Spring Constant Calculator
Calculate spring constant (k), force, or displacement using Hooke's Law. Covers series and parallel springs, oscillation period, natural frequency, and energy stored.
N
m
Spring Constant k
—
Potential Energy —
Extended More scenarios, charts & detailed breakdown ▾
N
m
Spring Constant k (N/m)
—
Potential Energy (J) —
Professional Full parameters & maximum detail ▾
N/m
N/m
Combined Springs
k (Series) —
k (Parallel) —
Oscillation
Oscillation Period (series k) —
Natural Frequency —
Energy & Units
Energy Stored (series k) —
Series k (lbs/in) —
How to Use This Calculator
- Enter force (N) and displacement (m) to find spring constant k.
- Use Find Force tab to calculate force from k and displacement.
- Use Find Displacement tab to solve for x.
- The Professional tab adds series/parallel combinations, oscillation period, and spring rate in lbs/in.
Formula
F = kx | k = F/x | x = F/k
PE = ½kx²
Series: 1/k_t = 1/k₁ + 1/k₂ | Parallel: k_t = k₁ + k₂
Period: T = 2π√(m/k)
Example
Force = 50 N, displacement = 0.25 m: k = 50/0.25 = 200 N/m. PE = ½ × 200 × 0.25² = 6.25 J.
Frequently Asked Questions
- Hooke's Law states F = kx, where F is force (N), k is the spring constant (N/m), and x is displacement (m). It holds for small deformations within the elastic limit.
- k = F/x. Apply a known force (or hang a known mass) and measure the displacement. For example, a 10 N force causing 0.05 m displacement gives k = 10/0.05 = 200 N/m.
- For springs in series: 1/k_total = 1/k₁ + 1/k₂. The combined spring is weaker than either spring alone — it stretches more for the same force.
- For springs in parallel: k_total = k₁ + k₂. The combined spring is stiffer — it deflects less for the same force.
- T = 2π√(m/k), where m is mass in kg and k is spring constant in N/m. A stiffer spring or lighter mass gives a shorter (faster) period.