Springs to your size: formula, coil check and a printable 3D model
Pick a spring type, set the wire, coil diameter and turns, and get the stiffness formula under DIN EN 13906, a check that the spring can be wound and a 3D model to print. It runs in your browser.
Opens without an account 3 times a day. A free account removes the limit.
- 5 spring typescompression, extension, torsion, conical, disc
- Index 4 to 12a check that the spring can be wound
- STL and 3MFa 3D model ready for the slicer
- 8 materialsfrom PLA to nylon and resin
What spring rate is
This free online tool from EduFacturing is a spring 3D model generator. It builds a 3D model of a spring and shows next to it the stiffness formula (the spring rate) for the chosen type: compression, extension with hook eyes, torsion with legs, conical, or the Belleville disc spring.
What sets it apart from a plain coil generator is the check. On every change it works out the spring index (mean diameter divided by wire diameter), the pitch and the solid length, the height once the coils touch, and flags anything outside the working range before you download.
The model is built in your browser. Nothing to install, no CAD program needed.
What the spring 3D model generator does
Builds compression, extension, torsion, conical and disc springs
Four are helical: compression, extension with hook eyes, torsion with two radial legs, and conical. The fifth is the disc spring: a shallow conical washer for a large force over a very short travel.
Shows the stiffness formula for each type
Compression and extension springs work in shear, so their formula uses the shear modulus G. A torsion spring bends, so its formula uses the elastic modulus E.
Checks that the spring can be wound
The index C = D/d, the pitch and the solid length update with every slider move. An index below 4 or above 12 is flagged.
Gives a 3D model of the spring to print
The wire is a round section swept along the helix and the model is a closed solid. Download it as STL or 3MF and drop it into the slicer.
When you need a 3D printable spring
A spring is rarely printed to carry load. It is printed to be seen, tried and ordered right.
A teaching model of a spring
A student moves the sliders and sees how wire, diameter and turns change the stiffness.
A fit check before you order
Print the spring at true size and check that it fits the pocket, bore or shaft before you order a steel one.
Dimensions for a steel spring order
Wire, mean diameter, active turns and free length are the dimensions a steel spring is wound to under DIN EN 13906.
A return spring for a mock-up or a lid
In a mechanism mock-up or a lid that only has to spring back, a plastic spring is enough.
How a spring is calculated
Every parameter change goes through four steps: geometry, solid, check and the formula for the type.
Geometry
The helix is built from the mean diameter D, the wire d, the active turns n and the free length L₀. The pitch is p ≈ (L₀ − 1.5·d) / n.
Solid
The round wire section is swept along the helix with a parallel-transport frame, so the wire stays round. On a compression spring the last turn closes so the end sits flat.
Check
The index C = D/d has to be between 4 and 12. The solid length of a compression spring is L_c ≈ (n + 2)·d, its height once the coils touch.
Formula
Next to the model sits the formula for how the chosen type is loaded, with its standard.
| Applies to | Formula | Meaning |
|---|---|---|
| Compression and extension | k = G·d⁴ / (8·D³·n) | stiffness in N/mm; G is the shear modulus |
| Extension | F = F₀ + k·s | F₀ is the initial tension of the close-wound spring, s is the travel |
| Torsion | k_θ = E·d⁴ / (64·D·n) | angular stiffness in N·mm/rad under DIN EN 13906-3; E is the elastic modulus |
| Conical | k = G·d⁴ / [2·n·(D₁ + D₂)·(D₁² + D₂²)] | initial stiffness; with D₁ = D₂ it becomes the compression formula |
| Disc | Almén and László, DIN 2092 | non-linear; with h₀/t around 1.4 the force can drop as it compresses further |
A formula for each type, a model for the slicer
A formula for each spring type
A torsion spring uses E and a compression spring uses G, as DIN EN 13906 separates them. One formula for all of them is wrong by construction.
The check is a number, not a guess
Index, pitch and solid length show as numbers on every change.
A 3D model ready for the slicer
A closed solid in STL or 3MF, with a round wire and a closed end on the compression spring, with no mesh repair before printing.
A printed spring is a model, not a load-bearing part. Plastic has a far lower shear modulus than steel and creeps under sustained load, so it is softer and fatigues sooner. For a real load, wind the spring in steel to the dimensions the tool shows.
The tool shows the formula and checks the geometry, but it does not give a force figure for a particular steel. For that the standard and the spring maker remain the reference.
Questions about spring rate and printing
Can you 3D print a spring?
Yes, but only a light one. Plastic is far softer than spring steel and creeps under sustained load. A printed spring is for models, fit checks and lightly loaded return elements.
How to calculate spring rate of a compression spring?
With k = G·d⁴ / (8·D³·n). G is the shear modulus, d the wire diameter, D the mean diameter and n the number of active turns. Doubling the wire makes the spring 16 times stiffer.
How to 3D print a spring with this tool?
Set the wire, diameter and turns, check that the index is between 4 and 12, then download the STL or 3MF and drop it into the slicer. For a real load, wind a steel spring to the same dimensions.
What is the spring index and what should it be?
The mean diameter divided by the wire diameter: C = D/d. The working range is 4 to 12. Below 4 the coil is hard to wind or print, above 12 the spring buckles sideways under load.
Why does a torsion spring use a different formula?
Because its load is a moment about the axis, which bends the wire instead of twisting it. So the formula uses the elastic modulus E: k_θ = E·d⁴ / (64·D·n).
Do I need an account to make a spring?
Without an account the tool opens 3 times a day. A free account removes the limit.
The spring tool is free. Pro opens the rest
Pro costs 15 EUR a month and opens 45 Pro tools.
In the Design group:
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Make a spring to your size
Opens without an account 3 times a day. A free account removes the limit.