Hooke's Law Calculator
A 200 N/m spring stretched 0.25 m pulls back with 50 N (F = kx) and stores 6.25 J of elastic energy.
50 N
- In kN
- 0.05 kN
- In mN
- 50000 mN
- In lbf
- 11.24044715 lbf
- In kgf
- 5.098581065 kgf
- In dyn
- 5000000 dyn
- Elastic potential energy ½kx²
- 6.25 J
Step-by-step solution
- F = k × x
- F = 200 × 0.25
- F = 50 N
Hooke's Law Formula
F = k x
F spring force, k spring constant (stiffness), x extension or compression; energy E = ½kx²
Worked Example
A spring with k = 200 N/m stretched 0.25 m:
- F = k × x
- F = 200 × 0.25
- F = 50 N
In mN: 50000 mN · In lbf: 11.24044715 lbf · In kgf: 5.098581065 kgf · In dyn: 5000000 dyn · Elastic potential energy ½kx²: 6.25 J
Springs in series and parallel
Two springs side by side (parallel) add: k = k₁ + k₂. End to end (series) they combine like resistors in parallel: 1/k = 1/k₁ + 1/k₂, so the pair is softer than either spring.
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G = 6.67430 × 10⁻¹¹ N·m²/kg², m₁ and m₂ the masses, r the distance between their centres
Example: Earth (5.972 × 10²⁴ kg) and the Moon (7.348 × 10²² kg) 384,400 km apart: Gravitational force F = 1.98211 × 10²⁰ N.
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F = m a
F net force (N), m mass (kg), a acceleration (m/s²)
Example: A 12 kg trolley accelerating at 2.5 m/s²: Net force F = 30 N.
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W = m g
W weight (N), m mass (kg), g gravitational acceleration (9.80665 m/s² standard on Earth)
Example: A 70 kg person standing on Earth: Weight on Earth W = 686.465 N.
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F = m v² / r
m mass, v speed, r radius of the circle; a = v²/r, ω = v/r
Example: A 1000 kg car taking a 50 m radius curve at 10 m/s: Centripetal force F = 2000 N.
Frequently asked questions
How do I find the spring constant from a graph?
Plot force against extension; the slope of the straight part is k. Beyond the elastic limit the line curves and Hooke’s law no longer applies.
Why is there a minus sign in some books?
F = −kx states that the restoring force opposes the displacement. The calculator works with magnitudes.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Hooke's Law Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/hookes-law-calculator/
IEEE
Scientific Converters, "Hooke's Law Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/hookes-law-calculator/