Calculate a tube or pipe bend radius from arc length and bend angle, or find the arc length or angle, with inside and outside radii from the tube OD.

Measure arc length along the tube centerline; bend angles up to 180°.

Tube outside diameter
Adds inside and outside bend radii and the CLR-to-OD (D) ratio.

Tube Bend Radius Formula

For an illustrative arithmetic example, a selected centerline radius can be twice the tube outside diameter. This does not establish a minimum safe radius or mean the bend is gentle:

R ≈ 2D
  • Where R is an approximate bend centerline radius (CLR)
  • D is the tube outside diameter (OD)

This 2×D relationship is not a universal design rule. The minimum achievable or recommended bend radius depends on material, wall thickness (D/t), tooling, bending method and acceptable ovality, thinning and wrinkling. The geometry modes solve ideal circular geometry: arc length = CLR × angle in radians. It preserves all four length units with per-field quantity conversion. Chord = 2 × CLR × sin(angle/2); centerline tangent setback = CLR × tan(angle/2), which is not finite at 180°. Setback here is not an outside-surface setback or tooling-specific bend deduction. The theoretical arc is not a complete production cut length.

Hand bender radius lookup

Select a Swagelok hand bender model that matches the tube’s actual outside diameter. Choose the tubing material and enter its wall thickness. The calculator checks the listed thickness range for that model and material, then gives the approximate centerline radius and the radius divided by the tube OD. For example, the MS-HTB-8M with 8 mm OD and 1.2 mm wall in qualifying annealed stainless steel gives a 24 mm centerline radius, or 3 times the OD.

The lookup uses model data from Swagelok’s hand bender product catalog and Hand Tube Bender Manual MS-13-43, Rev. G. It covers the listed annealed carbon and stainless steel tubing. The tubing specification, hardness and application limits in the manual still apply. Treat the result as the radius of the selected tool, not as a minimum for the material or for other benders. Medium-pressure tubing is outside the listed scope.

Definition

What is a tube bend radius?

A tube bend radius (often specified as the centerline radius, CLR) is the distance from the center of curvature of the bend to the centerline of the tube.

Choosing too small of a bend radius can reduce bend quality and may cause excessive ovality/flattening, wall thinning on the outside of the bend, or wrinkling/buckling on the inside. The bend angle does not determine the radius; it affects the arc length of the bend for a given radius.

Example Problem

How to calculate a bend radius?

The following arithmetic example uses a selected 2×D relationship only. Check bendability and tooling with the manufacturer before using a radius in production.

For this illustrative multiplication, use the tube outside diameter (OD). OD alone cannot establish a safe bend radius.

For this example problem, the outside diameter is 5 inches.

Next, simply use the formula above to estimate the bend radius:

R ≈ 2 × D

R ≈ 2 × 5

R ≈ 10 inches