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Spring Calculator

Spring rate, force, stress, and deflection for compression springs

Spring Rate

11 lbs/in

Force

2.631 lbs

Stress

23,361 psi

Spring Rate (k)

11

lbs/in

Force

2.631 lbs

Stress

23,361 psi

Index

9.09

Spring Details

Wahl Factor1.16
Solid Height0.66"
Max Deflection1.34"
Max Force14.101 lbs
Stored Energy0.3289 in\u00B7lbs
Wire Length18.85"

What You'll Need

Arduino Uno R4 Minima Microcontroller Board

Arduino Uno R4 Minima Microcontroller Board

$20-$284.6
View on Amazon
Raspberry Pi 4 Model B 4GB RAM Starter Kit

Raspberry Pi 4 Model B 4GB RAM Starter Kit

$75-$1004.6
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STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

$10-$154.5
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Klein Tools MM400 Multimeter, Digital Auto Ranging, AC/DC Voltage, Current, Capacitance, Frequency, Duty-Cycle, Diode, Continuity, Temp 600V

Klein Tools MM400 Multimeter, Digital Auto Ranging, AC/DC Voltage, Current, Capacitance, Frequency, Duty-Cycle, Diode, Continuity, Temp 600V

$32.994.4
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Fluke T5-600 Electrical Voltage, Continuity and Current Tester, Measures AC Current Up to 100 A Without Contact, Automatically Select AC/DC for Tests, Includes Detachable SlimReach Probe Tip

Fluke T5-600 Electrical Voltage, Continuity and Current Tester, Measures AC Current Up to 100 A Without Contact, Automatically Select AC/DC for Tests, Includes Detachable SlimReach Probe Tip

$131.994.5
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BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

$49.004.4
View on Amazon
Arduino Uno R4 Minima Microcontroller Board

Arduino Uno R4 Minima Microcontroller Board

$20-$284.6
View on Amazon
Raspberry Pi 4 Model B 4GB RAM Starter Kit

Raspberry Pi 4 Model B 4GB RAM Starter Kit

$75-$1004.6
View on Amazon
STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

$10-$154.5
View on Amazon
Klein Tools MM400 Multimeter, Digital Auto Ranging, AC/DC Voltage, Current, Capacitance, Frequency, Duty-Cycle, Diode, Continuity, Temp 600V

Klein Tools MM400 Multimeter, Digital Auto Ranging, AC/DC Voltage, Current, Capacitance, Frequency, Duty-Cycle, Diode, Continuity, Temp 600V

$32.994.4
View on Amazon
Fluke T5-600 Electrical Voltage, Continuity and Current Tester, Measures AC Current Up to 100 A Without Contact, Automatically Select AC/DC for Tests, Includes Detachable SlimReach Probe Tip

Fluke T5-600 Electrical Voltage, Continuity and Current Tester, Measures AC Current Up to 100 A Without Contact, Automatically Select AC/DC for Tests, Includes Detachable SlimReach Probe Tip

$131.994.5
View on Amazon
BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

$49.004.4
View on Amazon

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Example Calculations

1Music wire spring: d=0.055", D=0.5", N=10

Inputs

Wire Dia0.055 in
Coil Dia0.5 in
Active Coils10

Result

Spring Rate8.325 lbs/in
Force at 0.25"2.081 lbs

k = 11.5e6 × 0.055⁴ / (8 × 0.5³ × 10) = 8.325 lbs/in. F = 8.325 × 0.25 = 2.081 lbs.

2Stainless 302: d=0.032", D=0.3", N=8

Inputs

Wire Dia0.032 in
Coil Dia0.3 in
Active Coils8

Result

Spring Rate4.84 lbs/in

k = 10e6 × 0.032⁴ / (8 × 0.3³ × 8) = 4.84 lbs/in.

Frequently Asked Questions

Q

How do I calculate spring rate (k)?

Spring rate k = G × d⁴ / (8 × D³ × N), where G is shear modulus, d is wire diameter, D is mean coil diameter, and N is active coils. Music wire G = 11.5 Mpsi.

  • k = Gd⁴ / (8D³N)
  • Doubling wire diameter increases k by 16x
  • Doubling coil diameter decreases k by 8x
  • Doubling coils halves the spring rate
MaterialShear Modulus GTensile StrengthBest For
Music Wire11.5 Mpsi230 ksiGeneral purpose
Stainless 30210.0 Mpsi150 ksiCorrosion resistance
Chrome Vanadium11.2 Mpsi200 ksiHigh fatigue life
Phosphor Bronze5.9 Mpsi100 ksiElectrical conductivity
Q

What is the Wahl correction factor?

The Wahl factor K_w corrects for stress concentration on the inner coil surface. K_w = (4C-1)/(4C-4) + 0.615/C where C = D/d (spring index). It increases stress by 10-40%.

  • Spring index C = D/d
  • C = 4: K_w = 1.40 (high stress)
  • C = 8: K_w = 1.18 (good design)
  • C = 12: K_w = 1.12 (optimal range)
Q

What spring index should I target?

Spring index (C = D/d) between 4 and 12 is ideal. Below 4, the spring is hard to manufacture. Above 12, it tangles easily. C = 6-10 is the sweet spot.

  • C < 4: difficult to coil, high stress
  • C = 4-6: heavy duty, tight coil
  • C = 6-10: optimal range
  • C > 12: prone to tangling and buckling
Q

How do I find maximum safe deflection?

Maximum deflection = free length minus solid height. Solid height = (active coils + 2) × wire diameter for closed-ground ends. Never compress a spring to solid height in normal operation.

  • Solid height = (N+2) × d
  • Max deflection = free length - solid height
  • Design for 80% of max deflection
  • Going to solid damages the spring

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Last Updated: Jun 18, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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