Calculator Inputs
Use one solving method, then optionally add thickness, strain, or speed to extend the physics analysis.
Example Data Table
| Method | Inputs | Solved Radius | Bend Angle | Arc Length | Notes |
|---|---|---|---|---|---|
| Chord + Sagitta | Chord = 120 mm, Sagitta = 15 mm, Thickness = 6 mm | 127.5000 mm | 56.1455° | 124.9592 mm | Useful when width and rise are known. |
| Arc Length + Angle | Arc = 3.5 m, Angle = 60° | 3.3423 m | 60.0000° | 3.5000 m | Good for path travel and duct curves. |
| Allowable Strain + Thickness + Angle | Strain = 2%, Thickness = 8 mm, Angle = 90° | 200.0000 mm | 90.0000° | 314.1593 mm | Finds a minimum bend from strain tolerance. |
Formula Used
1) Chord and sagitta: R = c² / (8s) + s / 2
2) Arc length and angle: R = L / θ
3) Chord and angle: R = c / (2 sin(θ / 2))
4) Arc length: L = Rθ
5) Chord length: c = 2R sin(θ / 2)
6) Sagitta: s = R(1 - cos(θ / 2))
7) Curvature: κ = 1 / R
8) Outer fiber strain: ε ≈ t / (2R)
9) Minimum inside radius from allowable strain: Rinside,min = t / (2ε) - t / 2
10) Centripetal acceleration: a = v² / R
How to Use This Calculator
- Choose a calculation method that matches the values you already know.
- Select the length and angle units before entering numbers.
- Enter the required dimensions for that solving mode.
- Optionally add thickness and allowable strain for material checks.
- Optionally enter travel speed to estimate bend acceleration and traversal time.
- Press the calculate button. The result appears above the form, followed by the graph and export buttons.
FAQs
1) What is bend radius?
Bend radius is the distance from the center of curvature to the bent path. It describes how tight or gentle a curve is in a physical path or formed material.
2) Why does the calculator show centerline, inside, and outside radius?
These radii describe different reference locations through the thickness. Centerline radius helps geometry calculations, while inside and outside radii help manufacturing, clearance, and strain evaluation.
3) Which input method should I choose?
Choose the method that matches your known measurements. Sagitta methods work well from drawings, angle methods work from design data, and strain-based solving helps when material limits control the bend.
4) How does thickness affect the result?
Thickness does not change a purely geometric centerline solution, but it changes inside radius, outside radius, and estimated outer fiber strain. Thicker materials need larger bend radii to remain safe.
5) What does sagitta mean?
Sagitta is the maximum height between a chord and the arc. It is useful when you know the straight span and the rise of a curved segment.
6) Why is centripetal acceleration included?
In physics, motion along a curved path creates inward acceleration. Adding speed lets the calculator estimate the acceleration and rotation rate required to follow the bend.
7) Can I use inches or feet?
Yes. The calculator accepts millimeters, centimeters, meters, inches, and feet. It converts values internally, then returns results in your selected length unit.
8) What is a good safety check for bending?
Compare your actual inside radius against the minimum radius allowed by strain. If the actual radius is smaller, reduce thickness, reduce strain demand, or increase the bend radius.