BIZOMAT MAKEOS · Springs
Square versus Round Wire Spring Comparison (Rate, Load, Stress, Solid Length)
In the same space, would a square-wire or a round-wire compression spring of the same size give me the load I need within stress?
Side-by-side check of two compression springs with the same coil diameter, active coils, free and working lengths: one wound from square wire of side a (as the square-wire spring tool) and one from round wire of diameter a (as the compression spring tool) — rate, load at the working length, corrected stress, solid length — and which of them gives the load you need within the allowable stress.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wire size (square side or round diameter) | mm | Side of the square wire, and diameter of the round wire compared with it. |
| Mean coil diameter | mm | Mean coil diameter of both springs. |
| Active coils | coils | Active coils of both springs. |
| Shear modulus | GPa | Shear modulus of the wire. |
| Unloaded length | mm | Unloaded length of both springs. |
| Working length | mm | Length both are compressed to. |
| Allowable shear stress | MPa | Allowable corrected shear stress. |
| Load needed at the working length | N | Load the spring must give at the working length. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Wire size (square side or round diameter)
- What it is
- The wire size used for both springs: the side of the square wire, and the diameter of the round wire it is compared with.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Both spring rates rise with the fourth power of the wire size, and the solid length grows in proportion.
- Get it right
- The same number is used for both; for square wire it is the flat side, not the diagonal.
What this means: Mean coil diameter
- What it is
- The mean coil diameter shared by both springs, measured to the centre of the wire.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Both rates fall with the cube of the mean diameter; stress rises with it for a given load.
- Get it right
- Mean diameter = outside diameter − wire size; do not enter the outside diameter.
What this means: Active coils
- What it is
- The number of coils that deflect under load in both springs, excluding closed end coils that do not work.
- Units and format
- Enter a number in coils: a number of coils. The form accepts 0.5 coils to 10000 coils. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 coils as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rates fall in inverse proportion to the active coils, and the solid length grows with them.
- Get it right
- Count active coils only; the tool adds two inactive coils when it works out the solid length.
What this means: Shear modulus
- What it is
- The shear modulus of the spring wire material, from the wire supplier’s data sheet or a spring standard.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 79.3 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Both rates rise in direct proportion to the shear modulus.
- Get it right
- Enter gigapascals, not megapascals.
What this means: Unloaded length
- What it is
- The free length of both springs with no load on them, measured end to end.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer free length gives more deflection at the working length, so both loads and stresses rise.
- Get it right
- Measure the free length before the spring is fitted; it must be longer than the working length.
What this means: Working length
- What it is
- The length both springs are compressed to in service, at which the loads and stresses are compared.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A shorter working length means more deflection, so load and stress rise in proportion.
- Get it right
- It must lie between the solid length and the free length.
What this means: Allowable shear stress
- What it is
- The highest corrected shear stress you accept in the wire, from the wire supplier’s data or your spring standard for the duty.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Compare like with like: this is a corrected (curvature-factor) stress, so use an allowable defined the same way.
What this means: Load needed at the working length
- What it is
- The load the spring must deliver when compressed to the working length, set by the mechanism it serves.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the load at the working length, not the rate.
Method and formulas
- Square wire: k = G a⁴ ÷ (5.58 N_a D³); stress = 0.96 K F D ÷ (0.416 a³) (as the square-wire spring tool).
- Round wire: k = G d⁴ ÷ (8 D³ N_a); stress = K 8 F D ÷ π d³ with the Wahl factor (as the compression spring tool).
- Solid length = (active coils + 2) × wire size for closed and ground ends.
- Example: square wire gives 269.8 N at 564.77 MPa; round wire 188.18 N at 434.69 MPa.
Limitations
- Square wire assumed to stay square in the coil; in practice it becomes keystone-shaped.
- Static load; closed and ground ends for solid length.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Decide whether square wire gives enough extra load
- Compare die spring options in a fixed pocket
- Check solid length for both wire shapes
Who it is for
- Design engineers
- Toolmakers
- Spring buyers
What you get
- Rate and load of each spring
- Corrected stress of each
- Solid length and which meets the need
Interpreting the result
- Square wire stores more energy in the same space, but costs more and is harder to obtain.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 304–324. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
More force in less space: square-wire and nested springs
What it covers: What to do when a round-wire spring will not fit: square and rectangular wire, nested pairs, load sharing, coil clearance and hand of winding, compared on one fixture.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Square versus Round Wire Spring Comparison (Rate, Load, Stress, Solid Length) calculator