Spring Design Formulas

Spring Design Formulas

*For mobile phone viewing, please rotate your phone to landscape mode*


The design of custom springs is governed by just a few relatively simple equations.  The development of these equations dates back to 1660 when English scientist Robert Hooke published his Law of Elasticity – Hooke’s Law.  Hooke’s Law states that, for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load.   In mathematical terms, Hooke’s Law is expressed as F=-kx, where F is the applied Force, k is the spring constant, also called spring rate (R), and x is the displacement, also called deflection.  This equation, along with equations for calculating the spring rate (R) and the stress within the material form the basis for spring design.  Our Spring Design Formulas pages provide you with the appropriate equations for each spring type, along with some graphics showing a variety of spring configurations.  (Please note that spring designers use the symbol P for applied force or load and the symbol F for deflection.)  You can use these equations to get you started, but please consult us before finalizing anything.  With engineering degrees from Cornell University and the University of Virginia plus over 25 years of experience designing springs and wire forms, our engineering staff is ready to assist you.  We take the time to listen and understand your requirements and then, using industry standard software plus years of experience, we present you with options to consider.  From choosing the best material to optimizing the design with regard to piece cost, manufacturability and assembly considerations, we are here to assist you with each step, helping you to avoid costly mistakes.  Plus we are experts at designing springs for automated assembly.  Concerned about high temperatures? Or corrosion? Or magnetic properties?  As a custom spring manufacturer, we have faced all these issues before and are ready to put what we have learned to work for you.  Give us a call and we will be happy to assist – we are a spring manufacturer that loves a challenge!

Compression Spring FormulaExtension Spring FormulaTorsion Spring Formula

To use the design formulas you will need to know some specifics about the material you will be using. Here are the key parameters for some of the most common spring materials:

Material

Modulus Of
Elasticity
(E) (psi)

Tensile1
Design Limit
(% of MTL3)
Modulus Of
Rigidity (G)
(psi)
Torsional2
Design Limit
(% of MTL3)
Hard Drawn Wire
30,000,000
75
11,500,000
40
Music Wire
30,000,000
75
11,500,000
45
Stainless Steel - 302
28,000,000
75
10,000,000
35
Stainless Steel - 316
28,000,000
75
10,000,000
40
Stainless Steel - 17-7 PH
29,500,000
75
11,000,000
45
Phosphor Bronze
15,000,000
75
6,250,000
40
Beryllium Copper
18,500,000
75
7,000,000
45
Monel K 500
26,000,000
70
9,500,000
40
Inconel X-750
31,000,000
70
12,000,000
40

1Use for bending stress in Torsion Springs and Extension Spring hooks
2Use for torsional stress in coils of Compression and Extension Springs
3Minimum Tensile Strength

 

Minimum Tensile Strength (psi x 103)
Wire Dia. (Inches)
Hard Drawn
Music Wire
Stainless 302
Stainless 316
Stainless 17-7 PH
Phos. Bronze
Be Cu
Monel 600
Inconel X-750
.008
307
399
325
245
345
145
180
180
220
.009
305
393
325
245
345
145
180
180
220
.010
303
387
320
245
345
145
180
180
220
.011
301
382
318
240
340
145
180
180
220
.012
299
377
316
240
340
145
180
180
220
.013
297
373
314
240
340
145
180
180
220
.014
295
369
312
240
340
145
180
180
220
.015
293
365
310
240
340
145
180
180
220
.016
291
362
308
235
335
145
180
180
220
.017
289
362
306
235
335
145
180
180
220
.018
287
356
304
235
335
145
180
180
220
.019
285
356
302
235
335
145
180
180
220
.020
283
350
300
235
335
145
180
180
220
.021
281
350
298
235
330
145
180
180
220
.022
280
345
296
235
330
145
180
180
220
.023
278
345
294
235
330
145
180
180
220
.024
277
341
292
235
330
145
180
180
220
.025
275
341
290
235
330
145
180
180
220
.026
274
337
289
235
325
135
180
180
220
.027
272
337
287
235
325
135
180
180
220
.028
271
333
286
235
325
135
180
180
220
.029
267
333
284
235
325
135
180
180
220
.030
266
330
282
235
325
135
180
180
220
.031
266
330
280
235
320
135
180
180
220
.032
265
327
277
235
320
135
180
180
220
.033
264
327
276
235
320
135
180
180
220
.034
262
324
275
235
320
135
180
180
220
.035
261
324
274
235
320
135
180
180
220
.036
260
321
273
235
320
135
180
180
220
.037
258
321
272
235
320
135
180
180
220
.038
257
318
271
235
320
135
180
180
220
.039
256
318
270
235
320
135
180
180
220
.040
255
315
270
235
320
135
180
180
220
.041
255
315
269
235
320
135
170
180
220
.042
254
313
268
230
310
135
170
180
220
.043
252
313
267
230
310
135
170
180
220
.044
251
313
266
230
310
135
170
180
220
.045
250
309
264
230
310
135
170
180
220
.046
249
309
263
230
310
135
170
180
220
.047
248
309
262
230
310
135
170
180
220
.048
247
306
262
225
310
135
170
180
220
.049
246
306
261
225
310
135
170
180
220
.050
245
306
261
225
310
135
170
180
220
.051
244
303
261
225
310
135
170
180
220
.052
244
303
260
225
305
135
170
180
220
.053
243
303
260
225
305
135
170
180
220
.054
243
303
260
225
305
135
170
180
220
.055
242
300
260
220
305
135
170
180
220
.056
241
300
259
220
305
135
170
180
220
.057
240
300
258
220
305
135
170
180
220
.058
240
300
258
220
305
135
170
180
220
.059
239
296
257
220
305
135
170
180
220
.060
238
296
256
220
305
135
170
180
220
.061
237
296
255
220
305
135
170
180
220
.062
237
296
255
220
297
135
170
180
220
.063
236
293
254
215
297
130
170
180
220
.064
235
293
254
215
297
130
170
180
220
.065
235
293
254
215
297
130
170
180
220
.066
235
290
250
215
297
130
170
180
220
.067
234
290
250
215
297
130
170
180
220
.068
234
290
250
215
297
130
170
180
220
.069
233
290
250
215
297
130
170
180
220
.070
233
289
250
215
297
130
170
180
220
.071
233
288
250
215
297
130
170
180
220
.072
232
287
250
215
292
130
170
180
220
.073
232
287
250
210
292
130
170
180
220
.074
231
287
250
210
292
130
170
180
220
.075
231
287
250
210
292
130
170
180
220
.076
230
284
245
210
292
130
170
180
220
.077
230
284
245
210
292
130
170
180
220
.078
229
284
245
210
292
130
170
180
220
.079
229
284
245
210
292
130
170
180
220
.080
227
282
245
210
292
130
170
180
220

requestaquote2

join our newsletter(3)