CALCULATORS / SPRINGS AND ELASTIC ENERGY

Compression-spring rate and stress calculator

Close-coiled helical spring, linear elastic stiffness; no fatigue rating.

springs-compression.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	stiffnessN/mm	forceN
	2.46875	24.6875
	1.0112	10.112

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

force budget24.69 N✓ passes

BASELINE INPUTS

wire2 mmmeanDiameter20 mmactiveCoils8 shearModulus79 GPacompression10 mm

CALCULATED

stiffness2.4688 N/mm

force24.688 N

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Compression-spring rate and stress
# Scope: Close-coiled helical spring, linear elastic stiffness; no fatigue rating.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

wire = 2 mm
meanDiameter = 20 mm
activeCoils = 8
shearModulus = 79 GPa
compression = 10 mm

stiffness := shearModulus*wire^4/(8*meanDiameter^3*activeCoils) [N/mm]
force := stiffness*compression [N]

check force budget: force <= 30 N

scenario alternative: wire = 1.6 mm

Calculated from your source · not saved

Baseline · Baseline

force budget24.69 N ✓ passes

alternative · alternative

force budget10.11 N ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

stiffness: stiffness = shearModulus*wire^4/(8*meanDiameter^3*activeCoils) [N/mm]
force: force = stiffness*compression [N]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

wire: 2 mm
mean diameter: 20 mm
active coils: 8
shear modulus: 79 GPa
compression: 10 mm

Calculated

stiffness: 2.46875 N/mm
force: 24.6875 N

Assumptions and limits

Close-coiled helical spring, linear elastic stiffness; no fatigue rating.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Compression-spring rate and stress. Inputs: wire and mean coil diameters; active turns; modulus. Outputs: spring rate; deflection; wire stress. Model scope: Linear elasticity within the declared material range. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: wire and mean coil diameters, active turns, modulus
Outputs: spring rate, deflection, wire stress
Modes: calculate, compare, sweep
Drawing: Spring deformation

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS