Hooke’s Law Calculator
Find applied spring force, extension or spring constant in the elastic range. Distinguish applied and restoring forces and calculate stored elastic energy.
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Result
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Calculation steps
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How to calculate
In static balance, the applied force equalskx and the restoring force is−kx. Rearrange the linear equation to solve the selected unknown. Integrate the increasing force from zero extension to obtain stored energy.
Applied F=kx; restoring F=−kx; elastic energy U=kx²/2
Worked example
A spring withk=200N/m stretched5cm needs10N applied force, exerts−10N restoring force and stores0.25J.
Assumptions and input details
Use signed extension from the unstretched length: positive for stretch and negative for compression. The spring constant must be positive. Inferringk needs nonzero extension and force of the same sign. Known extension is limited to±1e6m. The model applies only within the spring’s linear elastic range; no yield limit is inferred. Entered base-unit magnitudes are limited to1e12 unless a tighter limit is stated. Results use floating-point arithmetic. These are ideal-model estimates, not equipment load ratings.
References: OpenStax Hooke’s law
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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