Spring Constant Calculator
Calculate a spring constant from force and extension, plus its period of oscillation.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
Estimate a linear spring constant from applied force and displacement, then model an ideal undamped mass–spring oscillator. Springs are treated as identical and connected in parallel; damping, nonlinear behavior and real-world mounting effects are not included.
Worked example
calculated with the default values below
Applied force 10 N · Extension or compression 0.05 m · Attached mass 1 kg · Springs in parallel 1 Spring constant 200.0000 N/m · Spring constant 0.20000 N/mm · Oscillation period 0.4443 s · Frequency 2.2508 Hz · Angular frequency 14.1421 rad/s · Energy stored 0.25000 J
Method and assumptions
Formula basis and scope
Hooke stiffness is force divided by displacement. The page divides total stiffness by the count of identical parallel springs; period uses 2π × sqrt(mass / total stiffness).
Assumes identical linear springs in parallel, negligible spring mass and no damping. It does not model springs in series or behavior beyond the elastic range.
Data sources
Disclaimer
These calculators give general conversion results. Rounding and the precision of the value you enter both affect the output, so treat displayed decimals as indicative rather than exact.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
k = F ÷ (x × N); ω = √(k×N ÷ m); T = 2π ÷ ω; U = ½ × k × N × x²
- F
- Force (N)
- x
- Displacement (m)
- N
- Number of springs
- m
- Mass (kg)
For identical springs in parallel, each stiffness = force ÷ displacement ÷ count. Total stiffness drives the ideal undamped period and frequency, defined only for positive mass and stiffness.
Frequently asked questions
Why is the oscillation period blank?
The ideal mass–spring period requires both positive mass and positive total spring stiffness. If either is zero, the model does not define a finite oscillation period.