BIZOMAT MAKEOS · Springs
Helical Compression Spring Design Check
What rate, load and stress will this compression spring have at its working length?
Rate, working load, Wahl-corrected shear stress, solid length, stress at solid, natural frequency and buckling ratio of a round-wire helical compression spring.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wire diameter | mm | Measured or specified wire diameter. |
| Mean coil diameter | mm | Mean coil diameter = outside diameter − wire diameter. |
| Active coils | coils | Coils that deflect; for closed ends this is total coils minus 2. |
| End type | choice | End form of the spring. |
| Shear modulus | GPa | Shear modulus of the wire (about 79 GPa for spring steel, about 69 GPa for stainless 302). |
| Unloaded (free) length | mm | Length with no load. |
| Working (compressed) length | mm | Installed or working length under the maximum load. |
| Allowable shear stress | MPa | Allowable shear stress for the wire material, size and duty (static or fatigue) from the spring maker or design data. |
| Wire density | kg/m³ | Wire material density (steel about 7850 kg/m³). |
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 diameter
- What it is
- The diameter of the round wire the spring is coiled from, measured with a micrometer or taken from the specification.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rate rises with the fourth power of the wire diameter, so small changes matter a lot.
- Get it right
- Measure the wire itself, not the coil.
What this means: Mean coil diameter
- What it is
- The mean coil diameter: the diameter of the circle through the centre of the wire, equal to the outside diameter minus one wire diameter.
- 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 16 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rate falls with the cube of the mean diameter.
- Get it right
- Do not enter the outside or inside diameter; convert it to the mean first.
What this means: Active coils
- What it is
- The number of active coils: the coils that are free to deflect, not counting closed or ground end coils that sit solid.
- 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
- The rate falls in proportion as active coils increase.
- Get it right
- Total coils and active coils differ; the end type sets how many extra coils the tool adds for the solid length.
What this means: End type
- What it is
- The form of the spring ends: closed (squared) or plain, each ground flat or not. It sets the total coil count and the solid length.
- Units and format
- Choose one of 4 options from the list: Closed and ground (squared and ground); Closed, not ground; Plain and ground; Plain (open).
- Example
- The form opens with “Closed and ground (squared and ground)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Check the drawing or the spring itself; closed and ground ends are common for stable seating.
What this means: Shear modulus
- What it is
- The shear modulus (modulus of rigidity) of the wire material, from the spring maker or material data.
- 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
- The rate rises in proportion to the shear modulus.
- Get it right
- Enter GPa, not MPa. Use the shear modulus, not the elastic (Young’s) modulus.
What this means: Unloaded (free) length
- What it is
- The free length of the spring with no load on it, measured over the ends.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure several springs if possible; free length varies with manufacture.
What this means: Working (compressed) length
- What it is
- The length of the spring when installed at the working position under the maximum load.
- 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 35 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 a higher load and stress.
- Get it right
- It must be shorter than the free length and longer than the solid length.
What this means: Allowable shear stress
- What it is
- The highest shear stress the wire may reach for its material, size and duty (static or fatigue), from the spring maker or design data.
- 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 700 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Fatigue duty needs a lower allowable than static duty; use the maker’s value for your case.
What this means: Wire density
- What it is
- The density of the wire material, used to work out the active coil mass and the spring’s natural frequency.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 50000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter kg/m³, not g/cm³: 1 g/cm³ is 1000 kg/m³.
Method and formulas
- Rate k = G d⁴ ÷ 8D³Na; index C = D ÷ d; Wahl K = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C.
- Load F = k(L₀ − L_w); stress τ = K × 8FD ÷ πd³.
- Total coils and solid length by end type: closed & ground Nt = Na + 2, Ls = Nt d; closed Nt = Na + 2, Ls = (Nt + 1)d; plain & ground Nt = Na + 1, Ls = Nt d; plain Nt = Na, Ls = (Nt + 1)d.
- Natural frequency (fixed ends) f = ½√(k ÷ m_active), m_active = ρπ²d²DNa ÷ 4.
- Example: 2 mm wire, 16 mm mean diameter and 8 active coils give k = 4.8401 N/mm, 72.601 N at 35 mm and τ = 437.8 MPa.
Limitations
- Round wire, uniform pitch and axial loading; hook or eccentric loads raise stress.
- Buckling depends on end restraint; the slenderness ratio is a screening value only.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a catalogue or custom spring against a duty
- Specify a replacement spring
- Check stress at solid before ordering
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Spring rate and working load
- Spring index and Wahl factor
- Corrected shear stress at working length and at solid
- Solid length, total coils and clash allowance
- Natural frequency and buckling ratio
Interpreting the result
- Keep the stress at solid below the allowable so the spring survives being fully compressed; keep C between about 4 and 12 for easy manufacture.
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
Stripping and stripper springs
In Blanking and Piercing Dies by the Numbers
What it covers: Why strip grips the punches, fixed and spring strippers, sizing MP-40's stripper springs for force, travel and regrinds, what they add to press load, and a stripper too weak to strip.
Method explained here · BIZOMAT original book
Checking a helical compression spring
What it covers: How to check a round-wire compression spring: rate from wire and coils, Wahl-corrected stress, solid length and clash allowance, buckling and natural frequency.
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.