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Spring Rate and Natural Frequency Calculator — result sheet
Estimate linear spring rate, stored elastic energy, and ideal small-oscillation frequency from force and deflection.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: k = F/x with x in metres; U = ½kx²; f = √(k/m)/(2π); T = 1/f.
Spring rate is the slope of an ideal linear force–deflection relation. This page also shows what that slope implies for stored elastic energy and an ideal mass–spring oscillator, while making its small-motion assumptions visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Applied force — N; minimum 1.0E-6; maximum 1000000000000
- Deflection — mm; minimum 1.0E-6; maximum 1000000000
- Oscillating mass — kg; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Applied force | 100 |
| Deflection | 20 |
| Oscillating mass | 2 |
100 N over 20 mm corresponds to 5,000 N/m, 1 J of elastic energy, and an ideal natural frequency of about 7.9577 Hz for a 2 kg mass.
Assumptions and limits
- Force and deflection describe the same linear spring response point.
- The entered deflection is converted from millimetres to metres before calculating k.
- The natural-frequency result models a massless spring, one attached mass, and no damping or preload.
- Real spring mass, coil geometry, buckling, friction, fatigue, nonlinear travel, and end conditions are excluded.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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