Radius Corner Calculator - Find Fillet Radius, Arc Length, Chord & Sagitta Easily

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

Rounded Corner Geometry Diagram

🧠 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

90° Right Angle Corner Example

💡 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 mm Arc length: L = r × θ_rad = 40 × (π/3) ≈ 41.89 mm

60° Fillet Example

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