FINAL TOOLBOX
01 // Chart Studio02 // Visual Solvers03 // Calculators04 // Formulas05 // Unicode & Symbols
03 // Bidirectional STEM Calculators // PHYSICSF = k × x

Hooke's Law Spring Force & Stiffness Calculator

Hooke's Law states that the restoring force F exerted by a linear elastic spring below its yield limit is directly proportional to its axial displacement x: F = k × x.

F = k × x
Pick which value you want to calculate (or type into any field):Solving for: F — Spring Restoring Force
Calculated

Axial tension or compression force in Newtons

0.1500,000.00

Spring rate in Newtons per meter (N/m)

15,000,000.00
unit

Extension or compression from free length in meters

0.00015
Calculated Result · Spring Restoring Force (F)
750N
Converted units:

Step-by-Step Calculation

01Canonical Law: F = k × x
02Given Inputs (Base Units): k (N/m) = 15,000, x = 0.05 m
03Solve for F (Spring Restoring Force): F = 750 N

Hooke's Law states that the restoring force F exerted by a linear elastic spring below its yield limit is directly proportional to its axial displacement x: F = k × x.

Real-World Reference Values

Mechanical Keyboard Switchk ≈ 1,100 N/m (45 cN @ 4mm)

Precision tactile actuation coil

Automotive Coilover Spring35,000 – 90,000 N/m

35 to 90 N/mm suspension wheel rate

Elastic Potential Energy (U_s)U_s = ½ k x²

Energy stored in the compressed spring

20-Row Comparison Table

Spring Restoring Force (F) · Spring Stiffness Constant (k (N/m))

Hooke's Law Spring Force & Stiffness Calculator — Spring Stiffness Constant → Spring Restoring Force
#Spring Stiffness Constant (k (N/m))Spring Restoring Force (N)Δ %
0115,000.00 Current750 N0.00%
0236,974.62 1,848.73 N+146.50%
0373,948.25 3,697.41 N+392.99%
04110,921.87 5,546.09 N+639.48%
05147,895.50 7,394.77 N+885.97%
06184,869.12 9,243.46 N+1132.46%
07221,842.75 11,092.14 N+1378.95%
08258,816.37 12,940.82 N+1625.44%
09295,789.99 14,789.50 N+1871.93%
10332,763.62 16,638.18 N+2118.42%
11369,737.24 18,486.86 N+2364.91%
12406,710.87 20,335.54 N+2611.41%
13443,684.49 22,184.22 N+2857.90%
14480,658.12 24,032.91 N+3104.39%
15517,631.74 25,881.59 N+3350.88%
16554,605.37 27,730.27 N+3597.37%
17591,578.99 29,578.95 N+3843.86%
18628,552.61 31,427.63 N+4090.35%
19665,526.24 33,276.31 N+4336.84%
20702,499.86 35,124.99 N+4583.33%
Was this tool helpful?

Frequently Asked Questions

Can I enter spring compression x in millimeters (mm) or inches (in)?+

Yes. Switch the inline unit selector on x to Millimeters (mm) or Inches (in) for direct engineering readouts.

How do springs combine in parallel vs in series?+

In parallel, stiffnesses add directly (k_eq = k₁ + k₂); in series, reciprocals add (1/k_eq = 1/k₁ + 1/k₂).

How much potential energy is stored at deflection x?+

Elastic potential energy equals the area under the force-displacement curve: U = 0.5 × F × x = 0.5 × k × x².