Radius Corner Calculator - Find Fillet Radius, Arc Length, Chord & Sagitta Easily
Free online radius corner (fillet) calculator. Enter radius, chord, arc length, or sagitta to compute all corner geometry values. Includes diagrams, formulas, and SVG export for CAD, CNC, or UI design.
When designing or machining parts, rounding a sharp corner is one of the most common operations — whether it's a metal part in CAD, a wooden panel, or a UI element with a smooth border.
The Radius Corner Calculator helps you find the missing geometry (radius, arc length, chord, sagitta, and area) for rounded corners quickly and visually.
🔍 What Is a Radius Corner (Fillet)?
A radius corner, or fillet, replaces a sharp corner with a circular arc of a certain radius r.
For example, imagine a 90° right-angle corner — if you "cut" the corner using a circle of radius 20 mm, you create a smooth transition between the two edges.
Why it matters:
- In CAD & CAM, you must know the radius to create a precise toolpath.
- In woodworking or laser cutting, radius ensures parts fit perfectly when assembled.
- In UI or web design, you may want visually balanced corner radii (
border-radius).
📐 Geometry of a Rounded Corner
A rounded corner can be fully described by five main geometric quantities:
| Symbol | Name | Description |
|---|---|---|
| r | Radius | The curvature radius of the circular arc |
| θ | Corner angle | The interior angle between the two lines (90° for right angles) |
| c | Chord | Straight-line distance between the two tangent points |
| s | Sagitta | Height of the arc (how far the arc "cuts into" the corner) |
| L | Arc length | Length along the circular edge |
🖼️ Diagram of a Rounded Corner
🧠 Core Formulas
If you know any two of these values (commonly r and θ), you can calculate the rest:
| Quantity | Formula (θ in radians) |
|---|---|
| Arc length | L = r × θ |
| Chord length | c = 2r × sin(θ / 2) |
| Sagitta | s = r × (1 - cos(θ / 2)) |
| Sector area | A_sector = (θ / 2) × r² |
| Triangle area | A_triangle = 0.5 × r² × sin(θ) |
| Segment area | A_segment = A_sector - A_triangle |
👉 Special Case: 90° Corner
For a right angle (θ = 90° = π/2 radians):
| Known | Formula | Example (r = 100 mm) |
|---|---|---|
| Arc length | L = πr/2 | 157.08 mm |
| Chord length | c = √2 × r | 141.42 mm |
| Sagitta | s = r(1 - 1/√2) | 29.29 mm |
| Segment area | A_segment = r²(π/4 - 0.5) | 28.54 cm² |
💡 How the Radius Corner Calculator Works
The calculator lets you choose an input mode, such as:
- Known radius → find all other values
- Known chord or arc length → compute radius and others
- Known sagitta (drop height) → solve for radius
- Known corner angle θ (for non-right angles, e.g., 60° or 120°)
The tool then:
- Uses trigonometric formulas to calculate the rest.
- Displays a live SVG diagram of the arc and corner.
- Converts units between mm, cm, inches, or pixels.
- Allows exporting the diagram as an SVG file.
🧩 Real-Life Examples
Example 1 – From Sagitta to Radius
You measured a rounded corner where the sagitta is 5 mm, and the corner is 90°.
Formula:
r = s / (1 - 1/√2)→r ≈ 5 / (1 - 0.7071) = 17.07 mm
So the corner's radius is ≈17 mm.
Example 2 – From Chord to Arc Length
A fillet has a chord c = 40 mm and the angle θ = 60°.
Radius:
r = c / (2 sin(θ/2)) = 40 / (2 × sin(30°)) = 40 mmArc length:L = r × θ_rad = 40 × (π/3) ≈ 41.89 mm
Example 3 – Compare Flat vs Rounded Corner Area
If you replace a 90° square corner with a rounded one (r = 50 mm):
- Original square area:
50² = 2500 mm² - Removed segment area:
A_segment = r²(π/4 - 0.5) = 50² × 0.2854 = 713.5 mm²
So you remove ~28% of the corner area — useful for material estimation in cutting or CNC.
⚙️ Applications
| Field | Example Use Case |
|---|---|
| Mechanical Design (CAD) | Define fillets for stress reduction |
| CNC & CAM | Compute toolpath offset or cutter radius |
| Woodworking / Metal Cutting | Estimate cut depth or material removed |
| UI / Web Design | Balance border-radius visually between layers |
| Laser Cutting / 3D Printing | Optimize corner radius for fitting parts |
🌐 Try It Online
You can use the interactive calculator at:
👉 Radius Corner Calculator – freecalculators.app/math/radius-corner-calculator
Simply input your known values, pick your units, and visualize the result instantly.
🧾 Frequently Asked Questions
❓ How do I calculate the corner radius from chord and sagitta?
Use the relation:
r = s/(1 - cos(θ/2)) or r = c²/(8s) + s/2
❓ What's the difference between a fillet and a chamfer?
A fillet is curved (defined by radius), while a chamfer is a straight bevel (defined by length or angle).
❓ How to calculate arc length from radius and angle?
Simple:
L = r × θ_rad
For 90°, L = πr/2.
❓ Can I use pixels as units?
Yes! Designers can use px to find visually consistent border-radius values for UI components.
🧮 Summary
| Known Quantity | Formula to Find Radius | Example |
|---|---|---|
| Arc Length (L) | r = L / θ_rad | L=157.08 mm → r=100 mm |
| Chord (c) | r = c / (2 sin(θ/2)) | c=141.4 mm → r=100 mm |
| Sagitta (s) | r = s / (1 - cos(θ/2)) | s=29.29 mm → r=100 mm |
✅ Conclusion
The Radius Corner Calculator is a practical tool for anyone dealing with curved geometry — from CNC machinists to web designers.
It saves time, avoids manual trigonometry errors, and provides instant visualization of your fillet geometry.
🎯 Whether you're cutting metal, designing furniture, or adjusting CSS corners, this calculator gives you precise, visual, and unit-consistent results — all in one place.
References
- Engineering Toolbox - Mechanical Engineering - Comprehensive engineering formulas and calculations
- Autodesk Fusion 360 - Best practices for fillet design in mechanical engineering
- MDN CSS Border-Radius - Web design applications of corner radius