DIY Cost Tools
Spring Force Calculator
Use Hooke’s law to calculate spring restoring force, force magnitude, and stored elastic energy. Start with the prefilled example or enter your measurements in SI units.
Spring constant must be positive. Displacement may be positive, negative, or zero. All fields are required. Numeric magnitude is limited to 1 trillion.
How to use
Convert inputs to the units printed on each field, enter a value in every box, and select Calculate. Default results appear on page load. Invalid entries clear old results and show an explanation. Answers display up to ten significant digits; measurement uncertainty and floating-point rounding affect precision.
Formula and explanation
F = −kx; force magnitude = k|x|; U = ½kx². Spring constant k is in newtons per metre. Signed displacement x is measured in metres from the spring’s zero-force position. The minus sign means the spring force opposes displacement; energy is nonnegative.
Worked example
With k = 200 N/m and x = 0.1 m, signed restoring force is −20 N, force magnitude is 20 N, and stored energy is 1 J.
Limitations and safety
Applies to an ideal linear spring within its elastic range. Excludes preload, coil binding, hysteresis, friction, damping, fatigue, and nonlinear spring rates. Displacement is measured from the zero-force position, not an arbitrary installed reference. This does not determine safe loads or certify a spring. High-energy springs can cause serious injury; use manufacturer ratings and a qualified professional for real mechanisms.
Frequently asked questions
Why is the force negative?
Force acts opposite the chosen positive displacement direction. A negative displacement gives positive restoring force.
Can I enter millimetres?
Divide millimetres by 1,000 to obtain metres before entering displacement.
Is N/mm the same as N/m?
No. Multiply a rate in N/mm by 1,000 to obtain N/m.
What happens at zero displacement?
Both restoring force and stored energy are zero for this ideal, unpreloaded spring.
Review notes
Reviewed October 1, 2026. Formulas checked against OpenStax University Physics. Default results and boundary cases were independently tested, along with blank, nonfinite, excessive, and invalid inputs. This calculator is an educational estimate, not an engineering safety assessment.