What Does the Reduction Ratio Calculator Compute?
The calculator returns the area ratio: starting cross-section area divided by final area. You enter the starting width and thickness, then choose a round, square or rectangular final section. The result shows as ratio : 1.
Wire Drawing Reduction Formula
| Quantity | Formula |
|---|---|
| Area ratio | A₀ ÷ A₁ |
| Reduction of area (%) | (A₀ − A₁) ÷ A₀ × 100 = (1 − 1 ÷ ratio) × 100 |
| Round wire, area ratio | (d₀ ÷ d₁)² |
| Final areas the calculator uses | Round π × (d ÷ 2)² · square a² · rectangle a × b |
A₀ is the starting area and A₁ the final area. The calculator takes the starting area as width × thickness.
Worked Example: Wire Drawing Reduction Ratio Calculation
Start with a 20 mm × 10 mm section and reduce it to a round of Ø 12 mm. Starting area = 20 × 10 = 200 mm². Final area = π × 6² = 113.10 mm². Area ratio = 200 ÷ 113.10 = 1.77 : 1. Reduction of area = (200 − 113.10) ÷ 200 = 43.4%.
Maximum Reduction in Wire Drawing
The theoretical limit for an ideal frictionless, non-hardening material is a single-pass reduction of about 63%. Real drawing stays well below it, because friction and work hardening raise the drawing force. Wire is drawn in several passes, each with a smaller reduction.
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Common Questions
What is the reduction ratio in wire drawing?
It is the starting cross-section area divided by the final area. A ratio of 1.77 : 1 means the area after the pass is 1 ÷ 1.77 of the area before. Reduction of area expresses the same change as a percentage.
How do you calculate reduction in wire drawing?
Reduction of area in percent is (A₀ − A₁) ÷ A₀ × 100, where A₀ is the area before the pass and A₁ the area after. For round wire it is (1 − (d₁ ÷ d₀)²) × 100, with d the diameters.
What is the maximum reduction in wire drawing?
For an ideal frictionless, non-hardening material, the limit is about 63% in one pass, which is a ratio of about 2.72 : 1. Real passes stay below that. The limit depends on the material, die and lubrication, so we confirm it per grade.
Can I use this calculator for rolling as well as drawing?
Yes, for the area ratio. It compares any two cross-sections. It does not model forces, die angle or the number of passes.