Automation Engineering

Spring Force Calculator (Hooke's Law)

Calculate spring restoring force from spring constant and displacement: F = kx.

Quick Answer

What force is exerted by a linear elastic spring under a given displacement?

Calculator

Spring force (restoring force) (N)
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Result Interpretation

The result shows Spring force (restoring force) in N, computed directly from the entered inputs using the formula defined for this tool.

Worked Example

Verified calculation

Given:

  • k = 49050
  • s = -0.1

Expected Result:

  • F = 4905

The actual numerical result is computed by the Runtime engine using the persisted tool definition. The values shown here come from verified test cases.

Formula / Method

restoring force = spring constant * -1 * extension or compression; result = spring constant

Spring force (restoring force).

Standards: ISO 10243:2016 (Springs Vocabulary), ASTM A228/A228M (Music Wire), or general mechanics textbooks (e.g., Hibbeler, Beer & Johnston)

Variables

SymbolLabelRoleDescription
k Spring constant INPUT Spring constant
s Displacement (extension or compression) INPUT Displacement (extension or compression)
F Spring force (restoring force) OUTPUT Spring force (restoring force)

Calculation Steps

  1. Enter the spring constant in N/m.
  2. Enter the displacement (extension or compression) in m.
  3. Step 1: Compute spring force (restoring force).
  4. Step 2: Compute spring force (restoring force).
  5. Read the spring force (restoring force) (N) from the results.

Engineering Summary

What force is exerted by a linear elastic spring under a given displacement? The calculation uses Hooke's Law for linear springs. This tool is applicable in mechanical engineering, statics, elasticity.

Notes / Limitations

  • ASSUMPTIONThe spring is massless, perfectly linear, and exhibits no hysteresis or creep.
  • ASSUMPTIONLoading is quasi-static; acceleration and inertial forces are negligible.
  • LIMITATIONDoes not account for damping, inertia, dynamic loading, or viscoelastic effects.
  • LIMITATIONCannot derive k from physical dimensions or material properties; k must be provided as input.
  • LIMITATIONProvides no warning or validation when displacement exceeds elastic limit.

Frequently Asked Questions

What does this calculator calculate?

The Spring Force Calculator (Hooke's Law) estimates Spring force (restoring force) based on the input parameters you provide

What units should I use for the inputs?

Enter each value in the units shown next to the input field: Spring constant (N/m), Displacement (extension or compression) (m). Make sure all inputs use the specified units for consistent results

How does Spring constant affect the results?

The spring constant directly affects: Spring force (restoring force). Increasing or decreasing this value will change these output values according to the engineering formula

How should I interpret the calculated results?

The calculator provides the following outputs: spring force (restoring force) in N. Results are computed from the input values using the defined calculation method. Always verify results against project-specific requirements and applicable standards

What assumptions does this calculator use?

This calculator uses verified engineering formulas; the calculation method is based on Hooke's Law for linear springs, and references ISO 10243:2016 (Springs Vocabulary), ASTM A228/A228M (Music Wire), or general mechanics textbooks (e.g., Hibbeler, Beer & Johnston). Results are approximate and should be validated against site-specific conditions, applicable codes, and professional engineering judgment

When is this calculation useful?

The Spring Force Calculator (Hooke's Law) is useful during preliminary design, feasibility studies, and quick engineering checks in mechanical engineering, statics, elasticity projects. It helps engineers and designers estimate key parameters before proceeding with detailed analysis

Technical Details
Assumption
The spring is massless, perfectly linear, and exhibits no hysteresis or creep.
Assumption
Loading is quasi-static; acceleration and inertial forces are negligible.
Limitation
Does not account for damping, inertia, dynamic loading, or viscoelastic effects.
Limitation
Cannot derive k from physical dimensions or material properties; k must be provided as input.
Limitation
Provides no warning or validation when displacement exceeds elastic limit.

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