radius?
A corner radius is the rounded transition between two straight edges that meet at a corner. Instead of a sharp point, the corner is replaced by an arc. You see this in CNC machining, sheet-metal design, woodworking, plastic part design, UI iconography, and architectural detailing. A properly chosen radius can improve strength, safety, aesthetics, and manufacturability.
This corner radius calculator helps you solve practical geometry in either direction: find the radius when you know measurements from a drawing, or compute derived values like chord, sagitta, and arc length when radius is already specified.
How to Use This Calculator
1) Radius from chord and sagitta
Use this when you can measure the straight distance across the arc (chord) and the rise from chord to arc (sagitta). This is common in reverse engineering and quality inspection.
2) Radius from setback and corner angle
In many CAD and machining workflows, fillets are defined by radius and angle through tangency points. If you know the distance from the original corner to each tangent point (setback) and the included corner angle, this mode returns the exact radius.
3) Corner values from radius and angle
Perfect for forward design: enter desired radius and angle, then get the chord, sagitta, arc length, and tangent setback instantly.
4) Corner values from radius and chord
Useful when radius is fixed (for tooling or style standards) and you need to know the angle and related geometry from a known span.
Why Corner Radius Matters in Real Projects
- Stress reduction: Rounded corners reduce stress concentration compared to sharp corners.
- Manufacturing limits: End mills and cutters have finite diameters; internal corners cannot be perfectly sharp.
- Safety and usability: Consumer products often use radiused edges to reduce injury risk.
- Fit and assembly: Mating components often require clearances based on realistic corner radii.
- Consistent style: Industrial and digital design systems use repeatable radius scales.
Definitions You Should Know
- Radius (R): Distance from arc center to arc edge.
- Chord (c): Straight-line distance between arc endpoints.
- Sagitta (s): Arc height measured from midpoint of chord to arc.
- Corner angle (α): Included angle between the two edges being filleted.
- Setback (d): Distance from sharp corner to tangent point on each edge.
- Arc length (L): Length along the curved portion.
Common Mistakes and How to Avoid Them
Mixing degrees and radians
Angles are entered in degrees in this tool. Internally, calculations convert to radians for trigonometric formulas and arc-length equations.
Using impossible combinations
For radius + chord mode, chord must be less than or equal to 2R. If chord is larger than diameter, no circular arc exists.
Inconsistent units
Keep all linear dimensions in the same unit (mm, cm, in, etc.). The calculator is unit-agnostic and preserves your chosen unit in outputs.
Practical Applications
Machining and Toolpaths
In CNC programs, fillet values affect cutter engagement and feed behavior. Knowing exact setbacks and arc lengths improves path quality and reduces tool wear.
Sheet Metal and Fabrication
Bend reliefs and corner rounds are often constrained by process and tooling. Radius calculations help prevent cracking and improve consistency in folded parts.
Product and Industrial Design
Visual softness, tactile comfort, and brand language frequently depend on corner radius systems. Designers can quickly test alternatives without recalculating by hand.
Final Notes
Corner geometry shows up everywhere—from mechanical parts to mobile app cards. A fast, reliable corner radius calculator saves time, reduces errors, and makes communication between design and manufacturing much easier. Use this tool early in concept work, then again during final detailing to verify production-ready dimensions.