BIZOMAT MAKEOS · Springs
Compression Spring Designer (Two Working Points)
What wire size, coils and free length make a compression spring that gives these two loads at these two lengths?
Synthesis of a round-wire helical compression spring from two working points: the rate and free length they require, the wire diameter that keeps the Wahl-corrected stress at the highest load within your allowable for the chosen mean diameter, active and total coils for the end type, solid length, clash allowance, stress at solid and buckling ratio, as a ready specification.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Working points | ||
| Load at the first point | N | Load at the first (installed) length. |
| Length at the first point | mm | Length at the first point. |
| Load at the second (maximum) point | N | Load at the maximum operating point. |
| Length at the second point | mm | Length at the maximum operating point. |
| Design choices | ||
| Mean coil diameter | mm | Mean coil diameter you can fit (outside diameter = D + d). |
| Allowable shear stress at the maximum load | MPa | Allowable corrected shear stress for the wire material and size at the maximum load. |
| Shear modulus | GPa | Shear modulus of the wire material (79.3 GPa for spring steel). |
| Ends | choice | End type, for total coils and solid length. |
| Clash allowance (share of the deflection) | % | Margin between the maximum operating length and solid, as a share of the deflection from free 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.
Working points
What this means: Load at the first point
- What it is
- The spring force needed at the first working length, usually the installed or preloaded position.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The force at that length, not the change in force between the two points.
What this means: Length at the first point
- What it is
- The overall spring length at the first working point, measured between the outer ends of the spring.
- 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.
- Get it right
- It must be longer than the second length.
What this means: Load at the second (maximum) point
- What it is
- The spring force at the second, most compressed working point; the wire is sized for this load.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Wire stress is proportional to this load, so a higher load needs thicker wire.
- Get it right
- It must exceed the first load.
What this means: Length at the second point
- What it is
- The spring length at the maximum working load, the shortest length the spring reaches in service.
- 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.
- Get it right
- Shorter than the first length; the clash check compares it with the solid length.
Design choices
What this means: Mean coil diameter
- What it is
- The mean coil diameter, from the centre of the wire on one side of the coil to the centre on the other side; outside diameter is D + d.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 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.
- Get it right
- Mean, not outside diameter: subtract one wire diameter from the outside diameter.
What this means: Allowable shear stress at the maximum load
- What it is
- The corrected shear stress the wire may carry at the maximum load, from the spring wire maker’s data for the material and wire size.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 550 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher allowable stress gives a thinner wire.
- Get it right
- Allowable stress depends on wire size; check it again for the wire diameter the tool selects.
What this means: Shear modulus
- What it is
- The shear modulus of the spring wire material, from the wire maker’s data sheet.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 200 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
- The number of active coils is directly proportional to G.
- Get it right
- In GPa, not MPa.
What this means: Ends
- What it is
- How the spring ends are formed, which sets the number of inactive end coils and the solid length.
- Units and format
- Choose one of 4 options from the list: Closed and ground; Closed, not ground; Plain and ground; Plain.
- Example
- The form opens with “Closed and ground” selected as a worked example. Choose the option that matches your case.
- Get it right
- Ground ends give a shorter solid length for the same coils, which helps the clash allowance.
What this means: Clash allowance (share of the deflection)
- What it is
- The margin you want between the second working length and the solid length, as a share of the deflection from free length to the second length.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change the design; it sets the pass or fail check on clash allowance.
- Get it right
- Type the percentage itself; 0 lets the spring reach solid at the maximum load.
Method and formulas
- Rate k = (F₂ − F₁) ÷ (L₁ − L₂); free length L₀ = L₁ + F₁ ÷ k.
- Wire diameter d from τ = K_W 8 F₂ D ÷ π d³, with K_W = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C and C = D ÷ d (solved iteratively).
- Active coils N_a = G d⁴ ÷ 8 D³ k; total coils and solid length from the end type.
- Clash = (L₂ − solid length) ÷ (L₀ − L₂); buckling ratio L₀ ÷ D.
- Example: 100 N at 60 mm and 250 N at 45 mm on a 20 mm mean diameter needs 3.0528 mm wire and 10.762 active coils.
Limitations
- Static or low-cycle duty; fatigue needs a stress range check.
- Round the wire to an available size and re-check with the compression spring calculator.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a spring for a valve, clamp or return mechanism
- Turn two load-length points into a spring specification
- Check whether a spring fits the space available
Who it is for
- Design engineers
- Spring buyers
- Product engineers
What you get
- Rate and free length
- Wire diameter and coils
- Solid length, clash, stress at solid and buckling
Interpreting the result
- If the clash allowance is too small, use a larger mean diameter (fewer coils) or a higher-strength wire.
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
Designing a compression spring from two working points
What it covers: How to design a compression spring from the forces needed at two lengths: rate, free length, wire size for a stress limit, coils, solid length, rounding to stock wire.
Method explained here · BIZOMAT original book
Find the surge inside a spring
In Vibrating Machine Elements by the Numbers
What it covers: Calculate a coil spring's surge frequencies, see how they break high-frequency isolation, and use the spring's mass correction and a soft pad to keep the isolator working.
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