Calculate fillet volume for straight edges or arc paths, plus weld volume, mass, and cost from radius, angle, length, density, and price.

Find the volume added or removed by a circular tangent fillet.

Greater than 0ยฐ and less than 180ยฐ; 90ยฐ is a square corner.

Related Calculators

Fillet Volume (Edge Fillet) Formula

The following formulas calculate the volume change from an edge fillet (material removed at a convex corner or added at a concave corner) for a given fillet radius, included interior angle, and fillet length (or arc path length).

A & = rยฒ(cot(ฮฑ) / (2) - (ฯ€ - ฮฑ) / (2)) \ V & = L A (straight edge) \ V & = (Rpsi) A (arc path, psi in radians)

Variables:

  • V is the volume change due to the fillet
  • A is the fillet cross-section area change
  • r is the fillet radius
  • ฮฑ is the included interior angle (in radians in the formula)
  • L is the straight edge length (for the straight-edge case)
  • R is the cross-section area-centroid path radius and ฯˆ is the sweep angle (for a non-overlapping arc sweep; ฯˆ in radians)
  • ฯ€ is the constant pi (approximately 3.14159)

To calculate the fillet volume change, first compute the cross-section area change A from the radius and angle, then multiply by the fillet length (straight edge L) or by the centroid arc length (s = Rฯˆ). The rigid cross-section must not cross the rotation axis or overlap during the sweep.

What is a Fillet?

A fillet is a rounded corner or edge that is typically added to a part to reduce stress concentration, improve aesthetics, or facilitate manufacturing. Fillets are commonly used in engineering and design to smooth out sharp edges and transitions between surfaces. They are often found in mechanical components, architectural designs, and various other applications where a smooth transition is beneficial.

How to Calculate Fillet Volume?

The following steps outline how to calculate the volume change from an edge fillet.

  1. Determine the fillet radius (r), included interior angle (ฮฑ), and the fillet length (L) (or arc-path geometry).
  2. Compute the cross-section area change: A = rยฒ( cot(ฮฑ/2) โˆ’ (ฯ€ โˆ’ ฮฑ)/2 ) (with ฮฑ in radians).
  3. Compute the volume change: V = LยทA for a straight edge, or V = (Rฯˆ)ยทA for an arc path (ฯˆ in radians).
  4. Check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge (straight edge, 90ยฐ corner).

Fillet radius (r) = 2 units

Interior angle (ฮฑ) = 90ยฐ

Edge length (L) = 10 units

Volume change (V) โ‰ˆ 8.584073 cubic units